home *** CD-ROM | disk | FTP | other *** search
/ BCI NET / BCI NET Dec 94.iso / archives / programming / source / thesource6.dms / thesource6.adf / Source / Compression / hcompress.lha / hcompress / doc / paper.tex < prev   
LaTeX Document  |  1992-04-22  |  19.4 KB

open in: MacOS 8.1     |     Win98     |     DOS

browse contents    |     view JSON data     |     view as text


This file was processed as: LaTeX Document (document/latex).

ConfidenceProgramDetectionMatch TypeSupport
100% dexvert LaTeX Document (document/latex) magic Supported
100% dexvert Texinfo Document (document/texInfo) magic Supported
1% dexvert Corel 10 Texture (image/corel10Texture) ext Unsupported
1% dexvert Croteam texture file (image/croteamTextureFile) ext Unsupported
1% dexvert Text File (text/txt) fallback Supported
100% file LaTeX document text default
99% file TeX document, ASCII text default
100% checkBytes Printable ASCII default
100% perlTextCheck Likely Text (Perl) default
100% siegfried x-fmt/111 Plain Text File default
100% detectItEasy Format: plain text[LF] default (weak)
100% xdgMime text/x-matlab default (weak)



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 25 20 50 61 70 65 72 20 | 66 6f 72 20 4e 41 53 41 |% Paper |for NASA|
|00000010| 20 77 6f 72 6b 73 68 6f | 70 20 61 74 20 44 43 43 | worksho|p at DCC|
|00000020| 20 27 39 32 20 6d 65 65 | 74 69 6e 67 0a 25 20 54 | '92 mee|ting.% T|
|00000030| 68 69 73 20 76 65 72 73 | 69 6f 6e 20 68 61 73 20 |his vers|ion has |
|00000040| 66 69 67 75 72 65 73 20 | 72 65 6d 6f 76 65 64 20 |figures |removed |
|00000050| 73 6f 20 74 68 61 74 20 | 66 69 6c 65 20 69 73 20 |so that |file is |
|00000060| 73 6d 61 6c 6c 20 65 6e | 6f 75 67 68 20 74 6f 20 |small en|ough to |
|00000070| 69 6e 63 6c 75 64 65 0a | 25 20 77 69 74 68 20 74 |include.|% with t|
|00000080| 68 65 20 64 69 73 74 72 | 69 62 75 74 69 6f 6e 20 |he distr|ibution |
|00000090| 76 65 72 73 69 6f 6e 20 | 6f 66 20 68 63 6f 6d 70 |version |of hcomp|
|000000a0| 72 65 73 73 2e 0a 25 20 | 52 2e 20 57 68 69 74 65 |ress..% |R. White|
|000000b0| 2c 20 31 38 20 4d 61 72 | 63 68 20 31 39 39 32 0a |, 18 Mar|ch 1992.|
|000000c0| 25 0a 5c 6d 61 67 6e 69 | 66 69 63 61 74 69 6f 6e |%.\magni|fication|
|000000d0| 5c 6d 61 67 73 74 65 70 | 31 0a 25 5c 69 6e 70 75 |\magstep|1.%\inpu|
|000000e0| 74 20 70 73 66 69 67 0a | 5c 74 6f 6c 65 72 61 6e |t psfig.|\toleran|
|000000f0| 63 65 3d 35 30 30 30 0a | 25 0a 5c 66 6f 6f 74 6c |ce=5000.|%.\footl|
|00000100| 69 6e 65 3d 7b 5c 68 66 | 69 6c 7d 20 5c 68 65 61 |ine={\hf|il} \hea|
|00000110| 64 6c 69 6e 65 3d 7b 5c | 68 66 69 6c 7d 0a 5c 70 |dline={\|hfil}.\p|
|00000120| 61 72 73 6b 69 70 3d 5c | 73 6d 61 6c 6c 73 6b 69 |arskip=\|smallski|
|00000130| 70 61 6d 6f 75 6e 74 0a | 5c 66 6f 6e 74 5c 62 69 |pamount.|\font\bi|
|00000140| 67 62 66 3d 63 6d 62 78 | 31 30 20 73 63 61 6c 65 |gbf=cmbx|10 scale|
|00000150| 64 5c 6d 61 67 73 74 65 | 70 31 0a 5c 66 6f 6e 74 |d\magste|p1.\font|
|00000160| 5c 73 6d 61 6c 6c 73 6c | 3d 63 6d 73 6c 31 30 20 |\smallsl|=cmsl10 |
|00000170| 61 74 20 31 30 74 72 75 | 65 70 74 0a 25 0a 5c 64 |at 10tru|ept.%.\d|
|00000180| 65 66 5c 65 74 61 6c 7b | 7b 5c 73 6c 20 65 74 20 |ef\etal{|{\sl et |
|00000190| 61 6c 7d 2e 7d 20 20 20 | 20 25 20 65 74 20 61 6c |al}.} | % et al|
|000001a0| 2e 20 69 6e 20 69 74 61 | 6c 69 63 73 0a 5c 64 65 |. in ita|lics.\de|
|000001b0| 66 5c 65 67 7b 7b 5c 73 | 6c 20 65 2e 67 2e 7d 2c |f\eg{{\s|l e.g.},|
|000001c0| 5c 20 7d 20 20 20 20 20 | 25 20 65 2e 67 2e 20 69 |\ } |% e.g. i|
|000001d0| 6e 20 69 74 61 6c 69 63 | 73 0a 5c 64 65 66 5c 61 |n italic|s.\def\a|
|000001e0| 73 2f 7b 5c 68 62 6f 78 | 7b 5c 74 74 22 7d 7d 0a |s/{\hbox|{\tt"}}.|
|000001f0| 5c 64 65 66 5c 73 65 63 | 74 69 6f 6e 23 31 5c 70 |\def\sec|tion#1\p|
|00000200| 61 72 7b 5c 62 69 67 62 | 72 65 61 6b 5c 63 65 6e |ar{\bigb|reak\cen|
|00000210| 74 65 72 6c 69 6e 65 7b | 5c 62 66 20 23 31 7d 5c |terline{|\bf #1}\|
|00000220| 6e 6f 62 72 65 61 6b 5c | 6d 65 64 73 6b 69 70 5c |nobreak\|medskip\|
|00000230| 6e 6f 62 72 65 61 6b 0a | 5c 6e 6f 69 6e 64 65 6e |nobreak.|\noinden|
|00000240| 74 20 7d 0a 5c 64 65 66 | 5c 62 75 6c 6c 7b 5c 69 |t }.\def|\bull{\i|
|00000250| 74 65 6d 7b 24 5c 62 75 | 6c 6c 65 74 24 7d 20 7d |tem{$\bu|llet$} }|
|00000260| 0a 5c 64 65 66 5c 62 75 | 6c 6c 61 7b 5c 69 74 65 |.\def\bu|lla{\ite|
|00000270| 6d 7b 24 5c 63 69 72 63 | 24 7d 20 7d 0a 5c 64 65 |m{$\circ|$} }.\de|
|00000280| 66 5c 68 74 2f 7b 48 2d | 74 72 61 6e 73 66 6f 72 |f\ht/{H-|transfor|
|00000290| 6d 7d 0a 25 0a 5c 63 65 | 6e 74 65 72 6c 69 6e 65 |m}.%.\ce|nterline|
|000002a0| 7b 5c 62 69 67 62 66 20 | 48 69 67 68 2d 50 65 72 |{\bigbf |High-Per|
|000002b0| 66 6f 72 6d 61 6e 63 65 | 20 43 6f 6d 70 72 65 73 |formance| Compres|
|000002c0| 73 69 6f 6e 20 6f 66 20 | 41 73 74 72 6f 6e 6f 6d |sion of |Astronom|
|000002d0| 69 63 61 6c 20 49 6d 61 | 67 65 73 7d 0a 5c 62 69 |ical Ima|ges}.\bi|
|000002e0| 67 73 6b 69 70 0a 5c 63 | 65 6e 74 65 72 6c 69 6e |gskip.\c|enterlin|
|000002f0| 65 7b 5c 73 6c 20 52 69 | 63 68 61 72 64 20 4c 2e |e{\sl Ri|chard L.|
|00000300| 20 57 68 69 74 65 7d 0a | 5c 73 6d 61 6c 6c 73 6b | White}.|\smallsk|
|00000310| 69 70 0a 5c 63 65 6e 74 | 65 72 6c 69 6e 65 7b 5c |ip.\cent|erline{\|
|00000320| 73 6c 20 4a 6f 69 6e 74 | 20 49 6e 73 74 69 74 75 |sl Joint| Institu|
|00000330| 74 65 20 66 6f 72 20 4c | 61 62 6f 72 61 74 6f 72 |te for L|aborator|
|00000340| 79 20 41 73 74 72 6f 70 | 68 79 73 69 63 73 2c 20 |y Astrop|hysics, |
|00000350| 55 6e 69 76 65 72 73 69 | 74 79 20 6f 66 20 43 6f |Universi|ty of Co|
|00000360| 6c 6f 72 61 64 6f 7d 0a | 5c 63 65 6e 74 65 72 6c |lorado}.|\centerl|
|00000370| 69 6e 65 7b 5c 73 6c 20 | 43 61 6d 70 75 73 20 42 |ine{\sl |Campus B|
|00000380| 6f 78 20 34 34 30 2c 20 | 42 6f 75 6c 64 65 72 2c |ox 440, |Boulder,|
|00000390| 20 43 4f 20 38 30 33 30 | 39 7d 0a 5c 63 65 6e 74 | CO 8030|9}.\cent|
|000003a0| 65 72 6c 69 6e 65 7b 5c | 73 6c 20 61 6e 64 7d 0a |erline{\|sl and}.|
|000003b0| 5c 63 65 6e 74 65 72 6c | 69 6e 65 7b 5c 73 6c 20 |\centerl|ine{\sl |
|000003c0| 53 70 61 63 65 20 54 65 | 6c 65 73 63 6f 70 65 20 |Space Te|lescope |
|000003d0| 53 63 69 65 6e 63 65 20 | 49 6e 73 74 69 74 75 74 |Science |Institut|
|000003e0| 65 7d 0a 5c 63 65 6e 74 | 65 72 6c 69 6e 65 7b 5c |e}.\cent|erline{\|
|000003f0| 73 6c 20 33 37 30 30 20 | 53 61 6e 20 4d 61 72 74 |sl 3700 |San Mart|
|00000400| 69 6e 20 44 72 69 76 65 | 2c 20 42 61 6c 74 69 6d |in Drive|, Baltim|
|00000410| 6f 72 65 2c 20 4d 44 20 | 32 31 32 31 38 7d 0a 5c |ore, MD |21218}.\|
|00000420| 73 6d 61 6c 6c 73 6b 69 | 70 0a 5c 63 65 6e 74 65 |smallski|p.\cente|
|00000430| 72 6c 69 6e 65 7b 5c 73 | 6c 20 72 6c 77 40 73 74 |rline{\s|l rlw@st|
|00000440| 73 63 69 2e 65 64 75 7d | 0a 5c 62 69 67 73 6b 69 |sci.edu}|.\bigski|
|00000450| 70 0a 5c 73 65 63 74 69 | 6f 6e 20 53 75 6d 6d 61 |p.\secti|on Summa|
|00000460| 72 79 0a 0a 41 73 74 72 | 6f 6e 6f 6d 69 63 61 6c |ry..Astr|onomical|
|00000470| 20 69 6d 61 67 65 73 20 | 68 61 76 65 20 73 6f 6d | images |have som|
|00000480| 65 20 72 61 74 68 65 72 | 20 75 6e 75 73 75 61 6c |e rather| unusual|
|00000490| 20 63 68 61 72 61 63 74 | 65 72 69 73 74 69 63 73 | charact|eristics|
|000004a0| 20 74 68 61 74 20 6d 61 | 6b 65 0a 6d 61 6e 79 20 | that ma|ke.many |
|000004b0| 65 78 69 73 74 69 6e 67 | 20 69 6d 61 67 65 20 63 |existing| image c|
|000004c0| 6f 6d 70 72 65 73 73 69 | 6f 6e 20 74 65 63 68 6e |ompressi|on techn|
|000004d0| 69 71 75 65 73 20 65 69 | 74 68 65 72 20 69 6e 65 |iques ei|ther ine|
|000004e0| 66 66 65 63 74 69 76 65 | 20 6f 72 0a 69 6e 61 70 |ffective| or.inap|
|000004f0| 70 6c 69 63 61 62 6c 65 | 2e 20 20 41 20 74 79 70 |plicable|. A typ|
|00000500| 69 63 61 6c 20 69 6d 61 | 67 65 20 63 6f 6e 73 69 |ical ima|ge consi|
|00000510| 73 74 73 20 6f 66 20 61 | 20 6e 65 61 72 6c 79 20 |sts of a| nearly |
|00000520| 66 6c 61 74 20 62 61 63 | 6b 67 72 6f 75 6e 64 0a |flat bac|kground.|
|00000530| 73 70 72 69 6e 6b 6c 65 | 64 20 77 69 74 68 20 70 |sprinkle|d with p|
|00000540| 6f 69 6e 74 20 73 6f 75 | 72 63 65 73 20 61 6e 64 |oint sou|rces and|
|00000550| 20 6f 63 63 61 73 69 6f | 6e 61 6c 20 65 78 74 65 | occasio|nal exte|
|00000560| 6e 64 65 64 20 73 6f 75 | 72 63 65 73 2e 20 20 54 |nded sou|rces. T|
|00000570| 68 65 0a 69 6d 61 67 65 | 73 20 61 72 65 20 6f 66 |he.image|s are of|
|00000580| 74 65 6e 20 6e 6f 69 73 | 79 2c 20 73 6f 20 74 68 |ten nois|y, so th|
|00000590| 61 74 20 6c 6f 73 73 6c | 65 73 73 20 63 6f 6d 70 |at lossl|ess comp|
|000005a0| 72 65 73 73 69 6f 6e 20 | 64 6f 65 73 20 6e 6f 74 |ression |does not|
|000005b0| 20 77 6f 72 6b 20 76 65 | 72 79 0a 77 65 6c 6c 3b | work ve|ry.well;|
|000005c0| 20 66 75 72 74 68 65 72 | 6d 6f 72 65 2c 20 74 68 | further|more, th|
|000005d0| 65 20 69 6d 61 67 65 73 | 20 61 72 65 20 75 73 75 |e images| are usu|
|000005e0| 61 6c 6c 79 20 73 75 62 | 6a 65 63 74 65 64 20 74 |ally sub|jected t|
|000005f0| 6f 20 73 74 72 69 6e 67 | 65 6e 74 0a 71 75 61 6e |o string|ent.quan|
|00000600| 74 69 74 61 74 69 76 65 | 20 61 6e 61 6c 79 73 69 |titative| analysi|
|00000610| 73 2c 20 73 6f 20 61 6e | 79 20 6c 6f 73 73 79 20 |s, so an|y lossy |
|00000620| 63 6f 6d 70 72 65 73 73 | 69 6f 6e 20 6d 65 74 68 |compress|ion meth|
|00000630| 6f 64 20 6d 75 73 74 20 | 62 65 20 70 72 6f 76 65 |od must |be prove|
|00000640| 6e 0a 6e 6f 74 20 74 6f | 20 64 69 73 63 61 72 64 |n.not to| discard|
|00000650| 20 75 73 65 66 75 6c 20 | 69 6e 66 6f 72 6d 61 74 | useful |informat|
|00000660| 69 6f 6e 2c 20 62 75 74 | 20 6d 75 73 74 20 69 6e |ion, but| must in|
|00000670| 73 74 65 61 64 20 64 69 | 73 63 61 72 64 20 6f 6e |stead di|scard on|
|00000680| 6c 79 20 74 68 65 0a 6e | 6f 69 73 65 2e 20 20 46 |ly the.n|oise. F|
|00000690| 69 6e 61 6c 6c 79 2c 20 | 74 68 65 20 69 6d 61 67 |inally, |the imag|
|000006a0| 65 73 20 63 61 6e 20 62 | 65 20 65 78 74 72 65 6d |es can b|e extrem|
|000006b0| 65 6c 79 20 6c 61 72 67 | 65 2e 20 20 46 6f 72 20 |ely larg|e. For |
|000006c0| 65 78 61 6d 70 6c 65 2c | 20 74 68 65 0a 53 70 61 |example,| the.Spa|
|000006d0| 63 65 20 54 65 6c 65 73 | 63 6f 70 65 20 53 63 69 |ce Teles|cope Sci|
|000006e0| 65 6e 63 65 20 49 6e 73 | 74 69 74 75 74 65 20 68 |ence Ins|titute h|
|000006f0| 61 73 20 64 69 67 69 74 | 69 7a 65 64 20 70 68 6f |as digit|ized pho|
|00000700| 74 6f 67 72 61 70 68 69 | 63 20 70 6c 61 74 65 73 |tographi|c plates|
|00000710| 0a 63 6f 76 65 72 69 6e | 67 20 74 68 65 20 65 6e |.coverin|g the en|
|00000720| 74 69 72 65 20 73 6b 79 | 2c 20 67 65 6e 65 72 61 |tire sky|, genera|
|00000730| 74 69 6e 67 20 31 35 30 | 30 20 69 6d 61 67 65 73 |ting 150|0 images|
|00000740| 20 65 61 63 68 20 68 61 | 76 69 6e 67 0a 24 31 34 | each ha|ving.$14|
|00000750| 30 30 30 5c 74 69 6d 65 | 73 31 34 30 30 30 24 20 |000\time|s14000$ |
|00000760| 31 36 2d 62 69 74 20 70 | 69 78 65 6c 73 2e 20 20 |16-bit p|ixels. |
|00000770| 53 65 76 65 72 61 6c 20 | 61 73 74 72 6f 6e 6f 6d |Several |astronom|
|00000780| 69 63 61 6c 20 67 72 6f | 75 70 73 20 61 72 65 20 |ical gro|ups are |
|00000790| 6e 6f 77 0a 63 6f 6e 73 | 74 72 75 63 74 69 6e 67 |now.cons|tructing|
|000007a0| 20 63 61 6d 65 72 61 73 | 20 77 69 74 68 20 6d 6f | cameras| with mo|
|000007b0| 73 61 69 63 73 20 6f 66 | 20 6c 61 72 67 65 20 43 |saics of| large C|
|000007c0| 43 44 73 20 28 65 61 63 | 68 20 24 32 30 34 38 5c |CDs (eac|h $2048\|
|000007d0| 74 69 6d 65 73 32 30 34 | 38 24 0a 6f 72 20 6c 61 |times204|8$.or la|
|000007e0| 72 67 65 72 29 3b 20 74 | 68 65 73 65 20 69 6e 73 |rger); t|hese ins|
|000007f0| 74 72 75 6d 65 6e 74 73 | 20 77 69 6c 6c 20 62 65 |truments| will be|
|00000800| 20 75 73 65 64 20 69 6e | 20 70 72 6f 6a 65 63 74 | used in| project|
|00000810| 73 20 74 68 61 74 20 67 | 65 6e 65 72 61 74 65 0a |s that g|enerate.|
|00000820| 64 61 74 61 20 61 74 20 | 61 20 72 61 74 65 20 65 |data at |a rate e|
|00000830| 78 63 65 65 64 69 6e 67 | 20 31 30 30 7e 4d 42 79 |xceeding| 100~MBy|
|00000840| 74 65 73 20 65 76 65 72 | 79 20 35 20 6d 69 6e 75 |tes ever|y 5 minu|
|00000850| 74 65 73 20 66 6f 72 20 | 6d 61 6e 79 20 79 65 61 |tes for |many yea|
|00000860| 72 73 2e 0a 0a 41 6e 20 | 65 66 66 65 63 74 69 76 |rs...An |effectiv|
|00000870| 65 20 74 65 63 68 6e 69 | 71 75 65 20 66 6f 72 20 |e techni|que for |
|00000880| 69 6d 61 67 65 20 63 6f | 6d 70 72 65 73 73 69 6f |image co|mpressio|
|00000890| 6e 20 6d 61 79 20 62 65 | 20 62 61 73 65 64 20 6f |n may be| based o|
|000008a0| 6e 20 74 68 65 20 5c 68 | 74 2f 0a 28 46 72 69 74 |n the \h|t/.(Frit|
|000008b0| 7a 65 20 5c 65 74 61 6c | 5c 20 31 39 37 37 29 2e |ze \etal|\ 1977).|
|000008c0| 20 20 54 68 65 20 6d 65 | 74 68 6f 64 20 74 68 61 | The me|thod tha|
|000008d0| 74 20 77 65 20 68 61 76 | 65 20 64 65 76 65 6c 6f |t we hav|e develo|
|000008e0| 70 65 64 20 63 61 6e 20 | 62 65 20 75 73 65 64 0a |ped can |be used.|
|000008f0| 66 6f 72 20 65 69 74 68 | 65 72 20 6c 6f 73 73 6c |for eith|er lossl|
|00000900| 65 73 73 20 6f 72 20 6c | 6f 73 73 79 20 63 6f 6d |ess or l|ossy com|
|00000910| 70 72 65 73 73 69 6f 6e | 2e 20 20 54 68 65 20 64 |pression|. The d|
|00000920| 69 67 69 74 69 7a 65 64 | 20 73 6b 79 20 73 75 72 |igitized| sky sur|
|00000930| 76 65 79 0a 69 6d 61 67 | 65 73 20 63 61 6e 20 62 |vey.imag|es can b|
|00000940| 65 20 63 6f 6d 70 72 65 | 73 73 65 64 20 62 79 20 |e compre|ssed by |
|00000950| 61 74 20 6c 65 61 73 74 | 20 61 20 66 61 63 74 6f |at least| a facto|
|00000960| 72 20 6f 66 20 31 30 20 | 77 69 74 68 20 6e 6f 20 |r of 10 |with no |
|00000970| 6e 6f 74 69 63 65 61 62 | 6c 65 0a 6c 6f 73 73 65 |noticeab|le.losse|
|00000980| 73 20 69 6e 20 74 68 65 | 20 61 73 74 72 6f 6d 65 |s in the| astrome|
|00000990| 74 72 69 63 20 61 6e 64 | 20 70 68 6f 74 6f 6d 65 |tric and| photome|
|000009a0| 74 72 69 63 20 70 72 6f | 70 65 72 74 69 65 73 20 |tric pro|perties |
|000009b0| 6f 66 20 74 68 65 20 63 | 6f 6d 70 72 65 73 73 65 |of the c|ompresse|
|000009c0| 64 0a 69 6d 61 67 65 73 | 2e 20 20 54 68 65 20 6d |d.images|. The m|
|000009d0| 65 74 68 6f 64 20 68 61 | 73 20 62 65 65 6e 20 64 |ethod ha|s been d|
|000009e0| 65 73 69 67 6e 65 64 20 | 74 6f 20 62 65 20 63 6f |esigned |to be co|
|000009f0| 6d 70 75 74 61 74 69 6f | 6e 61 6c 6c 79 20 65 66 |mputatio|nally ef|
|00000a00| 66 69 63 69 65 6e 74 3a | 0a 63 6f 6d 70 72 65 73 |ficient:|.compres|
|00000a10| 73 69 6f 6e 20 6f 72 20 | 64 65 63 6f 6d 70 72 65 |sion or |decompre|
|00000a20| 73 73 69 6f 6e 20 6f 66 | 20 61 20 24 35 31 32 5c |ssion of| a $512\|
|00000a30| 74 69 6d 65 73 35 31 32 | 24 20 69 6d 61 67 65 20 |times512|$ image |
|00000a40| 72 65 71 75 69 72 65 73 | 20 6f 6e 6c 79 20 34 0a |requires| only 4.|
|00000a50| 73 65 63 6f 6e 64 73 20 | 6f 6e 20 61 20 53 75 6e |seconds |on a Sun|
|00000a60| 20 53 50 41 52 43 73 74 | 61 74 69 6f 6e 7e 31 2e | SPARCst|ation~1.|
|00000a70| 20 20 54 68 65 20 61 6c | 67 6f 72 69 74 68 6d 20 | The al|gorithm |
|00000a80| 75 73 65 73 20 6f 6e 6c | 79 20 69 6e 74 65 67 65 |uses onl|y intege|
|00000a90| 72 0a 61 72 69 74 68 6d | 65 74 69 63 2c 20 73 6f |r.arithm|etic, so|
|00000aa0| 20 69 74 20 69 73 20 63 | 6f 6d 70 6c 65 74 65 6c | it is c|ompletel|
|00000ab0| 79 20 72 65 76 65 72 73 | 69 62 6c 65 20 69 6e 20 |y revers|ible in |
|00000ac0| 69 74 73 20 6c 6f 73 73 | 6c 65 73 73 20 6d 6f 64 |its loss|less mod|
|00000ad0| 65 2c 20 61 6e 64 20 69 | 74 0a 63 6f 75 6c 64 20 |e, and i|t.could |
|00000ae0| 65 61 73 69 6c 79 20 62 | 65 20 69 6d 70 6c 65 6d |easily b|e implem|
|00000af0| 65 6e 74 65 64 20 69 6e | 20 68 61 72 64 77 61 72 |ented in| hardwar|
|00000b00| 65 20 66 6f 72 20 73 70 | 61 63 65 20 61 70 70 6c |e for sp|ace appl|
|00000b10| 69 63 61 74 69 6f 6e 73 | 2e 0a 0a 5c 73 65 63 74 |ications|...\sect|
|00000b20| 69 6f 6e 20 31 2e 20 49 | 6e 74 72 6f 64 75 63 74 |ion 1. I|ntroduct|
|00000b30| 69 6f 6e 0a 0a 41 73 74 | 72 6f 6e 6f 6d 69 63 61 |ion..Ast|ronomica|
|00000b40| 6c 20 69 6d 61 67 65 73 | 20 63 6f 6e 73 69 73 74 |l images| consist|
|00000b50| 20 6c 61 72 67 65 6c 79 | 20 6f 66 20 65 6d 70 74 | largely| of empt|
|00000b60| 79 20 73 6b 79 2e 20 20 | 43 6f 6d 70 72 65 73 73 |y sky. |Compress|
|00000b70| 69 6f 6e 20 6f 66 20 73 | 75 63 68 0a 69 6d 61 67 |ion of s|uch.imag|
|00000b80| 65 73 20 63 61 6e 20 72 | 65 64 75 63 65 20 74 68 |es can r|educe th|
|00000b90| 65 20 76 6f 6c 75 6d 65 | 20 6f 66 20 64 61 74 61 |e volume| of data|
|00000ba0| 20 74 68 61 74 20 69 74 | 20 69 73 20 6e 65 63 65 | that it| is nece|
|00000bb0| 73 73 61 72 79 20 74 6f | 20 73 74 6f 72 65 20 28 |ssary to| store (|
|00000bc0| 61 6e 0a 69 6d 70 6f 72 | 74 61 6e 74 20 63 6f 6e |an.impor|tant con|
|00000bd0| 73 69 64 65 72 61 74 69 | 6f 6e 20 66 6f 72 20 6c |siderati|on for l|
|00000be0| 61 72 67 65 20 73 63 61 | 6c 65 20 64 69 67 69 74 |arge sca|le digit|
|00000bf0| 61 6c 20 73 6b 79 20 73 | 75 72 76 65 79 73 29 20 |al sky s|urveys) |
|00000c00| 61 6e 64 20 63 61 6e 0a | 73 68 6f 72 74 65 6e 20 |and can.|shorten |
|00000c10| 74 68 65 20 74 69 6d 65 | 20 72 65 71 75 69 72 65 |the time| require|
|00000c20| 64 20 74 6f 20 74 72 61 | 6e 73 6d 69 74 20 69 6d |d to tra|nsmit im|
|00000c30| 61 67 65 73 20 28 75 73 | 65 66 75 6c 20 66 6f 72 |ages (us|eful for|
|00000c40| 20 72 65 6d 6f 74 65 0a | 6f 62 73 65 72 76 69 6e | remote.|observin|
|00000c50| 67 20 6f 72 20 72 65 6d | 6f 74 65 20 61 63 63 65 |g or rem|ote acce|
|00000c60| 73 73 20 74 6f 20 64 61 | 74 61 20 61 72 63 68 69 |ss to da|ta archi|
|00000c70| 76 65 73 2e 29 0a 0a 44 | 61 74 61 20 63 6f 6d 70 |ves.)..D|ata comp|
|00000c80| 72 65 73 73 69 6f 6e 20 | 6d 65 74 68 6f 64 73 20 |ression |methods |
|00000c90| 63 61 6e 20 62 65 20 63 | 6c 61 73 73 69 66 69 65 |can be c|lassifie|
|00000ca0| 64 20 61 73 20 65 69 74 | 68 65 72 20 60 60 6c 6f |d as eit|her ``lo|
|00000cb0| 73 73 6c 65 73 73 27 27 | 0a 28 6d 65 61 6e 69 6e |ssless''|.(meanin|
|00000cc0| 67 20 74 68 61 74 20 74 | 68 65 20 6f 72 69 67 69 |g that t|he origi|
|00000cd0| 6e 61 6c 20 64 61 74 61 | 20 63 61 6e 20 62 65 20 |nal data| can be |
|00000ce0| 72 65 63 6f 6e 73 74 72 | 75 63 74 65 64 20 65 78 |reconstr|ucted ex|
|00000cf0| 61 63 74 6c 79 20 66 72 | 6f 6d 20 74 68 65 0a 63 |actly fr|om the.c|
|00000d00| 6f 6d 70 72 65 73 73 65 | 64 20 64 61 74 61 29 20 |ompresse|d data) |
|00000d10| 6f 72 20 60 60 6c 6f 73 | 73 79 27 27 20 28 6d 65 |or ``los|sy'' (me|
|00000d20| 61 6e 69 6e 67 20 74 68 | 61 74 20 74 68 65 20 75 |aning th|at the u|
|00000d30| 6e 63 6f 6d 70 72 65 73 | 73 65 64 20 69 6d 61 67 |ncompres|sed imag|
|00000d40| 65 20 69 73 0a 6e 6f 74 | 20 65 78 61 63 74 6c 79 |e is.not| exactly|
|00000d50| 20 74 68 65 20 73 61 6d | 65 20 61 73 20 74 68 65 | the sam|e as the|
|00000d60| 20 6f 72 69 67 69 6e 61 | 6c 2e 29 20 20 41 73 74 | origina|l.) Ast|
|00000d70| 72 6f 6e 6f 6d 65 72 73 | 20 6f 66 74 65 6e 20 69 |ronomers| often i|
|00000d80| 6e 73 69 73 74 20 74 68 | 61 74 0a 74 68 65 79 20 |nsist th|at.they |
|00000d90| 63 61 6e 20 61 63 63 65 | 70 74 20 6f 6e 6c 79 20 |can acce|pt only |
|00000da0| 6c 6f 73 73 6c 65 73 73 | 20 63 6f 6d 70 72 65 73 |lossless| compres|
|00000db0| 73 69 6f 6e 2c 20 69 6e | 20 70 61 72 74 20 62 65 |sion, in| part be|
|00000dc0| 63 61 75 73 65 20 6f 66 | 0a 63 6f 6e 73 65 72 76 |cause of|.conserv|
|00000dd0| 61 74 69 73 6d 2c 20 61 | 6e 64 20 69 6e 20 70 61 |atism, a|nd in pa|
|00000de0| 72 74 20 62 65 63 61 75 | 73 65 20 74 68 65 20 66 |rt becau|se the f|
|00000df0| 61 6d 69 6c 69 61 72 20 | 6c 6f 73 73 79 20 63 6f |amiliar |lossy co|
|00000e00| 6d 70 72 65 73 73 69 6f | 6e 0a 6d 65 74 68 6f 64 |mpressio|n.method|
|00000e10| 73 20 73 61 63 72 69 66 | 69 63 65 20 73 6f 6d 65 |s sacrif|ice some|
|00000e20| 20 69 6e 66 6f 72 6d 61 | 74 69 6f 6e 20 74 68 61 | informa|tion tha|
|00000e30| 74 20 69 73 20 6e 65 65 | 64 65 64 20 66 6f 72 20 |t is nee|ded for |
|00000e40| 61 63 63 75 72 61 74 65 | 0a 61 6e 61 6c 79 73 69 |accurate|.analysi|
|00000e50| 73 20 6f 66 20 69 6d 61 | 67 65 20 64 61 74 61 2e |s of ima|ge data.|
|00000e60| 20 20 48 6f 77 65 76 65 | 72 2c 20 73 69 6e 63 65 | Howeve|r, since|
|00000e70| 20 61 6c 6c 20 61 73 74 | 72 6f 6e 6f 6d 69 63 61 | all ast|ronomica|
|00000e80| 6c 20 69 6d 61 67 65 73 | 20 63 6f 6e 74 61 69 6e |l images| contain|
|00000e90| 0a 6e 6f 69 73 65 2c 20 | 77 68 69 63 68 20 69 73 |.noise, |which is|
|00000ea0| 20 69 6e 68 65 72 65 6e | 74 6c 79 20 69 6e 63 6f | inheren|tly inco|
|00000eb0| 6d 70 72 65 73 73 69 62 | 6c 65 2c 20 6c 6f 73 73 |mpressib|le, loss|
|00000ec0| 79 20 63 6f 6d 70 72 65 | 73 73 69 6f 6e 20 6d 65 |y compre|ssion me|
|00000ed0| 74 68 6f 64 73 0a 70 72 | 6f 64 75 63 65 20 6d 75 |thods.pr|oduce mu|
|00000ee0| 63 68 20 62 65 74 74 65 | 72 20 63 6f 6d 70 72 65 |ch bette|r compre|
|00000ef0| 73 73 69 6f 6e 20 72 65 | 73 75 6c 74 73 2e 0a 0a |ssion re|sults...|
|00000f00| 41 20 73 69 6d 70 6c 65 | 20 65 78 61 6d 70 6c 65 |A simple| example|
|00000f10| 20 6d 61 79 20 6d 61 6b | 65 20 74 68 69 73 20 63 | may mak|e this c|
|00000f20| 6c 65 61 72 2e 20 20 4f | 6e 65 20 6f 66 20 74 68 |lear. O|ne of th|
|00000f30| 65 20 73 69 6d 70 6c 65 | 73 74 20 64 61 74 61 0a |e simple|st data.|
|00000f40| 63 6f 6d 70 72 65 73 73 | 69 6f 6e 20 74 65 63 68 |compress|ion tech|
|00000f50| 6e 69 71 75 65 73 20 69 | 73 20 72 75 6e 2d 6c 65 |niques i|s run-le|
|00000f60| 6e 67 74 68 20 63 6f 64 | 69 6e 67 2c 20 69 6e 20 |ngth cod|ing, in |
|00000f70| 77 68 69 63 68 20 72 75 | 6e 73 20 6f 66 0a 63 6f |which ru|ns of.co|
|00000f80| 6e 73 65 63 75 74 69 76 | 65 20 70 69 78 65 6c 73 |nsecutiv|e pixels|
|00000f90| 20 68 61 76 69 6e 67 20 | 74 68 65 20 73 61 6d 65 | having |the same|
|00000fa0| 20 76 61 6c 75 65 20 61 | 72 65 20 63 6f 6d 70 72 | value a|re compr|
|00000fb0| 65 73 73 65 64 20 62 79 | 20 73 74 6f 72 69 6e 67 |essed by| storing|
|00000fc0| 20 74 68 65 0a 70 69 78 | 65 6c 20 76 61 6c 75 65 | the.pix|el value|
|00000fd0| 20 61 6e 64 20 74 68 65 | 20 72 65 70 65 74 69 74 | and the| repetit|
|00000fe0| 69 6f 6e 20 66 61 63 74 | 6f 72 2e 20 20 54 68 69 |ion fact|or. Thi|
|00000ff0| 73 20 6d 65 74 68 6f 64 | 20 69 73 20 75 73 65 64 |s method| is used|
|00001000| 20 69 6e 20 74 68 65 0a | 73 74 61 6e 64 61 72 64 | in the.|standard|
|00001010| 20 63 6f 6d 70 72 65 73 | 73 69 6f 6e 20 73 63 68 | compres|sion sch|
|00001020| 65 6d 65 20 66 6f 72 20 | 66 61 63 73 69 6d 69 6c |eme for |facsimil|
|00001030| 65 20 74 72 61 6e 73 6d | 69 73 73 69 6f 6e 73 2e |e transm|issions.|
|00001040| 0a 55 6e 66 6f 72 74 75 | 6e 61 74 65 6c 79 2c 20 |.Unfortu|nately, |
|00001050| 69 74 20 69 73 20 71 75 | 69 74 65 20 69 6e 65 66 |it is qu|ite inef|
|00001060| 66 65 63 74 69 76 65 20 | 66 6f 72 20 6c 6f 73 73 |fective |for loss|
|00001070| 6c 65 73 73 20 63 6f 6d | 70 72 65 73 73 69 6f 6e |less com|pression|
|00001080| 20 6f 66 0a 61 73 74 72 | 6f 6e 6f 6d 69 63 61 6c | of.astr|onomical|
|00001090| 20 69 6d 61 67 65 73 20 | 62 65 63 61 75 73 65 20 | images |because |
|000010a0| 65 76 65 6e 20 74 68 6f | 75 67 68 20 74 68 65 20 |even tho|ugh the |
|000010b0| 73 6b 79 20 69 73 20 7b | 5c 73 6c 20 6e 65 61 72 |sky is {|\sl near|
|000010c0| 6c 79 7d 0a 63 6f 6e 73 | 74 61 6e 74 2c 20 74 68 |ly}.cons|tant, th|
|000010d0| 65 20 6e 6f 69 73 65 20 | 69 6e 20 74 68 65 20 73 |e noise |in the s|
|000010e0| 6b 79 20 65 6e 73 75 72 | 65 73 20 74 68 61 74 20 |ky ensur|es that |
|000010f0| 6f 6e 6c 79 20 76 65 72 | 79 20 73 68 6f 72 74 20 |only ver|y short |
|00001100| 72 75 6e 73 20 6f 66 0a | 65 71 75 61 6c 20 70 69 |runs of.|equal pi|
|00001110| 78 65 6c 73 20 6f 63 63 | 75 72 2e 20 20 54 68 65 |xels occ|ur. The|
|00001120| 20 6f 62 76 69 6f 75 73 | 20 77 61 79 20 74 6f 20 | obvious| way to |
|00001130| 6d 61 6b 65 20 72 75 6e | 2d 6c 65 6e 67 74 68 20 |make run|-length |
|00001140| 63 6f 64 69 6e 67 20 6d | 6f 72 65 0a 65 66 66 65 |coding m|ore.effe|
|00001150| 63 74 69 76 65 20 69 73 | 20 74 6f 20 66 6f 72 63 |ctive is| to forc|
|00001160| 65 20 74 68 65 20 73 6b | 79 20 74 6f 20 62 65 20 |e the sk|y to be |
|00001170| 65 78 61 63 74 6c 79 20 | 63 6f 6e 73 74 61 6e 74 |exactly |constant|
|00001180| 20 62 79 20 73 65 74 74 | 69 6e 67 20 61 6c 6c 0a | by sett|ing all.|
|00001190| 70 69 78 65 6c 73 20 62 | 65 6c 6f 77 20 61 20 74 |pixels b|elow a t|
|000011a0| 68 72 65 73 68 6f 6c 64 | 20 28 63 68 6f 73 65 6e |hreshold| (chosen|
|000011b0| 20 74 6f 20 62 65 20 6a | 75 73 74 20 61 62 6f 76 | to be j|ust abov|
|000011c0| 65 20 74 68 65 20 73 6b | 79 29 20 74 6f 20 74 68 |e the sk|y) to th|
|000011d0| 65 20 6d 65 61 6e 0a 73 | 6b 79 20 76 61 6c 75 65 |e mean.s|ky value|
|000011e0| 2e 20 20 48 6f 77 65 76 | 65 72 2c 20 74 68 65 6e |. Howev|er, then|
|000011f0| 20 6f 6e 65 20 68 61 73 | 20 6c 6f 73 74 20 61 6e | one has| lost an|
|00001200| 79 20 69 6e 66 6f 72 6d | 61 74 69 6f 6e 20 61 62 |y inform|ation ab|
|00001210| 6f 75 74 20 6f 62 6a 65 | 63 74 73 0a 63 6c 6f 73 |out obje|cts.clos|
|00001220| 65 20 74 6f 20 74 68 65 | 20 64 65 74 65 63 74 69 |e to the| detecti|
|00001230| 6f 6e 20 6c 69 6d 69 74 | 2e 20 20 4f 6e 65 20 68 |on limit|. One h|
|00001240| 61 73 20 61 6c 73 6f 20 | 6c 6f 73 74 20 69 6e 66 |as also |lost inf|
|00001250| 6f 72 6d 61 74 69 6f 6e | 20 61 62 6f 75 74 0a 6c |ormation| about.l|
|00001260| 6f 63 61 6c 20 76 61 72 | 69 61 74 69 6f 6e 73 20 |ocal var|iations |
|00001270| 69 6e 20 74 68 65 20 73 | 6b 79 20 62 72 69 67 68 |in the s|ky brigh|
|00001280| 74 6e 65 73 73 2c 20 77 | 68 69 63 68 20 73 65 76 |tness, w|hich sev|
|00001290| 65 72 65 6c 79 20 6c 69 | 6d 69 74 73 20 74 68 65 |erely li|mits the|
|000012a0| 0a 61 63 63 75 72 61 63 | 79 20 6f 66 20 70 68 6f |.accurac|y of pho|
|000012b0| 74 6f 6d 65 74 72 79 20 | 61 6e 64 20 61 73 74 72 |tometry |and astr|
|000012c0| 6f 6d 65 74 72 79 20 6f | 6e 20 66 61 69 6e 74 20 |ometry o|n faint |
|000012d0| 6f 62 6a 65 63 74 73 2e | 20 20 57 6f 72 73 65 2c |objects.| Worse,|
|000012e0| 20 74 68 65 72 65 0a 6d | 61 79 20 62 65 20 65 78 | there.m|ay be ex|
|000012f0| 74 65 6e 64 65 64 2c 20 | 6c 6f 77 20 73 75 72 66 |tended, |low surf|
|00001300| 61 63 65 20 62 72 69 67 | 68 74 6e 65 73 73 20 6f |ace brig|htness o|
|00001310| 62 6a 65 63 74 73 20 74 | 68 61 74 20 61 72 65 20 |bjects t|hat are |
|00001320| 6e 6f 74 20 64 65 74 65 | 63 74 61 62 6c 65 0a 69 |not dete|ctable.i|
|00001330| 6e 20 61 20 73 69 6e 67 | 6c 65 20 70 69 78 65 6c |n a sing|le pixel|
|00001340| 20 62 75 74 20 74 68 61 | 74 20 61 72 65 20 65 61 | but tha|t are ea|
|00001350| 73 69 6c 79 20 64 65 74 | 65 63 74 65 64 20 77 68 |sily det|ected wh|
|00001360| 65 6e 20 74 68 65 20 69 | 6d 61 67 65 20 69 73 0a |en the i|mage is.|
|00001370| 73 6d 6f 6f 74 68 65 64 | 20 6f 76 65 72 20 61 20 |smoothed| over a |
|00001380| 6e 75 6d 62 65 72 20 6f | 66 20 70 69 78 65 6c 73 |number o|f pixels|
|00001390| 3b 20 73 75 63 68 20 66 | 61 69 6e 74 20 73 74 72 |; such f|aint str|
|000013a0| 75 63 74 75 72 65 73 20 | 61 72 65 0a 69 72 72 65 |uctures |are.irre|
|000013b0| 74 72 69 65 76 61 62 6c | 79 20 6c 6f 73 74 20 77 |trievabl|y lost w|
|000013c0| 68 65 6e 20 74 68 65 20 | 69 6d 61 67 65 20 69 73 |hen the |image is|
|000013d0| 20 74 68 72 65 73 68 6f | 6c 64 65 64 20 74 6f 20 | thresho|lded to |
|000013e0| 69 6d 70 72 6f 76 65 0a | 63 6f 6d 70 72 65 73 73 |improve.|compress|
|000013f0| 69 6f 6e 2e 0a 0a 5c 73 | 65 63 74 69 6f 6e 20 32 |ion...\s|ection 2|
|00001400| 2e 20 54 68 65 20 5c 68 | 74 2f 0a 0a 46 72 69 74 |. The \h|t/..Frit|
|00001410| 7a 65 20 5c 65 74 61 6c | 5c 20 28 31 39 37 37 3b |ze \etal|\ (1977;|
|00001420| 20 73 65 65 20 61 6c 73 | 6f 20 52 69 63 68 74 65 | see als|o Richte|
|00001430| 72 20 31 39 37 38 20 61 | 6e 64 20 43 61 70 61 63 |r 1978 a|nd Capac|
|00001440| 63 69 6f 6c 69 20 5c 65 | 74 61 6c 5c 20 31 39 38 |cioli \e|tal\ 198|
|00001450| 38 29 0a 68 61 76 65 20 | 64 65 76 65 6c 6f 70 65 |8).have |develope|
|00001460| 64 20 61 20 6d 75 63 68 | 20 62 65 74 74 65 72 20 |d a much| better |
|00001470| 63 6f 6d 70 72 65 73 73 | 69 6f 6e 20 6d 65 74 68 |compress|ion meth|
|00001480| 6f 64 20 66 6f 72 20 61 | 73 74 72 6f 6e 6f 6d 69 |od for a|stronomi|
|00001490| 63 61 6c 20 69 6d 61 67 | 65 73 0a 62 61 73 65 64 |cal imag|es.based|
|000014a0| 20 6f 6e 20 77 68 61 74 | 20 74 68 65 79 20 63 61 | on what| they ca|
|000014b0| 6c 6c 20 74 68 65 20 7b | 5c 73 6c 20 5c 68 74 2f |ll the {|\sl \ht/|
|000014c0| 7d 20 6f 66 20 74 68 65 | 20 69 6d 61 67 65 2e 20 |} of the| image. |
|000014d0| 20 41 20 73 69 6d 69 6c | 61 72 0a 74 72 61 6e 73 | A simil|ar.trans|
|000014e0| 66 6f 72 6d 20 63 61 6c | 6c 65 64 20 74 68 65 20 |form cal|led the |
|000014f0| 53 2d 74 72 61 6e 73 66 | 6f 72 6d 20 68 61 73 20 |S-transf|orm has |
|00001500| 61 6c 73 6f 20 62 65 65 | 6e 20 75 73 65 64 20 66 |also bee|n used f|
|00001510| 6f 72 20 69 6d 61 67 65 | 0a 63 6f 6d 70 72 65 73 |or image|.compres|
|00001520| 73 69 6f 6e 20 28 42 6c | 75 6d 65 20 5c 26 20 46 |sion (Bl|ume \& F|
|00001530| 61 6e 64 20 31 39 38 39 | 29 2e 20 20 54 68 65 20 |and 1989|). The |
|00001540| 5c 68 74 2f 20 69 73 20 | 61 20 74 77 6f 2d 64 69 |\ht/ is |a two-di|
|00001550| 6d 65 6e 73 69 6f 6e 61 | 6c 0a 67 65 6e 65 72 61 |mensiona|l.genera|
|00001560| 6c 69 7a 61 74 69 6f 6e | 20 6f 66 20 74 68 65 20 |lization| of the |
|00001570| 48 61 61 72 20 74 72 61 | 6e 73 66 6f 72 6d 20 28 |Haar tra|nsform (|
|00001580| 48 61 61 72 20 31 39 31 | 30 29 2e 20 20 54 68 65 |Haar 191|0). The|
|00001590| 20 5c 68 74 2f 20 69 73 | 0a 63 61 6c 63 75 6c 61 | \ht/ is|.calcula|
|000015a0| 74 65 64 20 66 6f 72 20 | 61 6e 20 69 6d 61 67 65 |ted for |an image|
|000015b0| 20 6f 66 20 73 69 7a 65 | 20 24 32 5e 4e 5c 74 69 | of size| $2^N\ti|
|000015c0| 6d 65 73 20 32 5e 4e 24 | 20 61 73 20 66 6f 6c 6c |mes 2^N$| as foll|
|000015d0| 6f 77 73 3a 0a 0a 5c 6d | 65 64 73 6b 69 70 0a 5c |ows:..\m|edskip.\|
|000015e0| 62 75 6c 6c 61 20 44 69 | 76 69 64 65 20 74 68 65 |bulla Di|vide the|
|000015f0| 20 69 6d 61 67 65 20 75 | 70 20 69 6e 74 6f 20 62 | image u|p into b|
|00001600| 6c 6f 63 6b 73 20 6f 66 | 20 24 32 5c 74 69 6d 65 |locks of| $2\time|
|00001610| 73 32 24 20 70 69 78 65 | 6c 73 2e 20 20 43 61 6c |s2$ pixe|ls. Cal|
|00001620| 6c 20 74 68 65 0a 34 20 | 70 69 78 65 6c 73 20 69 |l the.4 |pixels i|
|00001630| 6e 20 61 20 62 6c 6f 63 | 6b 20 24 61 5f 7b 30 30 |n a bloc|k $a_{00|
|00001640| 7d 24 2c 20 24 61 5f 7b | 31 30 7d 24 2c 20 24 61 |}$, $a_{|10}$, $a|
|00001650| 5f 7b 30 31 7d 24 2c 20 | 61 6e 64 20 24 61 5f 7b |_{01}$, |and $a_{|
|00001660| 31 31 7d 24 2e 0a 0a 5c | 62 75 6c 6c 61 20 46 6f |11}$...\|bulla Fo|
|00001670| 72 20 65 61 63 68 20 62 | 6c 6f 63 6b 20 63 6f 6d |r each b|lock com|
|00001680| 70 75 74 65 20 34 20 63 | 6f 65 66 66 69 63 69 65 |pute 4 c|oefficie|
|00001690| 6e 74 73 3a 0a 0a 24 24 | 5c 65 71 61 6c 69 67 6e |nts:..$$|\eqalign|
|000016a0| 7b 0a 68 5f 30 20 26 3d | 20 28 61 5f 7b 31 31 7d |{.h_0 &=| (a_{11}|
|000016b0| 2b 61 5f 7b 31 30 7d 2b | 61 5f 7b 30 31 7d 2b 61 |+a_{10}+|a_{01}+a|
|000016c0| 5f 7b 30 30 7d 29 2f 32 | 5c 63 72 0a 68 5f 78 20 |_{00})/2|\cr.h_x |
|000016d0| 26 3d 20 28 61 5f 7b 31 | 31 7d 2b 61 5f 7b 31 30 |&= (a_{1|1}+a_{10|
|000016e0| 7d 2d 61 5f 7b 30 31 7d | 2d 61 5f 7b 30 30 7d 29 |}-a_{01}|-a_{00})|
|000016f0| 2f 32 5c 63 72 0a 68 5f | 79 20 26 3d 20 28 61 5f |/2\cr.h_|y &= (a_|
|00001700| 7b 31 31 7d 2d 61 5f 7b | 31 30 7d 2b 61 5f 7b 30 |{11}-a_{|10}+a_{0|
|00001710| 31 7d 2d 61 5f 7b 30 30 | 7d 29 2f 32 5c 63 72 0a |1}-a_{00|})/2\cr.|
|00001720| 68 5f 63 20 26 3d 20 28 | 61 5f 7b 31 31 7d 2d 61 |h_c &= (|a_{11}-a|
|00001730| 5f 7b 31 30 7d 2d 61 5f | 7b 30 31 7d 2b 61 5f 7b |_{10}-a_|{01}+a_{|
|00001740| 30 30 7d 29 2f 32 5c 63 | 72 0a 7d 24 24 0a 5c 62 |00})/2\c|r.}$$.\b|
|00001750| 75 6c 6c 61 20 43 6f 6e | 73 74 72 75 63 74 20 61 |ulla Con|struct a|
|00001760| 20 24 32 5e 7b 4e 2d 31 | 7d 5c 74 69 6d 65 73 20 | $2^{N-1|}\times |
|00001770| 32 5e 7b 4e 2d 31 7d 24 | 20 69 6d 61 67 65 20 66 |2^{N-1}$| image f|
|00001780| 72 6f 6d 20 74 68 65 20 | 24 68 5f 30 24 20 76 61 |rom the |$h_0$ va|
|00001790| 6c 75 65 73 0a 66 6f 72 | 20 65 61 63 68 20 24 32 |lues.for| each $2|
|000017a0| 5c 74 69 6d 65 73 32 24 | 20 62 6c 6f 63 6b 2e 20 |\times2$| block. |
|000017b0| 20 44 69 76 69 64 65 20 | 74 68 61 74 20 69 6d 61 | Divide |that ima|
|000017c0| 67 65 20 75 70 20 69 6e | 74 6f 20 24 32 5c 74 69 |ge up in|to $2\ti|
|000017d0| 6d 65 73 32 24 20 62 6c | 6f 63 6b 73 0a 61 6e 64 |mes2$ bl|ocks.and|
|000017e0| 20 72 65 70 65 61 74 20 | 74 68 65 20 61 62 6f 76 | repeat |the abov|
|000017f0| 65 20 63 61 6c 63 75 6c | 61 74 69 6f 6e 2e 20 20 |e calcul|ation. |
|00001800| 52 65 70 65 61 74 20 74 | 68 69 73 20 70 72 6f 63 |Repeat t|his proc|
|00001810| 65 73 73 20 24 4e 24 20 | 74 69 6d 65 73 2c 0a 72 |ess $N$ |times,.r|
|00001820| 65 64 75 63 69 6e 67 20 | 74 68 65 20 69 6d 61 67 |educing |the imag|
|00001830| 65 20 69 6e 20 73 69 7a | 65 20 62 79 20 61 20 66 |e in siz|e by a f|
|00001840| 61 63 74 6f 72 20 6f 66 | 20 32 20 61 74 20 65 61 |actor of| 2 at ea|
|00001850| 63 68 20 73 74 65 70 2c | 20 75 6e 74 69 6c 20 6f |ch step,| until o|
|00001860| 6e 6c 79 0a 6f 6e 65 20 | 24 68 5f 30 24 20 76 61 |nly.one |$h_0$ va|
|00001870| 6c 75 65 20 72 65 6d 61 | 69 6e 73 2e 0a 0a 5c 6d |lue rema|ins...\m|
|00001880| 65 64 73 6b 69 70 0a 5c | 6e 6f 69 6e 64 65 6e 74 |edskip.\|noindent|
|00001890| 0a 54 68 69 73 20 63 61 | 6c 63 75 6c 61 74 69 6f |.This ca|lculatio|
|000018a0| 6e 20 63 61 6e 20 62 65 | 20 65 61 73 69 6c 79 20 |n can be| easily |
|000018b0| 69 6e 76 65 72 74 65 64 | 20 74 6f 20 72 65 63 6f |inverted| to reco|
|000018c0| 76 65 72 20 74 68 65 20 | 6f 72 69 67 69 6e 61 6c |ver the |original|
|000018d0| 20 69 6d 61 67 65 0a 66 | 72 6f 6d 20 69 74 73 20 | image.f|rom its |
|000018e0| 74 72 61 6e 73 66 6f 72 | 6d 2e 20 20 54 68 65 20 |transfor|m. The |
|000018f0| 74 72 61 6e 73 66 6f 72 | 6d 20 69 73 20 65 78 61 |transfor|m is exa|
|00001900| 63 74 6c 79 20 72 65 76 | 65 72 73 69 62 6c 65 20 |ctly rev|ersible |
|00001910| 75 73 69 6e 67 20 69 6e | 74 65 67 65 72 0a 61 72 |using in|teger.ar|
|00001920| 69 74 68 6d 65 74 69 63 | 20 69 66 20 6f 6e 65 20 |ithmetic| if one |
|00001930| 64 6f 65 73 20 6e 6f 74 | 20 64 69 76 69 64 65 20 |does not| divide |
|00001940| 62 79 20 32 20 66 6f 72 | 20 74 68 65 20 66 69 72 |by 2 for| the fir|
|00001950| 73 74 20 73 65 74 20 6f | 66 0a 63 6f 65 66 66 69 |st set o|f.coeffi|
|00001960| 63 69 65 6e 74 73 2e 20 | 20 49 74 20 69 73 20 73 |cients. | It is s|
|00001970| 74 72 61 69 67 68 74 66 | 6f 72 77 61 72 64 20 74 |traightf|orward t|
|00001980| 6f 20 65 78 74 65 6e 64 | 20 74 68 65 20 64 65 66 |o extend| the def|
|00001990| 69 6e 69 74 69 6f 6e 20 | 6f 66 20 74 68 65 0a 74 |inition |of the.t|
|000019a0| 72 61 6e 73 66 6f 72 6d | 20 73 6f 20 74 68 61 74 |ransform| so that|
|000019b0| 20 69 74 20 63 61 6e 20 | 62 65 20 63 6f 6d 70 75 | it can |be compu|
|000019c0| 74 65 64 20 66 6f 72 20 | 6e 6f 6e 2d 73 71 75 61 |ted for |non-squa|
|000019d0| 72 65 20 69 6d 61 67 65 | 73 20 74 68 61 74 20 64 |re image|s that d|
|000019e0| 6f 20 6e 6f 74 0a 68 61 | 76 65 20 73 69 64 65 73 |o not.ha|ve sides|
|000019f0| 20 74 68 61 74 20 61 72 | 65 20 70 6f 77 65 72 73 | that ar|e powers|
|00001a00| 20 6f 66 20 32 2e 20 20 | 54 68 65 20 5c 68 74 2f | of 2. |The \ht/|
|00001a10| 20 63 61 6e 20 62 65 20 | 70 65 72 66 6f 72 6d 65 | can be |performe|
|00001a20| 64 20 69 6e 20 70 6c 61 | 63 65 0a 69 6e 20 6d 65 |d in pla|ce.in me|
|00001a30| 6d 6f 72 79 20 61 6e 64 | 20 69 73 20 76 65 72 79 |mory and| is very|
|00001a40| 20 66 61 73 74 20 74 6f | 20 63 6f 6d 70 75 74 65 | fast to| compute|
|00001a50| 2c 20 72 65 71 75 69 72 | 69 6e 67 20 61 62 6f 75 |, requir|ing abou|
|00001a60| 74 20 24 31 36 4d 5e 32 | 2f 33 24 0a 28 69 6e 74 |t $16M^2|/3$.(int|
|00001a70| 65 67 65 72 29 20 61 64 | 64 69 74 69 6f 6e 73 20 |eger) ad|ditions |
|00001a80| 66 6f 72 20 61 20 24 4d | 5c 74 69 6d 65 73 20 4d |for a $M|\times M|
|00001a90| 24 20 69 6d 61 67 65 2e | 0a 0a 54 68 65 20 5c 68 |$ image.|..The \h|
|00001aa0| 74 2f 20 69 73 20 61 20 | 73 69 6d 70 6c 65 20 32 |t/ is a |simple 2|
|00001ab0| 2d 64 69 6d 65 6e 73 69 | 6f 6e 61 6c 20 77 61 76 |-dimensi|onal wav|
|00001ac0| 65 6c 65 74 20 74 72 61 | 6e 73 66 6f 72 6d 2e 20 |elet tra|nsform. |
|00001ad0| 20 49 74 20 68 61 73 20 | 73 65 76 65 72 61 6c 0a | It has |several.|
|00001ae0| 61 64 76 61 6e 74 61 67 | 65 73 20 6f 76 65 72 20 |advantag|es over |
|00001af0| 73 6f 6d 65 20 6f 74 68 | 65 72 20 77 61 76 65 6c |some oth|er wavel|
|00001b00| 65 74 20 74 72 61 6e 73 | 66 6f 72 6d 73 20 74 68 |et trans|forms th|
|00001b10| 61 74 20 68 61 76 65 20 | 62 65 65 6e 20 61 70 70 |at have |been app|
|00001b20| 6c 69 65 64 20 74 6f 0a | 69 6d 61 67 65 20 63 6f |lied to.|image co|
|00001b30| 6d 70 72 65 73 73 69 6f | 6e 20 28 5c 65 67 20 44 |mpressio|n (\eg D|
|00001b40| 61 75 62 65 63 68 69 65 | 73 20 31 39 38 38 29 2e |aubechie|s 1988).|
|00001b50| 20 20 46 69 72 73 74 2c | 20 74 68 65 20 74 72 61 | First,| the tra|
|00001b60| 6e 73 66 6f 72 6d 20 63 | 61 6e 20 62 65 0a 70 65 |nsform c|an be.pe|
|00001b70| 72 66 6f 72 6d 65 64 20 | 65 6e 74 69 72 65 6c 79 |rformed |entirely|
|00001b80| 20 77 69 74 68 20 69 6e | 74 65 67 65 72 20 61 72 | with in|teger ar|
|00001b90| 69 74 68 6d 65 74 69 63 | 2c 20 6d 61 6b 69 6e 67 |ithmetic|, making|
|00001ba0| 20 69 74 20 65 78 61 63 | 74 6c 79 0a 72 65 76 65 | it exac|tly.reve|
|00001bb0| 72 73 69 62 6c 65 2e 20 | 20 43 6f 6e 73 65 71 75 |rsible. | Consequ|
|00001bc0| 65 6e 74 6c 79 20 69 74 | 20 63 61 6e 20 62 65 20 |ently it| can be |
|00001bd0| 75 73 65 64 20 66 6f 72 | 20 65 69 74 68 65 72 20 |used for| either |
|00001be0| 6c 6f 73 73 6c 65 73 73 | 20 6f 72 20 6c 6f 73 73 |lossless| or loss|
|00001bf0| 79 0a 63 6f 6d 70 72 65 | 73 73 69 6f 6e 20 28 61 |y.compre|ssion (a|
|00001c00| 73 20 69 6e 64 69 63 61 | 74 65 64 20 62 65 6c 6f |s indica|ted belo|
|00001c10| 77 29 20 61 6e 64 20 6f | 6e 65 20 64 6f 65 73 20 |w) and o|ne does |
|00001c20| 6e 6f 74 20 6e 65 65 64 | 20 61 20 73 70 65 63 69 |not need| a speci|
|00001c30| 61 6c 0a 74 65 63 68 6e | 69 71 75 65 20 66 6f 72 |al.techn|ique for|
|00001c40| 20 74 68 65 20 63 61 73 | 65 20 6f 66 20 6c 6f 73 | the cas|e of los|
|00001c50| 73 6c 65 73 73 20 63 6f | 6d 70 72 65 73 73 69 6f |sless co|mpressio|
|00001c60| 6e 20 28 61 73 20 77 61 | 73 20 72 65 71 75 69 72 |n (as wa|s requir|
|00001c70| 65 64 2c 20 5c 65 67 2c | 0a 66 6f 72 20 74 68 65 |ed, \eg,|.for the|
|00001c80| 20 4a 50 45 47 20 63 6f | 6d 70 72 65 73 73 69 6f | JPEG co|mpressio|
|00001c90| 6e 20 73 74 61 6e 64 61 | 72 64 2e 29 0a 0a 41 20 |n standa|rd.)..A |
|00001ca0| 73 65 63 6f 6e 64 20 6d | 61 6a 6f 72 20 61 64 76 |second m|ajor adv|
|00001cb0| 61 6e 74 61 67 65 20 69 | 73 20 74 68 61 74 20 74 |antage i|s that t|
|00001cc0| 68 65 20 5c 68 74 2f 20 | 69 73 20 61 20 6e 61 74 |he \ht/ |is a nat|
|00001cd0| 69 76 65 6c 79 20 32 2d | 64 69 6d 65 6e 73 69 6f |ively 2-|dimensio|
|00001ce0| 6e 61 6c 0a 77 61 76 65 | 6c 65 74 20 74 72 61 6e |nal.wave|let tran|
|00001cf0| 73 66 6f 72 6d 2e 20 20 | 54 68 65 20 73 74 61 6e |sform. |The stan|
|00001d00| 64 61 72 64 20 31 2d 64 | 69 6d 65 6e 73 69 6f 6e |dard 1-d|imension|
|00001d10| 61 6c 20 77 61 76 65 6c | 65 74 20 74 72 61 6e 73 |al wavel|et trans|
|00001d20| 66 6f 72 6d 73 20 61 72 | 65 0a 65 78 74 65 6e 64 |forms ar|e.extend|
|00001d30| 65 64 20 74 6f 20 74 77 | 6f 20 64 69 6d 65 6e 73 |ed to tw|o dimens|
|00001d40| 69 6f 6e 73 20 62 79 20 | 74 72 61 6e 73 66 6f 72 |ions by |transfor|
|00001d50| 6d 69 6e 67 20 74 68 65 | 20 69 6d 61 67 65 20 66 |ming the| image f|
|00001d60| 69 72 73 74 20 61 6c 6f | 6e 67 20 74 68 65 0a 72 |irst alo|ng the.r|
|00001d70| 6f 77 73 2c 20 74 68 65 | 6e 20 61 6c 6f 6e 67 20 |ows, the|n along |
|00001d80| 74 68 65 20 63 6f 6c 75 | 6d 6e 73 2e 20 20 55 6e |the colu|mns. Un|
|00001d90| 66 6f 72 74 75 6e 61 74 | 65 6c 79 2c 20 74 68 69 |fortunat|ely, thi|
|00001da0| 73 20 67 65 6e 65 72 61 | 74 65 73 20 6d 61 6e 79 |s genera|tes many|
|00001db0| 0a 77 61 76 65 6c 65 74 | 20 63 6f 65 66 66 69 63 |.wavelet| coeffic|
|00001dc0| 69 65 6e 74 73 20 74 68 | 61 74 20 61 72 65 20 68 |ients th|at are h|
|00001dd0| 69 67 68 20 66 72 65 71 | 75 65 6e 63 79 20 28 68 |igh freq|uency (h|
|00001de0| 65 6e 63 65 20 6c 6f 63 | 61 6c 69 7a 65 64 29 20 |ence loc|alized) |
|00001df0| 69 6e 20 74 68 65 0a 24 | 78 24 2d 64 69 72 65 63 |in the.$|x$-direc|
|00001e00| 74 69 6f 6e 20 62 75 74 | 20 6c 6f 77 20 66 72 65 |tion but| low fre|
|00001e10| 71 75 65 6e 63 79 20 28 | 68 65 6e 63 65 20 67 6c |quency (|hence gl|
|00001e20| 6f 62 61 6c 29 20 69 6e | 20 74 68 65 20 24 79 24 |obal) in| the $y$|
|00001e30| 2d 64 69 72 65 63 74 69 | 6f 6e 2e 0a 53 75 63 68 |-directi|on..Such|
|00001e40| 20 63 6f 65 66 66 69 63 | 69 65 6e 74 73 20 61 72 | coeffic|ients ar|
|00001e50| 65 20 63 6f 75 6e 74 65 | 72 20 74 6f 20 74 68 65 |e counte|r to the|
|00001e60| 20 70 68 69 6c 6f 73 6f | 70 68 79 20 6f 66 20 74 | philoso|phy of t|
|00001e70| 68 65 20 77 61 76 65 6c | 65 74 0a 74 72 61 6e 73 |he wavel|et.trans|
|00001e80| 66 6f 72 6d 3a 20 20 68 | 69 67 68 2d 66 72 65 71 |form: h|igh-freq|
|00001e90| 75 65 6e 63 79 20 62 61 | 73 69 73 20 66 75 6e 63 |uency ba|sis func|
|00001ea0| 74 69 6f 6e 73 20 73 68 | 6f 75 6c 64 20 62 65 20 |tions sh|ould be |
|00001eb0| 63 6f 6e 66 69 6e 65 64 | 20 74 6f 20 61 0a 72 65 |confined| to a.re|
|00001ec0| 6c 61 74 69 76 65 6c 79 | 20 73 6d 61 6c 6c 20 61 |latively| small a|
|00001ed0| 72 65 61 20 6f 66 20 74 | 68 65 20 69 6d 61 67 65 |rea of t|he image|
|00001ee0| 2e 20 20 44 69 73 63 61 | 72 64 69 6e 67 20 74 68 |. Disca|rding th|
|00001ef0| 65 73 65 20 6d 69 78 65 | 64 2d 73 63 61 6c 65 0a |ese mixe|d-scale.|
|00001f00| 74 65 72 6d 73 2c 20 77 | 68 69 63 68 20 6d 61 79 |terms, w|hich may|
|00001f10| 20 62 65 20 6e 65 67 6c | 69 67 69 62 6c 65 20 63 | be negl|igible c|
|00001f20| 6f 6d 70 61 72 65 64 20 | 74 6f 20 74 68 65 20 6e |ompared |to the n|
|00001f30| 6f 69 73 65 2c 20 67 65 | 6e 65 72 61 74 65 73 20 |oise, ge|nerates |
|00001f40| 76 65 72 79 0a 6f 62 6a | 65 63 74 69 6f 6e 61 62 |very.obj|ectionab|
|00001f50| 6c 65 20 61 72 74 69 66 | 61 63 74 73 20 61 72 6f |le artif|acts aro|
|00001f60| 75 6e 64 20 70 6f 69 6e | 74 20 73 6f 75 72 63 65 |und poin|t source|
|00001f70| 73 20 61 6e 64 20 65 64 | 67 65 73 20 69 6e 20 74 |s and ed|ges in t|
|00001f80| 68 65 20 69 6d 61 67 65 | 2e 0a 54 68 65 20 5c 68 |he image|..The \h|
|00001f90| 74 2f 2c 20 6f 6e 20 74 | 68 65 20 6f 74 68 65 72 |t/, on t|he other|
|00001fa0| 20 68 61 6e 64 2c 20 69 | 73 20 61 20 66 75 6c 6c | hand, i|s a full|
|00001fb0| 79 20 32 2d 64 69 6d 65 | 6e 73 69 6f 6e 61 6c 20 |y 2-dime|nsional |
|00001fc0| 77 61 76 65 6c 65 74 0a | 74 72 61 6e 73 66 6f 72 |wavelet.|transfor|
|00001fd0| 6d 2c 20 77 69 74 68 20 | 61 6c 6c 20 68 69 67 68 |m, with |all high|
|00001fe0| 20 66 72 65 71 75 65 6e | 63 79 20 74 65 72 6d 73 | frequen|cy terms|
|00001ff0| 20 62 65 69 6e 67 20 63 | 6f 6d 70 6c 65 74 65 6c | being c|ompletel|
|00002000| 79 20 6c 6f 63 61 6c 69 | 7a 65 64 2e 0a 49 74 20 |y locali|zed..It |
|00002010| 69 73 20 63 6f 6e 73 65 | 71 75 65 6e 74 6c 79 20 |is conse|quently |
|00002020| 6d 6f 72 65 20 73 75 69 | 74 61 62 6c 65 20 66 6f |more sui|table fo|
|00002030| 72 20 69 6d 61 67 65 20 | 63 6f 6d 70 72 65 73 73 |r image |compress|
|00002040| 69 6f 6e 20 61 6e 64 20 | 70 72 6f 64 75 63 65 73 |ion and |produces|
|00002050| 0a 66 65 77 65 72 20 61 | 72 74 69 66 61 63 74 73 |.fewer a|rtifacts|
|00002060| 2e 0a 0a 41 20 70 6f 73 | 73 69 62 6c 65 20 64 69 |...A pos|sible di|
|00002070| 73 61 64 76 61 6e 74 61 | 67 65 20 6f 66 20 74 68 |sadvanta|ge of th|
|00002080| 65 20 5c 68 74 2f 20 69 | 73 20 74 68 61 74 20 6f |e \ht/ i|s that o|
|00002090| 74 68 65 72 20 77 61 76 | 65 6c 65 74 20 74 72 61 |ther wav|elet tra|
|000020a0| 6e 73 66 6f 72 6d 73 0a | 74 61 6b 65 20 62 65 74 |nsforms.|take bet|
|000020b0| 74 65 72 20 61 64 76 61 | 6e 74 61 67 65 20 6f 66 |ter adva|ntage of|
|000020c0| 20 74 68 65 20 63 6f 6e | 74 69 6e 75 69 74 79 20 | the con|tinuity |
|000020d0| 6f 66 20 70 69 78 65 6c | 20 76 61 6c 75 65 73 20 |of pixel| values |
|000020e0| 77 69 74 68 69 6e 20 69 | 6d 61 67 65 73 2c 0a 73 |within i|mages,.s|
|000020f0| 6f 20 74 68 61 74 20 74 | 68 65 79 20 63 61 6e 20 |o that t|hey can |
|00002100| 70 72 6f 64 75 63 65 20 | 68 69 67 68 65 72 20 63 |produce |higher c|
|00002110| 6f 6d 70 72 65 73 73 69 | 6f 6e 73 20 66 6f 72 20 |ompressi|ons for |
|00002120| 76 65 72 79 20 73 6d 6f | 6f 74 68 20 69 6d 61 67 |very smo|oth imag|
|00002130| 65 73 2e 0a 48 6f 77 65 | 76 65 72 2c 20 66 6f 72 |es..Howe|ver, for|
|00002140| 20 61 73 74 72 6f 6d 69 | 63 61 6c 20 69 6d 61 67 | astromi|cal imag|
|00002150| 65 73 20 28 77 68 69 63 | 68 20 61 72 65 20 6d 6f |es (whic|h are mo|
|00002160| 73 74 6c 79 20 66 6c 61 | 74 20 73 6b 79 20 73 70 |stly fla|t sky sp|
|00002170| 72 69 6e 6b 6c 65 64 0a | 77 69 74 68 20 70 6f 69 |rinkled.|with poi|
|00002180| 6e 74 20 73 6f 75 72 63 | 65 73 29 20 74 68 65 20 |nt sourc|es) the |
|00002190| 73 6d 6f 6f 74 68 6e 65 | 73 73 20 62 75 69 6c 74 |smoothne|ss built|
|000021a0| 20 69 6e 74 6f 20 68 69 | 67 68 65 72 2d 6f 72 64 | into hi|gher-ord|
|000021b0| 65 72 20 74 72 61 6e 73 | 66 6f 72 6d 73 0a 63 61 |er trans|forms.ca|
|000021c0| 6e 20 61 63 74 75 61 6c | 6c 79 20 72 65 64 75 63 |n actual|ly reduc|
|000021d0| 65 20 74 68 65 20 65 66 | 66 65 63 74 69 76 65 6e |e the ef|fectiven|
|000021e0| 65 73 73 20 6f 66 20 63 | 6f 6d 70 72 65 73 73 69 |ess of c|ompressi|
|000021f0| 6f 6e 2c 20 62 65 63 61 | 75 73 65 20 6f 6e 65 20 |on, beca|use one |
|00002200| 6d 75 73 74 0a 6b 65 65 | 70 20 6d 6f 72 65 20 63 |must.kee|p more c|
|00002210| 6f 65 66 66 69 63 69 65 | 6e 74 73 20 74 6f 20 64 |oefficie|nts to d|
|00002220| 65 73 63 72 69 62 65 20 | 65 61 63 68 20 70 6f 69 |escribe |each poi|
|00002230| 6e 74 20 73 6f 75 72 63 | 65 2e 0a 0a 5c 73 65 63 |nt sourc|e...\sec|
|00002240| 74 69 6f 6e 20 33 2e 20 | 43 6f 6d 70 72 65 73 73 |tion 3. |Compress|
|00002250| 69 6f 6e 20 55 73 69 6e | 67 20 74 68 65 20 5c 68 |ion Usin|g the \h|
|00002260| 74 2f 0a 0a 49 66 20 74 | 68 65 20 69 6d 61 67 65 |t/..If t|he image|
|00002270| 20 69 73 20 6e 65 61 72 | 6c 79 20 6e 6f 69 73 65 | is near|ly noise|
|00002280| 6c 65 73 73 2c 20 74 68 | 65 20 5c 68 74 2f 20 69 |less, th|e \ht/ i|
|00002290| 73 20 73 6f 6d 65 77 68 | 61 74 20 65 61 73 69 65 |s somewh|at easie|
|000022a0| 72 20 74 6f 0a 63 6f 6d | 70 72 65 73 73 20 74 68 |r to.com|press th|
|000022b0| 61 6e 20 74 68 65 20 6f | 72 69 67 69 6e 61 6c 20 |an the o|riginal |
|000022c0| 69 6d 61 67 65 20 62 65 | 63 61 75 73 65 20 74 68 |image be|cause th|
|000022d0| 65 20 64 69 66 66 65 72 | 65 6e 63 65 73 20 6f 66 |e differ|ences of|
|000022e0| 20 61 64 6a 61 63 65 6e | 74 0a 70 69 78 65 6c 73 | adjacen|t.pixels|
|000022f0| 20 28 61 73 20 63 6f 6d | 70 75 74 65 64 20 69 6e | (as com|puted in|
|00002300| 20 74 68 65 20 5c 68 74 | 2f 29 20 74 65 6e 64 20 | the \ht|/) tend |
|00002310| 74 6f 20 62 65 20 73 6d | 61 6c 6c 65 72 20 74 68 |to be sm|aller th|
|00002320| 61 6e 20 74 68 65 20 6f | 72 69 67 69 6e 61 6c 0a |an the o|riginal.|
|00002330| 70 69 78 65 6c 20 76 61 | 6c 75 65 73 20 66 6f 72 |pixel va|lues for|
|00002340| 20 73 6d 6f 6f 74 68 20 | 69 6d 61 67 65 73 2e 20 | smooth |images. |
|00002350| 20 43 6f 6e 73 65 71 75 | 65 6e 74 6c 79 20 66 65 | Consequ|ently fe|
|00002360| 77 65 72 20 62 69 74 73 | 20 61 72 65 20 72 65 71 |wer bits| are req|
|00002370| 75 69 72 65 64 0a 74 6f | 20 73 74 6f 72 65 20 74 |uired.to| store t|
|00002380| 68 65 20 76 61 6c 75 65 | 73 20 6f 66 20 74 68 65 |he value|s of the|
|00002390| 20 5c 68 74 2f 20 63 6f | 65 66 66 69 63 69 65 6e | \ht/ co|efficien|
|000023a0| 74 73 20 74 68 61 6e 20 | 61 72 65 20 72 65 71 75 |ts than |are requ|
|000023b0| 69 72 65 64 20 66 6f 72 | 20 74 68 65 0a 6f 72 69 |ired for| the.ori|
|000023c0| 67 69 6e 61 6c 20 69 6d | 61 67 65 2e 20 20 46 6f |ginal im|age. Fo|
|000023d0| 72 20 76 65 72 79 20 73 | 6d 6f 6f 74 68 20 69 6d |r very s|mooth im|
|000023e0| 61 67 65 73 20 74 68 65 | 20 70 69 78 65 6c 20 76 |ages the| pixel v|
|000023f0| 61 6c 75 65 73 20 6d 61 | 79 20 62 65 0a 63 6f 6e |alues ma|y be.con|
|00002400| 73 74 61 6e 74 20 6f 76 | 65 72 20 6c 61 72 67 65 |stant ov|er large|
|00002410| 20 72 65 67 69 6f 6e 73 | 2c 20 6c 65 61 64 69 6e | regions|, leadin|
|00002420| 67 20 74 6f 20 74 72 61 | 6e 73 66 6f 72 6d 20 63 |g to tra|nsform c|
|00002430| 6f 65 66 66 69 63 69 65 | 6e 74 73 20 74 68 61 74 |oefficie|nts that|
|00002440| 0a 61 72 65 20 7a 65 72 | 6f 20 6f 76 65 72 20 6c |.are zer|o over l|
|00002450| 61 72 67 65 20 61 72 65 | 61 73 2e 0a 0a 4e 6f 69 |arge are|as...Noi|
|00002460| 73 79 20 69 6d 61 67 65 | 73 20 73 74 69 6c 6c 20 |sy image|s still |
|00002470| 64 6f 20 6e 6f 74 20 63 | 6f 6d 70 72 65 73 73 20 |do not c|ompress |
|00002480| 77 65 6c 6c 20 77 68 65 | 6e 20 74 72 61 6e 73 66 |well whe|n transf|
|00002490| 6f 72 6d 65 64 2c 20 74 | 68 6f 75 67 68 2e 0a 53 |ormed, t|hough..S|
|000024a0| 75 70 70 6f 73 65 20 74 | 68 65 72 65 20 69 73 20 |uppose t|here is |
|000024b0| 6e 6f 69 73 65 20 24 5c | 73 69 67 6d 61 24 20 69 |noise $\|sigma$ i|
|000024c0| 6e 20 65 61 63 68 20 70 | 69 78 65 6c 20 6f 66 20 |n each p|ixel of |
|000024d0| 74 68 65 20 6f 72 69 67 | 69 6e 61 6c 20 69 6d 61 |the orig|inal ima|
|000024e0| 67 65 2e 0a 54 68 65 6e | 20 66 72 6f 6d 20 73 69 |ge..Then| from si|
|000024f0| 6d 70 6c 65 20 70 72 6f | 70 61 67 61 74 69 6f 6e |mple pro|pagation|
|00002500| 20 6f 66 20 65 72 72 6f | 72 73 2c 20 74 68 65 20 | of erro|rs, the |
|00002510| 6e 6f 69 73 65 20 69 6e | 20 65 61 63 68 20 6f 66 |noise in| each of|
|00002520| 20 74 68 65 20 5c 68 74 | 2f 0a 63 6f 65 66 66 69 | the \ht|/.coeffi|
|00002530| 63 69 65 6e 74 73 20 69 | 73 20 61 6c 73 6f 20 24 |cients i|s also $|
|00002540| 5c 73 69 67 6d 61 24 2e | 20 20 54 6f 20 63 6f 6d |\sigma$.| To com|
|00002550| 70 72 65 73 73 20 6e 6f | 69 73 79 20 69 6d 61 67 |press no|isy imag|
|00002560| 65 73 2c 20 64 69 76 69 | 64 65 20 65 61 63 68 0a |es, divi|de each.|
|00002570| 63 6f 65 66 66 69 63 69 | 65 6e 74 20 62 79 20 24 |coeffici|ent by $|
|00002580| 53 5c 73 69 67 6d 61 24 | 2c 20 77 68 65 72 65 20 |S\sigma$|, where |
|00002590| 24 53 5c 73 69 6d 31 24 | 20 69 73 20 63 68 6f 73 |$S\sim1$| is chos|
|000025a0| 65 6e 20 61 63 63 6f 72 | 64 69 6e 67 20 74 6f 20 |en accor|ding to |
|000025b0| 68 6f 77 0a 6d 75 63 68 | 20 6c 6f 73 73 20 69 73 |how.much| loss is|
|000025c0| 20 61 63 63 65 70 74 61 | 62 6c 65 2e 20 20 54 68 | accepta|ble. Th|
|000025d0| 69 73 20 72 65 64 75 63 | 65 73 20 74 68 65 20 6e |is reduc|es the n|
|000025e0| 6f 69 73 65 20 69 6e 20 | 74 68 65 20 74 72 61 6e |oise in |the tran|
|000025f0| 73 66 6f 72 6d 20 74 6f | 0a 24 30 2e 35 2f 53 24 |sform to|.$0.5/S$|
|00002600| 2c 20 73 6f 20 74 68 61 | 74 20 6c 61 72 67 65 20 |, so tha|t large |
|00002610| 70 6f 72 74 69 6f 6e 73 | 20 6f 66 20 74 68 65 20 |portions| of the |
|00002620| 74 72 61 6e 73 66 6f 72 | 6d 20 61 72 65 20 7a 65 |transfor|m are ze|
|00002630| 72 6f 20 28 6f 72 20 6e | 65 61 72 6c 79 0a 7a 65 |ro (or n|early.ze|
|00002640| 72 6f 29 20 61 6e 64 20 | 74 68 65 20 74 72 61 6e |ro) and |the tran|
|00002650| 73 66 6f 72 6d 20 69 73 | 20 68 69 67 68 6c 79 20 |sform is| highly |
|00002660| 63 6f 6d 70 72 65 73 73 | 69 62 6c 65 2e 0a 0a 57 |compress|ible...W|
|00002670| 68 79 20 69 73 20 74 68 | 69 73 20 62 65 74 74 65 |hy is th|is bette|
|00002680| 72 20 74 68 61 6e 20 73 | 69 6d 70 6c 79 20 74 68 |r than s|imply th|
|00002690| 72 65 73 68 6f 6c 64 69 | 6e 67 20 74 68 65 20 6f |resholdi|ng the o|
|000026a0| 72 69 67 69 6e 61 6c 20 | 69 6d 61 67 65 3f 20 20 |riginal |image? |
|000026b0| 41 73 0a 64 69 73 63 75 | 73 73 65 64 20 61 62 6f |As.discu|ssed abo|
|000026c0| 76 65 2c 20 69 66 20 77 | 65 20 73 69 6d 70 6c 79 |ve, if w|e simply|
|000026d0| 20 64 69 76 69 64 65 20 | 74 68 65 20 69 6d 61 67 | divide |the imag|
|000026e0| 65 20 62 79 20 24 5c 73 | 69 67 6d 61 24 20 74 68 |e by $\s|igma$ th|
|000026f0| 65 6e 20 77 65 20 6c 6f | 73 65 0a 61 6c 6c 20 69 |en we lo|se.all i|
|00002700| 6e 66 6f 72 6d 61 74 69 | 6f 6e 20 6f 6e 20 6f 62 |nformati|on on ob|
|00002710| 6a 65 63 74 73 20 74 68 | 61 74 20 61 72 65 20 77 |jects th|at are w|
|00002720| 69 74 68 69 6e 20 24 31 | 5c 73 69 67 6d 61 24 20 |ithin $1|\sigma$ |
|00002730| 6f 66 20 73 6b 79 20 69 | 6e 20 61 20 7b 5c 73 6c |of sky i|n a {\sl|
|00002740| 0a 73 69 6e 67 6c 65 7d | 20 70 69 78 65 6c 2c 20 |.single}| pixel, |
|00002750| 62 75 74 20 74 68 61 74 | 20 61 72 65 20 64 65 74 |but that| are det|
|00002760| 65 63 74 61 62 6c 65 20 | 62 79 20 61 76 65 72 61 |ectable |by avera|
|00002770| 67 69 6e 67 20 61 20 7b | 5c 73 6c 20 62 6c 6f 63 |ging a {|\sl bloc|
|00002780| 6b 7d 20 6f 66 0a 70 69 | 78 65 6c 73 2e 20 20 4f |k} of.pi|xels. O|
|00002790| 6e 20 74 68 65 20 6f 74 | 68 65 72 20 68 61 6e 64 |n the ot|her hand|
|000027a0| 2c 20 69 6e 20 64 69 76 | 69 64 69 6e 67 20 74 68 |, in div|iding th|
|000027b0| 65 20 5c 68 74 2f 20 62 | 79 20 24 5c 73 69 67 6d |e \ht/ b|y $\sigm|
|000027c0| 61 24 2c 20 77 65 0a 70 | 72 65 73 65 72 76 65 20 |a$, we.p|reserve |
|000027d0| 74 68 65 20 69 6e 66 6f | 72 6d 61 74 69 6f 6e 20 |the info|rmation |
|000027e0| 6f 6e 20 61 6e 79 20 6f | 62 6a 65 63 74 20 74 68 |on any o|bject th|
|000027f0| 61 74 20 69 73 20 64 65 | 74 65 63 74 61 62 6c 65 |at is de|tectable|
|00002800| 20 62 79 20 73 75 6d 6d | 69 6e 67 20 61 0a 62 6c | by summ|ing a.bl|
|00002810| 6f 63 6b 20 6f 66 20 70 | 69 78 65 6c 73 21 20 20 |ock of p|ixels! |
|00002820| 54 68 65 20 71 75 61 6e | 74 69 7a 65 64 20 5c 68 |The quan|tized \h|
|00002830| 74 2f 20 70 72 65 73 65 | 72 76 65 73 20 74 68 65 |t/ prese|rves the|
|00002840| 20 6d 65 61 6e 20 6f 66 | 20 74 68 65 20 69 6d 61 | mean of| the ima|
|00002850| 67 65 0a 66 6f 72 20 65 | 76 65 72 79 20 62 6c 6f |ge.for e|very blo|
|00002860| 63 6b 20 6f 66 20 70 69 | 78 65 6c 73 20 68 61 76 |ck of pi|xels hav|
|00002870| 69 6e 67 20 61 20 6d 65 | 61 6e 20 73 69 67 6e 69 |ing a me|an signi|
|00002880| 66 69 63 61 6e 74 6c 79 | 20 64 69 66 66 65 72 65 |ficantly| differe|
|00002890| 6e 74 20 74 68 61 6e 0a | 74 68 61 74 20 6f 66 20 |nt than.|that of |
|000028a0| 6e 65 69 67 68 62 6f 72 | 69 6e 67 20 62 6c 6f 63 |neighbor|ing bloc|
|000028b0| 6b 73 20 6f 66 20 70 69 | 78 65 6c 73 2e 0a 0a 41 |ks of pi|xels...A|
|000028c0| 73 20 61 6e 20 65 78 61 | 6d 70 6c 65 2c 20 46 69 |s an exa|mple, Fi|
|000028d0| 67 75 72 65 20 31 20 73 | 68 6f 77 73 20 61 20 24 |gure 1 s|hows a $|
|000028e0| 31 32 38 5c 74 69 6d 65 | 73 31 32 38 24 20 73 65 |128\time|s128$ se|
|000028f0| 63 74 69 6f 6e 0a 28 24 | 33 2e 36 5c 74 69 6d 65 |ction.($|3.6\time|
|00002900| 73 33 2e 36 24 7e 61 72 | 63 6d 69 6e 29 20 66 72 |s3.6$~ar|cmin) fr|
|00002910| 6f 6d 20 61 20 64 69 67 | 69 74 69 7a 65 64 20 76 |om a dig|itized v|
|00002920| 65 72 73 69 6f 6e 20 6f | 66 20 74 68 65 20 50 61 |ersion o|f the Pa|
|00002930| 6c 6f 6d 61 72 0a 4f 62 | 73 65 72 76 61 74 6f 72 |lomar.Ob|servator|
|00002940| 79 2d 2d 4e 61 74 69 6f | 6e 61 6c 20 47 65 6f 67 |y--Natio|nal Geog|
|00002950| 72 61 70 68 69 63 20 53 | 6f 63 69 65 74 79 20 53 |raphic S|ociety S|
|00002960| 6b 79 20 53 75 72 76 65 | 79 20 70 6c 61 74 65 0a |ky Surve|y plate.|
|00002970| 63 6f 6e 74 61 69 6e 69 | 6e 67 20 74 68 65 20 43 |containi|ng the C|
|00002980| 6f 6d 61 20 63 6c 75 73 | 74 65 72 20 6f 66 20 67 |oma clus|ter of g|
|00002990| 61 6c 61 78 69 65 73 2e | 0a 46 69 67 75 72 65 73 |alaxies.|.Figures|
|000029a0| 20 32 2c 20 33 2c 20 61 | 6e 64 20 34 20 73 68 6f | 2, 3, a|nd 4 sho|
|000029b0| 77 20 74 68 65 20 72 65 | 73 75 6c 74 69 6e 67 0a |w the re|sulting.|
|000029c0| 69 6d 61 67 65 20 66 6f | 72 20 24 53 20 5c 73 69 |image fo|r $S \si|
|000029d0| 6d 65 71 20 30 2e 35 24 | 2c 20 31 2c 20 61 6e 64 |meq 0.5$|, 1, and|
|000029e0| 20 32 2e 20 20 54 68 65 | 73 65 20 69 6d 61 67 65 | 2. The|se image|
|000029f0| 73 20 61 72 65 20 63 6f | 6d 70 72 65 73 73 65 64 |s are co|mpressed|
|00002a00| 20 62 79 0a 66 61 63 74 | 6f 72 73 20 6f 66 20 31 | by.fact|ors of 1|
|00002a10| 30 2c 20 32 30 2c 20 61 | 6e 64 20 36 30 20 75 73 |0, 20, a|nd 60 us|
|00002a20| 69 6e 67 20 74 68 65 20 | 63 6f 64 69 6e 67 20 73 |ing the |coding s|
|00002a30| 63 68 65 6d 65 20 64 65 | 73 63 72 69 62 65 64 20 |cheme de|scribed |
|00002a40| 62 65 6c 6f 77 2e 20 20 | 0a 49 6e 20 61 6c 6c 20 |below. |.In all |
|00002a50| 63 61 73 65 73 20 61 20 | 6c 6f 67 61 72 69 74 68 |cases a |logarith|
|00002a60| 6d 69 63 20 67 72 61 79 | 20 73 63 61 6c 65 20 69 |mic gray| scale i|
|00002a70| 73 20 75 73 65 64 20 74 | 6f 20 73 68 6f 77 20 74 |s used t|o show t|
|00002a80| 68 65 20 6d 61 78 69 6d | 75 6d 20 64 65 74 61 69 |he maxim|um detai|
|00002a90| 6c 0a 69 6e 20 74 68 65 | 20 69 6d 61 67 65 20 6e |l.in the| image n|
|00002aa0| 65 61 72 20 74 68 65 20 | 73 6b 79 20 62 61 63 6b |ear the |sky back|
|00002ab0| 67 72 6f 75 6e 64 20 6c | 65 76 65 6c 3b 20 74 68 |ground l|evel; th|
|00002ac0| 65 20 6e 6f 69 73 65 20 | 69 73 20 63 6c 65 61 72 |e noise |is clear|
|00002ad0| 6c 79 0a 76 69 73 69 62 | 6c 65 20 69 6e 20 46 69 |ly.visib|le in Fi|
|00002ae0| 67 75 72 65 7e 31 2e 20 | 20 54 68 65 0a 69 6d 61 |gure~1. | The.ima|
|00002af0| 67 65 20 63 6f 6d 70 72 | 65 73 73 65 64 20 62 79 |ge compr|essed by|
|00002b00| 20 61 20 66 61 63 74 6f | 72 20 6f 66 20 31 30 20 | a facto|r of 10 |
|00002b10| 69 73 20 68 61 72 64 6c | 79 20 64 69 73 74 69 6e |is hardl|y distin|
|00002b20| 67 75 69 73 68 61 62 6c | 65 20 66 72 6f 6d 20 74 |guishabl|e from t|
|00002b30| 68 65 0a 6f 72 69 67 69 | 6e 61 6c 2e 20 20 49 6e |he.origi|nal. In|
|00002b40| 20 71 75 61 6e 74 69 7a | 69 6e 67 20 74 68 65 20 | quantiz|ing the |
|00002b50| 5c 68 74 2f 20 77 65 20 | 68 61 76 65 20 61 64 61 |\ht/ we |have ada|
|00002b60| 70 74 69 76 65 6c 79 20 | 66 69 6c 74 65 72 65 64 |ptively |filtered|
|00002b70| 20 74 68 65 0a 6f 72 69 | 67 69 6e 61 6c 20 69 6d | the.ori|ginal im|
|00002b80| 61 67 65 20 62 79 20 64 | 69 73 63 61 72 64 69 6e |age by d|iscardin|
|00002b90| 67 20 69 6e 66 6f 72 6d | 61 74 69 6f 6e 20 6f 6e |g inform|ation on|
|00002ba0| 20 73 6f 6d 65 20 73 63 | 61 6c 65 73 20 61 6e 64 | some sc|ales and|
|00002bb0| 20 6b 65 65 70 69 6e 67 | 0a 69 6e 66 6f 72 6d 61 | keeping|.informa|
|00002bc0| 74 69 6f 6e 20 6f 6e 20 | 6f 74 68 65 72 20 73 63 |tion on |other sc|
|00002bd0| 61 6c 65 73 2e 20 20 54 | 68 69 73 20 61 64 61 70 |ales. T|his adap|
|00002be0| 74 69 76 65 20 66 69 6c | 74 65 72 69 6e 67 20 69 |tive fil|tering i|
|00002bf0| 73 20 6d 6f 73 74 20 61 | 70 70 61 72 65 6e 74 0a |s most a|pparent.|
|00002c00| 66 6f 72 20 68 69 67 68 | 20 63 6f 6d 70 72 65 73 |for high| compres|
|00002c10| 73 69 6f 6e 20 66 61 63 | 74 6f 72 73 20 28 46 69 |sion fac|tors (Fi|
|00002c20| 67 2e 7e 34 29 2c 20 77 | 68 65 72 65 20 74 68 65 |g.~4), w|here the|
|00002c30| 20 73 6b 79 20 68 61 73 | 20 62 65 65 6e 20 73 6d | sky has| been sm|
|00002c40| 6f 6f 74 68 65 64 0a 6f | 76 65 72 20 6c 61 72 67 |oothed.o|ver larg|
|00002c50| 65 20 61 72 65 61 73 20 | 77 68 69 6c 65 20 74 68 |e areas |while th|
|00002c60| 65 20 69 6d 61 67 65 73 | 20 6f 66 20 73 74 61 72 |e images| of star|
|00002c70| 73 20 68 61 76 65 20 68 | 61 72 64 6c 79 20 62 65 |s have h|ardly be|
|00002c80| 65 6e 20 61 66 66 65 63 | 74 65 64 2e 0a 0a 25 5c |en affec|ted...%\|
|00002c90| 74 6f 70 69 6e 73 65 72 | 74 0a 25 5c 74 61 62 73 |topinser|t.%\tabs|
|00002ca0| 6b 69 70 3d 30 70 74 20 | 70 6c 75 73 31 66 69 6c |kip=0pt |plus1fil|
|00002cb0| 0a 25 5c 68 61 6c 69 67 | 6e 20 74 6f 5c 68 73 69 |.%\halig|n to\hsi|
|00002cc0| 7a 65 7b 26 5c 68 62 6f | 78 20 74 6f 33 2e 32 74 |ze{&\hbo|x to3.2t|
|00002cd0| 72 75 65 69 6e 7b 5c 68 | 73 73 20 23 5c 68 73 73 |ruein{\h|ss #\hss|
|00002ce0| 7d 5c 63 72 0a 25 5c 70 | 73 66 69 67 7b 66 69 67 |}\cr.%\p|sfig{fig|
|00002cf0| 75 72 65 3d 6f 72 69 67 | 2e 70 73 2c 77 69 64 74 |ure=orig|.ps,widt|
|00002d00| 68 3d 33 2e 38 74 72 75 | 65 69 6e 7d 26 0a 25 5c |h=3.8tru|ein}&.%\|
|00002d10| 70 73 66 69 67 7b 66 69 | 67 75 72 65 3d 78 31 30 |psfig{fi|gure=x10|
|00002d20| 2e 70 73 2c 77 69 64 74 | 68 3d 33 2e 38 74 72 75 |.ps,widt|h=3.8tru|
|00002d30| 65 69 6e 7d 5c 63 72 0a | 25 7b 5c 73 6d 61 6c 6c |ein}\cr.|%{\small|
|00002d40| 73 6c 20 46 69 67 75 72 | 65 20 31 2e 20 20 4f 72 |sl Figur|e 1. Or|
|00002d50| 69 67 69 6e 61 6c 20 69 | 6d 61 67 65 20 6f 66 20 |iginal i|mage of |
|00002d60| 43 6f 6d 61 20 63 6c 75 | 73 74 65 72 2e 7d 26 0a |Coma clu|ster.}&.|
|00002d70| 25 7b 5c 73 6d 61 6c 6c | 73 6c 20 46 69 67 75 72 |%{\small|sl Figur|
|00002d80| 65 20 32 2e 20 20 52 65 | 73 75 6c 74 20 6f 66 20 |e 2. Re|sult of |
|00002d90| 63 6f 6d 70 72 65 73 73 | 69 6f 6e 20 62 79 20 66 |compress|ion by f|
|00002da0| 61 63 74 6f 72 20 6f 66 | 20 31 30 2e 7d 5c 63 72 |actor of| 10.}\cr|
|00002db0| 0a 25 5c 6e 6f 61 6c 69 | 67 6e 7b 5c 6d 65 64 73 |.%\noali|gn{\meds|
|00002dc0| 6b 69 70 7d 0a 25 5c 70 | 73 66 69 67 7b 66 69 67 |kip}.%\p|sfig{fig|
|00002dd0| 75 72 65 3d 78 32 30 2e | 70 73 2c 77 69 64 74 68 |ure=x20.|ps,width|
|00002de0| 3d 33 2e 38 74 72 75 65 | 69 6e 7d 26 0a 25 5c 70 |=3.8true|in}&.%\p|
|00002df0| 73 66 69 67 7b 66 69 67 | 75 72 65 3d 78 35 30 2e |sfig{fig|ure=x50.|
|00002e00| 70 73 2c 77 69 64 74 68 | 3d 33 2e 38 74 72 75 65 |ps,width|=3.8true|
|00002e10| 69 6e 7d 5c 63 72 0a 25 | 7b 5c 73 6d 61 6c 6c 73 |in}\cr.%|{\smalls|
|00002e20| 6c 20 46 69 67 75 72 65 | 20 33 2e 20 20 52 65 73 |l Figure| 3. Res|
|00002e30| 75 6c 74 20 6f 66 20 63 | 6f 6d 70 72 65 73 73 69 |ult of c|ompressi|
|00002e40| 6f 6e 20 62 79 20 66 61 | 63 74 6f 72 20 6f 66 20 |on by fa|ctor of |
|00002e50| 32 30 2e 7d 26 0a 25 7b | 5c 73 6d 61 6c 6c 73 6c |20.}&.%{|\smallsl|
|00002e60| 20 46 69 67 75 72 65 20 | 34 2e 20 20 52 65 73 75 | Figure |4. Resu|
|00002e70| 6c 74 20 6f 66 20 63 6f | 6d 70 72 65 73 73 69 6f |lt of co|mpressio|
|00002e80| 6e 20 62 79 20 66 61 63 | 74 6f 72 20 6f 66 20 36 |n by fac|tor of 6|
|00002e90| 30 2e 7d 5c 63 72 0a 25 | 7d 0a 25 5c 65 6e 64 69 |0.}\cr.%|}.%\endi|
|00002ea0| 6e 73 65 72 74 0a 0a 54 | 68 65 20 61 64 61 70 74 |nsert..T|he adapt|
|00002eb0| 69 76 65 20 66 69 6c 74 | 65 72 69 6e 67 20 69 73 |ive filt|ering is|
|00002ec0| 2c 20 69 6e 20 69 74 73 | 65 6c 66 2c 20 6f 66 20 |, in its|elf, of |
|00002ed0| 63 6f 6e 73 69 64 65 72 | 61 62 6c 65 20 69 6e 74 |consider|able int|
|00002ee0| 65 72 65 73 74 20 61 73 | 20 61 6e 0a 61 6e 61 6c |erest as| an.anal|
|00002ef0| 79 74 69 63 61 6c 20 74 | 6f 6f 6c 20 66 6f 72 20 |ytical t|ool for |
|00002f00| 69 6d 61 67 65 73 20 28 | 43 61 70 61 63 63 69 6f |images (|Capaccio|
|00002f10| 6c 69 20 5c 65 74 61 6c | 5c 20 31 39 38 38 29 2e |li \etal|\ 1988).|
|00002f20| 20 20 46 6f 72 20 65 78 | 61 6d 70 6c 65 2c 20 6f | For ex|ample, o|
|00002f30| 6e 65 0a 63 61 6e 20 75 | 73 65 20 74 68 65 20 61 |ne.can u|se the a|
|00002f40| 64 61 70 74 69 76 65 20 | 73 6d 6f 6f 74 68 69 6e |daptive |smoothin|
|00002f50| 67 20 6f 66 20 74 68 65 | 20 5c 68 74 2f 20 74 6f |g of the| \ht/ to|
|00002f60| 20 73 6d 6f 6f 74 68 20 | 74 68 65 20 73 6b 79 20 | smooth |the sky |
|00002f70| 77 69 74 68 6f 75 74 0a | 61 66 66 65 63 74 69 6e |without.|affectin|
|00002f80| 67 20 6f 62 6a 65 63 74 | 73 20 64 65 74 65 63 74 |g object|s detect|
|00002f90| 65 64 20 61 62 6f 76 65 | 20 74 68 65 20 28 6c 6f |ed above| the (lo|
|00002fa0| 63 61 6c 6c 79 20 64 65 | 74 65 72 6d 69 6e 65 64 |cally de|termined|
|00002fb0| 29 20 73 6b 79 3b 20 74 | 68 65 6e 20 61 6e 0a 61 |) sky; t|hen an.a|
|00002fc0| 63 63 75 72 61 74 65 20 | 73 6b 79 20 76 61 6c 75 |ccurate |sky valu|
|00002fd0| 65 20 63 61 6e 20 62 65 | 20 64 65 74 65 72 6d 69 |e can be| determi|
|00002fe0| 6e 65 64 20 62 79 20 72 | 65 66 65 72 65 6e 63 65 |ned by r|eference|
|00002ff0| 20 74 6f 20 61 6e 79 20 | 6e 65 61 72 62 79 20 70 | to any |nearby p|
|00003000| 69 78 65 6c 2e 0a 0a 54 | 68 65 20 62 6c 6f 63 6b |ixel...T|he block|
|00003010| 69 6e 65 73 73 20 74 68 | 61 74 20 69 73 20 76 69 |iness th|at is vi|
|00003020| 73 69 62 6c 65 20 69 6e | 20 46 69 67 75 72 65 7e |sible in| Figure~|
|00003030| 34 20 69 73 20 74 68 65 | 20 72 65 73 75 6c 74 20 |4 is the| result |
|00003040| 6f 66 20 64 69 66 66 65 | 72 65 6e 63 65 0a 63 6f |of diffe|rence.co|
|00003050| 65 66 66 69 63 69 65 6e | 74 73 20 62 65 69 6e 67 |efficien|ts being|
|00003060| 20 73 65 74 20 74 6f 20 | 7a 65 72 6f 20 6f 76 65 | set to |zero ove|
|00003070| 72 20 6c 61 72 67 65 20 | 61 72 65 61 73 2c 20 73 |r large |areas, s|
|00003080| 6f 20 74 68 61 74 20 62 | 6c 6f 63 6b 73 20 6f 66 |o that b|locks of|
|00003090| 0a 70 69 78 65 6c 73 20 | 61 72 65 20 72 65 70 6c |.pixels |are repl|
|000030a0| 61 63 65 64 20 62 79 20 | 74 68 65 69 72 20 61 76 |aced by |their av|
|000030b0| 65 72 61 67 65 73 2e 20 | 20 49 74 20 69 73 20 70 |erages. | It is p|
|000030c0| 6f 73 73 69 62 6c 65 20 | 74 6f 20 65 6c 69 6d 69 |ossible |to elimi|
|000030d0| 6e 61 74 65 20 74 68 65 | 0a 62 6c 6f 63 6b 73 20 |nate the|.blocks |
|000030e0| 62 79 20 61 6e 20 61 70 | 70 72 6f 70 72 69 61 74 |by an ap|propriat|
|000030f0| 65 20 66 69 6c 74 65 72 | 69 6e 67 20 6f 66 20 74 |e filter|ing of t|
|00003100| 68 65 20 69 6d 61 67 65 | 2e 20 20 41 20 73 69 6d |he image|. A sim|
|00003110| 70 6c 65 20 62 75 74 0a | 65 66 66 65 63 74 69 76 |ple but.|effectiv|
|00003120| 65 20 66 69 6c 74 65 72 | 20 63 61 6e 20 62 65 20 |e filter| can be |
|00003130| 64 65 72 69 76 65 64 20 | 62 79 20 73 69 6d 70 6c |derived |by simpl|
|00003140| 79 20 61 64 6a 75 73 74 | 69 6e 67 20 74 68 65 20 |y adjust|ing the |
|00003150| 5c 68 74 2f 0a 63 6f 65 | 66 66 69 63 69 65 6e 74 |\ht/.coe|fficient|
|00003160| 73 20 61 73 20 74 68 65 | 20 74 72 61 6e 73 66 6f |s as the| transfo|
|00003170| 72 6d 20 69 73 20 69 6e | 76 65 72 74 65 64 20 74 |rm is in|verted t|
|00003180| 6f 20 70 72 6f 64 75 63 | 65 20 61 20 73 6d 6f 6f |o produc|e a smoo|
|00003190| 74 68 20 69 6d 61 67 65 | 3b 0a 61 73 20 6c 6f 6e |th image|;.as lon|
|000031a0| 67 20 61 73 20 63 68 61 | 6e 67 65 73 20 69 6e 20 |g as cha|nges in |
|000031b0| 74 68 65 20 63 6f 65 66 | 66 69 63 69 65 6e 74 73 |the coef|ficients|
|000031c0| 20 61 72 65 20 6c 69 6d | 69 74 65 64 20 74 6f 20 | are lim|ited to |
|000031d0| 24 5c 70 6d 20 53 5c 73 | 69 67 6d 61 2f 32 24 2c |$\pm S\s|igma/2$,|
|000031e0| 0a 74 68 65 20 72 65 73 | 75 6c 74 69 6e 67 20 69 |.the res|ulting i|
|000031f0| 6d 61 67 65 20 77 69 6c | 6c 20 73 74 69 6c 6c 20 |mage wil|l still |
|00003200| 62 65 20 63 6f 6e 73 69 | 73 74 65 6e 74 20 77 69 |be consi|stent wi|
|00003210| 74 68 20 74 68 65 20 74 | 68 72 65 73 68 6f 6c 64 |th the t|hreshold|
|00003220| 65 64 0a 5c 68 74 2f 2e | 0a 0a 5c 73 65 63 74 69 |ed.\ht/.|..\secti|
|00003230| 6f 6e 20 34 2e 20 45 66 | 66 69 63 69 65 6e 74 20 |on 4. Ef|ficient |
|00003240| 43 6f 64 69 6e 67 0a 0a | 54 68 65 20 71 75 61 6e |Coding..|The quan|
|00003250| 74 69 7a 65 64 20 5c 68 | 74 2f 20 68 61 73 20 61 |tized \h|t/ has a|
|00003260| 20 72 61 74 68 65 72 20 | 70 65 63 75 6c 69 61 72 | rather |peculiar|
|00003270| 20 73 74 72 75 63 74 75 | 72 65 2e 20 20 4e 6f 74 | structu|re. Not|
|00003280| 20 6f 6e 6c 79 20 61 72 | 65 20 6c 61 72 67 65 0a | only ar|e large.|
|00003290| 61 72 65 61 73 20 6f 66 | 20 74 68 65 20 74 72 61 |areas of| the tra|
|000032a0| 6e 73 66 6f 72 6d 20 69 | 6d 61 67 65 20 7a 65 72 |nsform i|mage zer|
|000032b0| 6f 2c 20 62 75 74 20 74 | 68 65 20 6e 6f 6e 2d 7a |o, but t|he non-z|
|000032c0| 65 72 6f 20 76 61 6c 75 | 65 73 20 61 72 65 20 73 |ero valu|es are s|
|000032d0| 74 72 6f 6e 67 6c 79 0a | 63 6f 6e 63 65 6e 74 72 |trongly.|concentr|
|000032e0| 61 74 65 64 20 69 6e 20 | 74 68 65 20 6c 6f 77 65 |ated in |the lowe|
|000032f0| 72 2d 6f 72 64 65 72 20 | 63 6f 65 66 66 69 63 69 |r-order |coeffici|
|00003300| 65 6e 74 73 2e 20 20 54 | 68 65 20 62 65 73 74 20 |ents. T|he best |
|00003310| 61 70 70 72 6f 61 63 68 | 20 77 65 0a 68 61 76 65 |approach| we.have|
|00003320| 20 66 6f 75 6e 64 20 74 | 6f 20 63 6f 64 65 20 74 | found t|o code t|
|00003330| 68 65 20 63 6f 65 66 66 | 69 63 69 65 6e 74 20 76 |he coeff|icient v|
|00003340| 61 6c 75 65 73 20 65 66 | 66 69 63 69 65 6e 74 6c |alues ef|ficientl|
|00003350| 79 20 69 73 20 71 75 61 | 64 74 72 65 65 0a 63 6f |y is qua|dtree.co|
|00003360| 64 69 6e 67 20 6f 66 20 | 65 61 63 68 20 62 69 74 |ding of |each bit|
|00003370| 70 6c 61 6e 65 20 6f 66 | 20 74 68 65 20 74 72 61 |plane of| the tra|
|00003380| 6e 73 66 6f 72 6d 20 61 | 72 72 61 79 2e 20 20 51 |nsform a|rray. Q|
|00003390| 75 61 64 74 72 65 65 20 | 63 6f 64 69 6e 67 20 68 |uadtree |coding h|
|000033a0| 61 73 0a 62 65 65 6e 20 | 75 73 65 64 20 66 6f 72 |as.been |used for|
|000033b0| 20 6d 61 6e 79 20 70 75 | 72 70 6f 73 65 73 20 28 | many pu|rposes (|
|000033c0| 73 65 65 20 53 61 6d 65 | 74 20 31 39 38 34 20 66 |see Same|t 1984 f|
|000033d0| 6f 72 20 61 20 72 65 76 | 69 65 77 29 3b 20 74 68 |or a rev|iew); th|
|000033e0| 65 0a 70 61 72 74 69 63 | 75 6c 61 72 20 66 6f 72 |e.partic|ular for|
|000033f0| 6d 20 77 65 20 61 72 65 | 20 75 73 69 6e 67 20 77 |m we are| using w|
|00003400| 61 73 20 73 75 67 67 65 | 73 74 65 64 20 62 79 20 |as sugge|sted by |
|00003410| 48 75 61 6e 67 20 61 6e | 64 20 42 69 6a 61 6f 75 |Huang an|d Bijaou|
|00003420| 69 20 28 31 39 39 31 29 | 0a 66 6f 72 20 69 6d 61 |i (1991)|.for ima|
|00003430| 67 65 20 63 6f 6d 70 72 | 65 73 73 69 6f 6e 2e 0a |ge compr|ession..|
|00003440| 0a 5c 6d 65 64 73 6b 69 | 70 0a 5c 62 75 6c 6c 61 |.\medski|p.\bulla|
|00003450| 20 44 69 76 69 64 65 20 | 74 68 65 20 62 69 74 70 | Divide |the bitp|
|00003460| 6c 61 6e 65 20 75 70 20 | 69 6e 74 6f 20 34 20 71 |lane up |into 4 q|
|00003470| 75 61 64 72 61 6e 74 73 | 2e 20 20 46 6f 72 20 65 |uadrants|. For e|
|00003480| 61 63 68 20 71 75 61 64 | 72 61 6e 74 20 63 6f 64 |ach quad|rant cod|
|00003490| 65 0a 61 20 60 31 27 20 | 69 66 20 74 68 65 72 65 |e.a `1' |if there|
|000034a0| 20 61 72 65 20 61 6e 79 | 20 31 2d 62 69 74 73 20 | are any| 1-bits |
|000034b0| 69 6e 20 74 68 65 20 71 | 75 61 64 72 61 6e 74 2c |in the q|uadrant,|
|000034c0| 20 65 6c 73 65 20 63 6f | 64 65 20 61 20 60 30 27 | else co|de a `0'|
|000034d0| 2e 0a 0a 5c 62 75 6c 6c | 61 20 53 75 62 64 69 76 |...\bull|a Subdiv|
|000034e0| 69 64 65 20 65 61 63 68 | 20 71 75 61 64 72 61 6e |ide each| quadran|
|000034f0| 74 20 74 68 61 74 20 69 | 73 20 6e 6f 74 20 61 6c |t that i|s not al|
|00003500| 6c 20 7a 65 72 6f 20 69 | 6e 74 6f 20 34 20 6d 6f |l zero i|nto 4 mo|
|00003510| 72 65 20 70 69 65 63 65 | 73 0a 61 6e 64 20 63 6f |re piece|s.and co|
|00003520| 64 65 20 74 68 65 6d 20 | 73 69 6d 69 6c 61 72 6c |de them |similarl|
|00003530| 79 2e 20 20 43 6f 6e 74 | 69 6e 75 65 20 75 6e 74 |y. Cont|inue unt|
|00003540| 69 6c 20 6f 6e 65 20 69 | 73 20 64 6f 77 6e 20 74 |il one i|s down t|
|00003550| 6f 20 74 68 65 20 6c 65 | 76 65 6c 20 6f 66 0a 69 |o the le|vel of.i|
|00003560| 6e 64 69 76 69 64 75 61 | 6c 20 70 69 78 65 6c 73 |ndividua|l pixels|
|00003570| 2e 0a 0a 5c 6d 65 64 73 | 6b 69 70 0a 5c 6e 6f 69 |...\meds|kip.\noi|
|00003580| 6e 64 65 6e 74 0a 54 68 | 69 73 20 63 6f 64 69 6e |ndent.Th|is codin|
|00003590| 67 20 28 77 68 69 63 68 | 20 48 75 61 6e 67 20 61 |g (which| Huang a|
|000035a0| 6e 64 20 42 69 6a 61 75 | 6f 69 20 63 61 6c 6c 20 |nd Bijau|oi call |
|000035b0| 60 60 68 69 65 72 61 72 | 63 68 69 63 20 34 2d 62 |``hierar|chic 4-b|
|000035c0| 69 74 20 6f 6e 65 27 27 | 0a 63 6f 64 69 6e 67 29 |it one''|.coding)|
|000035d0| 20 69 73 20 6f 62 76 69 | 6f 75 73 6c 79 20 76 65 | is obvi|ously ve|
|000035e0| 72 79 20 77 65 6c 6c 20 | 73 75 69 74 65 64 20 74 |ry well |suited t|
|000035f0| 6f 20 74 68 65 20 5c 68 | 74 2f 20 69 6d 61 67 65 |o the \h|t/ image|
|00003600| 20 62 65 63 61 75 73 65 | 0a 73 75 63 63 65 73 73 | because|.success|
|00003610| 69 76 65 6c 79 20 6c 6f | 77 65 72 20 6f 72 64 65 |ively lo|wer orde|
|00003620| 72 73 20 6f 66 20 74 68 | 65 20 5c 68 74 2f 20 63 |rs of th|e \ht/ c|
|00003630| 6f 65 66 66 69 63 69 65 | 6e 74 73 20 61 72 65 20 |oefficie|nts are |
|00003640| 6c 6f 63 61 74 65 64 20 | 69 6e 0a 73 75 63 63 65 |located |in.succe|
|00003650| 73 73 69 76 65 6c 79 20 | 64 69 76 69 64 65 64 20 |ssively |divided |
|00003660| 71 75 61 64 72 61 6e 74 | 73 20 6f 66 20 74 68 65 |quadrant|s of the|
|00003670| 20 69 6d 61 67 65 2e 0a | 0a 57 65 20 66 6f 6c 6c | image..|.We foll|
|00003680| 6f 77 20 74 68 65 20 71 | 75 61 64 74 72 65 65 20 |ow the q|uadtree |
|00003690| 63 6f 64 69 6e 67 20 77 | 69 74 68 20 61 20 66 69 |coding w|ith a fi|
|000036a0| 78 65 64 20 48 75 66 66 | 6d 61 6e 20 63 6f 64 69 |xed Huff|man codi|
|000036b0| 6e 67 20 74 68 61 74 20 | 75 73 65 73 20 33 0a 62 |ng that |uses 3.b|
|000036c0| 69 74 73 20 66 6f 72 20 | 71 75 61 64 74 72 65 65 |its for |quadtree|
|000036d0| 20 76 61 6c 75 65 73 20 | 74 68 61 74 20 61 72 65 | values |that are|
|000036e0| 20 63 6f 6d 6d 6f 6e 20 | 28 5c 65 67 20 30 30 30 | common |(\eg 000|
|000036f0| 31 2c 20 30 30 31 30 2c | 20 30 31 30 30 2c 20 61 |1, 0010,| 0100, a|
|00003700| 6e 64 0a 31 30 30 30 29 | 20 61 6e 64 20 75 73 65 |nd.1000)| and use|
|00003710| 73 20 34 20 6f 72 20 35 | 20 62 69 74 73 20 66 6f |s 4 or 5| bits fo|
|00003720| 72 20 6c 65 73 73 20 63 | 6f 6d 6d 6f 6e 20 76 61 |r less c|ommon va|
|00003730| 6c 75 65 73 2e 20 20 54 | 68 69 73 20 72 65 64 75 |lues. T|his redu|
|00003740| 63 65 73 20 74 68 65 0a | 66 69 6e 61 6c 20 63 6f |ces the.|final co|
|00003750| 6d 70 72 65 73 73 65 64 | 20 66 69 6c 65 20 73 69 |mpressed| file si|
|00003760| 7a 65 20 62 79 20 61 62 | 6f 75 74 20 31 30 5c 25 |ze by ab|out 10\%|
|00003770| 20 61 74 20 6c 69 74 74 | 6c 65 20 63 6f 6d 70 75 | at litt|le compu|
|00003780| 74 61 74 69 6f 6e 61 6c | 20 63 6f 73 74 2e 0a 53 |tational| cost..S|
|00003790| 6c 69 67 68 74 6c 79 20 | 62 65 74 74 65 72 20 63 |lightly |better c|
|000037a0| 6f 6d 70 72 65 73 73 69 | 6f 6e 20 63 61 6e 20 62 |ompressi|on can b|
|000037b0| 65 20 61 63 68 69 65 76 | 65 64 20 62 79 20 66 6f |e achiev|ed by fo|
|000037c0| 6c 6c 6f 77 69 6e 67 20 | 71 75 61 64 74 72 65 65 |llowing |quadtree|
|000037d0| 0a 63 6f 64 69 6e 67 20 | 77 69 74 68 20 61 72 69 |.coding |with ari|
|000037e0| 74 68 6d 65 74 69 63 20 | 63 6f 64 69 6e 67 20 28 |thmetic |coding (|
|000037f0| 57 69 74 74 65 6e 2c 20 | 42 65 6c 6c 2c 20 61 6e |Witten, |Bell, an|
|00003800| 64 20 43 6c 65 61 72 79 | 20 31 39 38 37 29 2c 20 |d Cleary| 1987), |
|00003810| 62 75 74 20 74 68 65 0a | 43 50 55 20 63 6f 73 74 |but the.|CPU cost|
|00003820| 73 20 6f 66 20 61 72 69 | 74 68 6d 65 74 69 63 20 |s of ari|thmetic |
|00003830| 63 6f 64 69 6e 67 20 61 | 72 65 20 6e 6f 74 2c 20 |coding a|re not, |
|00003840| 69 6e 20 6f 75 72 20 76 | 69 65 77 2c 20 6a 75 73 |in our v|iew, jus|
|00003850| 74 69 66 69 65 64 20 66 | 6f 72 0a 33 2d 2d 34 5c |tified f|or.3--4\|
|00003860| 25 20 62 65 74 74 65 72 | 20 63 6f 6d 70 72 65 73 |% better| compres|
|00003870| 73 69 6f 6e 2e 20 20 57 | 65 20 68 61 76 65 20 61 |sion. W|e have a|
|00003880| 6c 73 6f 20 74 72 69 65 | 64 20 75 73 69 6e 67 20 |lso trie|d using |
|00003890| 61 72 69 74 68 6d 65 74 | 69 63 20 63 6f 64 69 6e |arithmet|ic codin|
|000038a0| 67 0a 64 69 72 65 63 74 | 6c 79 20 6f 6e 20 74 68 |g.direct|ly on th|
|000038b0| 65 20 5c 68 74 2f 2c 0a | 77 69 74 68 20 76 61 72 |e \ht/,.|with var|
|000038c0| 69 6f 75 73 20 63 6f 6e | 74 65 78 74 73 20 6f 66 |ious con|texts of|
|000038d0| 20 6e 65 69 67 68 62 6f | 72 69 6e 67 20 70 69 78 | neighbo|ring pix|
|000038e0| 65 6c 73 2c 20 62 75 74 | 20 66 69 6e 64 20 69 74 |els, but| find it|
|000038f0| 20 74 6f 20 62 65 0a 62 | 6f 74 68 20 63 6f 6d 70 | to be.b|oth comp|
|00003900| 75 74 61 74 69 6f 6e 61 | 6c 6c 79 20 69 6e 65 66 |utationa|lly inef|
|00003910| 66 69 63 69 65 6e 74 20 | 61 6e 64 20 6e 6f 74 20 |ficient |and not |
|00003920| 73 69 67 6e 69 66 69 63 | 61 6e 74 6c 79 20 62 65 |signific|antly be|
|00003930| 74 74 65 72 20 74 68 61 | 6e 0a 71 75 61 64 74 72 |tter tha|n.quadtr|
|00003940| 65 65 20 63 6f 64 69 6e | 67 2e 0a 0a 46 6f 72 20 |ee codin|g...For |
|00003950| 63 6f 6d 70 6c 65 74 65 | 6c 79 20 72 61 6e 64 6f |complete|ly rando|
|00003960| 6d 20 62 69 74 70 6c 61 | 6e 65 73 2c 20 71 75 61 |m bitpla|nes, qua|
|00003970| 64 74 72 65 65 20 63 6f | 64 69 6e 67 20 63 61 6e |dtree co|ding can|
|00003980| 20 61 63 74 75 61 6c 6c | 79 20 75 73 65 20 6d 6f | actuall|y use mo|
|00003990| 72 65 0a 73 74 6f 72 61 | 67 65 20 74 68 61 6e 20 |re.stora|ge than |
|000039a0| 73 69 6d 70 6c 79 20 77 | 72 69 74 69 6e 67 20 74 |simply w|riting t|
|000039b0| 68 65 20 62 69 74 70 6c | 61 6e 65 20 64 69 72 65 |he bitpl|ane dire|
|000039c0| 63 74 6c 79 3b 20 69 6e | 20 74 68 61 74 20 63 61 |ctly; in| that ca|
|000039d0| 73 65 20 77 65 0a 6a 75 | 73 74 20 64 75 6d 70 20 |se we.ju|st dump |
|000039e0| 74 68 65 20 62 69 74 70 | 6c 61 6e 65 20 77 69 74 |the bitp|lane wit|
|000039f0| 68 20 6e 6f 20 63 6f 64 | 69 6e 67 2e 0a 0a 4e 6f |h no cod|ing...No|
|00003a00| 74 65 20 74 68 61 74 20 | 62 79 20 63 6f 64 69 6e |te that |by codin|
|00003a10| 67 20 74 68 65 20 74 72 | 61 6e 73 66 6f 72 6d 20 |g the tr|ansform |
|00003a20| 6f 6e 65 20 62 69 74 70 | 6c 61 6e 65 20 61 74 20 |one bitp|lane at |
|00003a30| 61 20 74 69 6d 65 2c 20 | 74 68 65 20 63 6f 6d 70 |a time, |the comp|
|00003a40| 72 65 73 73 65 64 0a 64 | 61 74 61 20 63 61 6e 20 |ressed.d|ata can |
|00003a50| 62 65 20 76 69 65 77 65 | 64 20 61 73 20 61 6e 20 |be viewe|d as an |
|00003a60| 69 6e 63 72 65 6d 65 6e | 74 61 6c 20 64 65 73 63 |incremen|tal desc|
|00003a70| 72 69 70 74 69 6f 6e 20 | 6f 66 20 74 68 65 20 69 |ription |of the i|
|00003a80| 6d 61 67 65 2e 20 20 4f | 6e 65 20 63 61 6e 0a 69 |mage. O|ne can.i|
|00003a90| 6e 69 74 69 61 6c 6c 79 | 20 74 72 61 6e 73 6d 69 |nitially| transmi|
|00003aa0| 74 20 61 20 63 72 75 64 | 65 20 72 65 70 72 65 73 |t a crud|e repres|
|00003ab0| 65 6e 74 61 74 69 6f 6e | 20 6f 66 20 74 68 65 20 |entation| of the |
|00003ac0| 69 6d 61 67 65 20 75 73 | 69 6e 67 20 6f 6e 6c 79 |image us|ing only|
|00003ad0| 20 74 68 65 0a 73 6d 61 | 6c 6c 20 61 6d 6f 75 6e | the.sma|ll amoun|
|00003ae0| 74 20 6f 66 20 64 61 74 | 61 20 74 68 61 74 20 69 |t of dat|a that i|
|00003af0| 73 20 72 65 71 75 69 72 | 65 64 20 66 6f 72 20 74 |s requir|ed for t|
|00003b00| 68 65 20 73 70 61 72 73 | 65 6c 79 20 70 6f 70 75 |he spars|ely popu|
|00003b10| 6c 61 74 65 64 2c 20 6d | 6f 73 74 0a 73 69 67 6e |lated, m|ost.sign|
|00003b20| 69 66 69 63 61 6e 74 20 | 62 69 74 20 70 6c 61 6e |ificant |bit plan|
|00003b30| 65 73 2e 20 20 54 68 65 | 6e 20 74 68 65 20 6c 6f |es. The|n the lo|
|00003b40| 77 65 72 20 62 69 74 20 | 70 6c 61 6e 65 73 20 63 |wer bit |planes c|
|00003b50| 61 6e 20 62 65 20 61 64 | 64 65 64 20 6f 6e 65 20 |an be ad|ded one |
|00003b60| 62 79 0a 6f 6e 65 20 75 | 6e 74 69 6c 20 74 68 65 |by.one u|ntil the|
|00003b70| 20 64 65 73 69 72 65 64 | 20 61 63 63 75 72 61 63 | desired| accurac|
|00003b80| 79 20 69 73 20 72 65 71 | 75 69 72 65 64 2e 20 20 |y is req|uired. |
|00003b90| 54 68 69 73 20 63 6f 75 | 6c 64 20 62 65 20 75 73 |This cou|ld be us|
|00003ba0| 65 66 75 6c 2c 20 66 6f | 72 0a 65 78 61 6d 70 6c |eful, fo|r.exampl|
|00003bb0| 65 2c 20 69 66 20 74 68 | 65 20 64 61 74 61 20 69 |e, if th|e data i|
|00003bc0| 73 20 74 6f 20 62 65 20 | 72 65 74 72 69 65 76 65 |s to be |retrieve|
|00003bd0| 64 20 66 72 6f 6d 20 61 | 20 72 65 6d 6f 74 65 20 |d from a| remote |
|00003be0| 64 61 74 61 62 61 73 65 | 20 2d 2d 2d 20 6f 6e 65 |database| --- one|
|00003bf0| 0a 63 6f 75 6c 64 20 65 | 78 61 6d 69 6e 65 20 74 |.could e|xamine t|
|00003c00| 68 65 20 63 72 75 64 65 | 20 76 65 72 73 69 6f 6e |he crude| version|
|00003c10| 20 6f 66 20 74 68 65 20 | 69 6d 61 67 65 20 28 72 | of the |image (r|
|00003c20| 65 74 72 69 65 76 65 64 | 20 76 65 72 79 20 71 75 |etrieved| very qu|
|00003c30| 69 63 6b 6c 79 29 0a 61 | 6e 64 20 61 62 6f 72 74 |ickly).a|nd abort|
|00003c40| 20 74 68 65 20 74 72 61 | 6e 73 6d 69 73 73 69 6f | the tra|nsmissio|
|00003c50| 6e 20 6f 66 20 74 68 65 | 20 72 65 73 74 20 6f 66 |n of the| rest of|
|00003c60| 20 74 68 65 20 64 61 74 | 61 20 69 66 20 74 68 65 | the dat|a if the|
|00003c70| 20 69 6d 61 67 65 20 69 | 73 0a 6a 75 64 67 65 64 | image i|s.judged|
|00003c80| 20 74 6f 20 62 65 20 75 | 6e 69 6e 74 65 72 65 73 | to be u|ninteres|
|00003c90| 74 69 6e 67 2e 0a 0a 5c | 73 65 63 74 69 6f 6e 20 |ting...\|section |
|00003ca0| 35 2e 20 41 73 74 72 6f | 6d 65 74 72 69 63 20 61 |5. Astro|metric a|
|00003cb0| 6e 64 20 50 68 6f 74 6f | 6d 65 74 72 69 63 20 50 |nd Photo|metric P|
|00003cc0| 72 6f 70 65 72 74 69 65 | 73 20 6f 66 20 43 6f 6d |ropertie|s of Com|
|00003cd0| 70 72 65 73 73 65 64 20 | 49 6d 61 67 65 73 0a 0a |pressed |Images..|
|00003ce0| 41 73 74 72 6f 6e 6f 6d | 69 63 61 6c 20 69 6d 61 |Astronom|ical ima|
|00003cf0| 67 65 73 20 61 72 65 20 | 6e 6f 74 20 73 69 6d 70 |ges are |not simp|
|00003d00| 6c 79 20 73 75 62 6a 65 | 63 74 65 64 20 74 6f 20 |ly subje|cted to |
|00003d10| 76 69 73 75 61 6c 20 65 | 78 61 6d 69 6e 61 74 69 |visual e|xaminati|
|00003d20| 6f 6e 2c 0a 62 75 74 20 | 61 72 65 20 61 6c 73 6f |on,.but |are also|
|00003d30| 20 73 75 62 6a 65 63 74 | 65 64 20 74 6f 20 63 61 | subject|ed to ca|
|00003d40| 72 65 66 75 6c 20 71 75 | 61 6e 74 69 74 61 74 69 |reful qu|antitati|
|00003d50| 76 65 20 61 6e 61 6c 79 | 73 69 73 2e 20 20 46 6f |ve analy|sis. Fo|
|00003d60| 72 20 65 78 61 6d 70 6c | 65 2c 0a 66 6f 72 20 74 |r exampl|e,.for t|
|00003d70| 68 65 20 69 6d 61 67 65 | 20 69 6e 20 46 69 67 75 |he image| in Figu|
|00003d80| 72 65 7e 31 20 6f 6e 65 | 20 77 6f 75 6c 64 20 74 |re~1 one| would t|
|00003d90| 79 70 69 63 61 6c 6c 79 | 20 6c 69 6b 65 20 74 6f |ypically| like to|
|00003da0| 20 64 6f 20 61 73 74 72 | 6f 6d 65 74 72 69 63 0a | do astr|ometric.|
|00003db0| 28 70 6f 73 69 74 69 6f | 6e 61 6c 29 20 6d 65 61 |(positio|nal) mea|
|00003dc0| 73 75 72 65 6d 65 6e 74 | 73 20 6f 66 20 6f 62 6a |surement|s of obj|
|00003dd0| 65 63 74 73 20 74 6f 20 | 61 6e 20 61 63 63 75 72 |ects to |an accur|
|00003de0| 61 63 79 20 6d 75 63 68 | 20 62 65 74 74 65 72 20 |acy much| better |
|00003df0| 74 68 61 6e 0a 31 20 70 | 69 78 65 6c 2c 20 70 68 |than.1 p|ixel, ph|
|00003e00| 6f 74 6f 6d 65 74 72 69 | 63 20 28 62 72 69 67 68 |otometri|c (brigh|
|00003e10| 74 6e 65 73 73 29 20 6d | 65 61 73 75 72 65 6d 65 |tness) m|easureme|
|00003e20| 6e 74 73 20 6f 66 20 6f | 62 6a 65 63 74 73 20 74 |nts of o|bjects t|
|00003e30| 6f 20 61 6e 20 61 63 63 | 75 72 61 63 79 0a 6c 69 |o an acc|uracy.li|
|00003e40| 6d 69 74 65 64 20 6f 6e | 6c 79 20 62 79 20 74 68 |mited on|ly by th|
|00003e50| 65 20 64 65 74 65 63 74 | 6f 72 20 72 65 73 70 6f |e detect|or respo|
|00003e60| 6e 73 65 20 61 6e 64 20 | 74 68 65 20 6e 6f 69 73 |nse and |the nois|
|00003e70| 65 2c 20 61 6e 64 20 61 | 63 63 75 72 61 74 65 0a |e, and a|ccurate.|
|00003e80| 6d 65 61 73 75 72 65 6d | 65 6e 74 73 20 6f 66 20 |measurem|ents of |
|00003e90| 74 68 65 20 73 75 72 66 | 61 63 65 20 62 72 69 67 |the surf|ace brig|
|00003ea0| 68 74 6e 65 73 73 20 6f | 66 20 65 78 74 65 6e 64 |htness o|f extend|
|00003eb0| 65 64 20 73 6f 75 72 63 | 65 73 2e 0a 0a 57 65 20 |ed sourc|es...We |
|00003ec0| 68 61 76 65 20 64 6f 6e | 65 20 73 6f 6d 65 20 65 |have don|e some e|
|00003ed0| 78 70 65 72 69 6d 65 6e | 74 73 20 74 6f 20 73 74 |xperimen|ts to st|
|00003ee0| 75 64 79 20 74 68 65 20 | 64 65 67 72 61 64 61 74 |udy the |degradat|
|00003ef0| 69 6f 6e 20 6f 66 20 61 | 73 74 72 6f 6d 65 74 72 |ion of a|strometr|
|00003f00| 79 20 61 6e 64 0a 70 68 | 6f 74 6f 6d 65 74 72 79 |y and.ph|otometry|
|00003f10| 20 6f 6e 20 74 68 65 20 | 63 6f 6d 70 72 65 73 73 | on the |compress|
|00003f20| 65 64 20 69 6d 61 67 65 | 73 20 63 6f 6d 70 61 72 |ed image|s compar|
|00003f30| 65 64 20 74 6f 20 74 68 | 65 20 6f 72 69 67 69 6e |ed to th|e origin|
|00003f40| 61 6c 20 69 6d 61 67 65 | 73 20 28 57 68 69 74 65 |al image|s (White|
|00003f50| 2c 0a 50 6f 73 74 6d 61 | 6e 2c 20 61 6e 64 20 4c |,.Postma|n, and L|
|00003f60| 61 74 74 61 6e 7a 69 20 | 31 39 39 31 29 2e 20 20 |attanzi |1991). |
|00003f70| 45 76 65 6e 20 74 68 65 | 20 6d 6f 73 74 20 68 69 |Even the| most hi|
|00003f80| 67 68 6c 79 20 63 6f 6d | 70 72 65 73 73 65 64 20 |ghly com|pressed |
|00003f90| 69 6d 61 67 65 73 20 68 | 61 76 65 20 76 65 72 79 |images h|ave very|
|00003fa0| 0a 67 6f 6f 64 20 70 68 | 6f 74 6f 6d 65 74 72 69 |.good ph|otometri|
|00003fb0| 63 20 70 72 6f 70 65 72 | 74 69 65 73 20 66 6f 72 |c proper|ties for|
|00003fc0| 20 62 6f 74 68 20 70 6f | 69 6e 74 20 73 6f 75 72 | both po|int sour|
|00003fd0| 63 65 73 20 61 6e 64 20 | 65 78 74 65 6e 64 65 64 |ces and |extended|
|00003fe0| 20 73 6f 75 72 63 65 73 | 3b 0a 69 6e 64 65 65 64 | sources|;.indeed|
|00003ff0| 2c 20 70 68 6f 74 6f 6d | 65 74 72 79 20 6f 66 20 |, photom|etry of |
|00004000| 65 78 74 65 6e 64 65 64 | 20 6f 62 6a 65 63 74 73 |extended| objects|
|00004010| 20 63 61 6e 20 62 65 20 | 69 6d 70 72 6f 76 65 64 | can be |improved|
|00004020| 20 62 79 20 74 68 65 20 | 61 64 61 70 74 69 76 65 | by the |adaptive|
|00004030| 0a 66 69 6c 74 65 72 69 | 6e 67 20 6f 66 20 74 68 |.filteri|ng of th|
|00004040| 65 20 48 2d 74 72 61 6e | 73 66 6f 72 6d 20 28 43 |e H-tran|sform (C|
|00004050| 61 70 70 61 63 69 6f 6c | 69 20 5c 65 74 61 6c 5c |appaciol|i \etal\|
|00004060| 20 31 39 38 38 29 2e 20 | 20 41 73 74 72 6f 6d 65 | 1988). | Astrome|
|00004070| 74 72 79 20 69 73 20 68 | 61 72 64 6c 79 0a 61 66 |try is h|ardly.af|
|00004080| 66 65 63 74 65 64 20 62 | 79 20 74 68 65 20 63 6f |fected b|y the co|
|00004090| 6d 70 72 65 73 73 69 6f | 6e 20 66 6f 72 20 6d 6f |mpressio|n for mo|
|000040a0| 64 65 73 74 20 63 6f 6d | 70 72 65 73 73 69 6f 6e |dest com|pression|
|000040b0| 20 66 61 63 74 6f 72 73 | 20 28 75 70 20 74 6f 20 | factors| (up to |
|000040c0| 61 62 6f 75 74 20 61 0a | 66 61 63 74 6f 72 20 6f |about a.|factor o|
|000040d0| 66 20 32 30 20 66 6f 72 | 20 6f 75 72 20 64 69 67 |f 20 for| our dig|
|000040e0| 69 74 69 7a 65 64 20 70 | 68 6f 74 6f 67 72 61 70 |itized p|hotograp|
|000040f0| 68 69 63 20 70 6c 61 74 | 65 73 29 2c 20 62 75 74 |hic plat|es), but|
|00004100| 20 64 6f 65 73 20 62 65 | 67 69 6e 20 74 6f 20 64 | does be|gin to d|
|00004110| 65 67 72 61 64 65 20 66 | 6f 72 0a 74 68 65 20 6d |egrade f|or.the m|
|00004120| 6f 73 74 20 68 69 67 68 | 6c 79 20 63 6f 6d 70 72 |ost high|ly compr|
|00004130| 65 73 73 65 64 20 69 6d | 61 67 65 73 2e 0a 0a 54 |essed im|ages...T|
|00004140| 68 65 73 65 20 72 65 73 | 75 6c 74 73 20 61 72 65 |hese res|ults are|
|00004150| 20 62 61 73 65 64 20 6f | 6e 20 74 65 73 74 73 20 | based o|n tests |
|00004160| 63 61 72 72 69 65 64 20 | 6f 75 74 20 77 69 74 68 |carried |out with|
|00004170| 20 74 6f 6f 6c 73 20 6f | 70 74 69 6d 69 7a 65 64 | tools o|ptimized|
|00004180| 20 66 6f 72 0a 74 68 65 | 20 6f 72 69 67 69 6e 61 | for.the| origina|
|00004190| 6c 20 69 6d 61 67 65 73 | 3b 20 69 74 20 69 73 20 |l images|; it is |
|000041a0| 6c 69 6b 65 6c 79 20 74 | 68 65 20 62 65 73 74 20 |likely t|he best |
|000041b0| 72 65 73 75 6c 74 73 20 | 77 69 6c 6c 20 62 65 20 |results |will be |
|000041c0| 6f 62 74 61 69 6e 65 64 | 20 66 6f 72 0a 68 69 67 |obtained| for.hig|
|000041d0| 68 6c 79 20 63 6f 6d 70 | 72 65 73 73 65 64 20 69 |hly comp|ressed i|
|000041e0| 6d 61 67 65 73 20 6f 6e | 6c 79 20 77 69 74 68 20 |mages on|ly with |
|000041f0| 61 6e 61 6c 79 73 69 73 | 20 74 6f 6f 6c 73 20 73 |analysis| tools s|
|00004200| 70 65 63 69 66 69 63 61 | 6c 6c 79 20 61 64 61 70 |pecifica|lly adap|
|00004210| 74 65 64 0a 74 6f 20 74 | 68 65 20 70 65 63 75 6c |ted.to t|he pecul|
|00004220| 69 61 72 20 6e 6f 69 73 | 65 20 63 68 61 72 61 63 |iar nois|e charac|
|00004230| 74 65 72 69 73 74 69 63 | 73 20 6f 66 20 74 68 65 |teristic|s of the|
|00004240| 20 63 6f 6d 70 72 65 73 | 73 65 64 20 69 6d 61 67 | compres|sed imag|
|00004250| 65 73 2e 0a 0a 5c 73 65 | 63 74 69 6f 6e 20 36 2e |es...\se|ction 6.|
|00004260| 20 43 6f 6e 63 6c 75 73 | 69 6f 6e 73 0a 0a 49 6e | Conclus|ions..In|
|00004270| 20 6f 72 64 65 72 20 74 | 6f 20 63 6f 6e 73 74 72 | order t|o constr|
|00004280| 75 63 74 20 74 68 65 20 | 47 75 69 64 65 20 53 74 |uct the |Guide St|
|00004290| 61 72 20 43 61 74 61 6c | 6f 67 20 66 6f 72 20 75 |ar Catal|og for u|
|000042a0| 73 65 20 69 6e 20 70 6f | 69 6e 74 69 6e 67 20 74 |se in po|inting t|
|000042b0| 68 65 0a 48 75 62 62 6c | 65 20 53 70 61 63 65 20 |he.Hubbl|e Space |
|000042c0| 54 65 6c 65 73 63 6f 70 | 65 2c 20 74 68 65 20 53 |Telescop|e, the S|
|000042d0| 70 61 63 65 20 54 65 6c | 65 73 63 6f 70 65 20 53 |pace Tel|escope S|
|000042e0| 63 69 65 6e 63 65 20 49 | 6e 73 74 69 74 75 74 65 |cience I|nstitute|
|000042f0| 20 73 63 61 6e 6e 65 64 | 0a 61 6e 64 20 64 69 67 | scanned|.and dig|
|00004300| 69 74 69 7a 65 64 20 77 | 69 64 65 2d 66 69 65 6c |itized w|ide-fiel|
|00004310| 64 20 70 68 6f 74 6f 67 | 72 61 70 68 69 63 20 70 |d photog|raphic p|
|00004320| 6c 61 74 65 73 20 63 6f | 76 65 72 69 6e 67 20 74 |lates co|vering t|
|00004330| 68 65 20 65 6e 74 69 72 | 65 20 73 6b 79 2e 0a 54 |he entir|e sky..T|
|00004340| 68 65 20 64 69 67 69 74 | 69 7a 65 64 20 70 6c 61 |he digit|ized pla|
|00004350| 74 65 73 20 61 72 65 20 | 6f 66 20 67 72 65 61 74 |tes are |of great|
|00004360| 20 75 74 69 6c 69 74 79 | 2c 20 62 75 74 20 74 6f | utility|, but to|
|00004370| 20 64 61 74 65 20 69 74 | 20 68 61 73 20 62 65 65 | date it| has bee|
|00004380| 6e 0a 69 6d 70 6f 73 73 | 69 62 6c 65 20 74 6f 20 |n.imposs|ible to |
|00004390| 64 69 73 74 72 69 62 75 | 74 65 20 74 68 65 20 73 |distribu|te the s|
|000043a0| 63 61 6e 73 20 62 65 63 | 61 75 73 65 20 6f 66 20 |cans bec|ause of |
|000043b0| 74 68 65 20 6d 61 73 73 | 69 76 65 20 76 6f 6c 75 |the mass|ive volu|
|000043c0| 6d 65 20 6f 66 0a 64 61 | 74 61 20 69 6e 76 6f 6c |me of.da|ta invol|
|000043d0| 76 65 64 20 28 61 20 74 | 6f 74 61 6c 20 6f 66 20 |ved (a t|otal of |
|000043e0| 61 62 6f 75 74 20 36 30 | 30 7e 47 62 79 74 65 73 |about 60|0~Gbytes|
|000043f0| 29 2e 20 20 55 73 69 6e | 67 20 74 68 65 20 63 6f |). Usin|g the co|
|00004400| 6d 70 72 65 73 73 69 6f | 6e 0a 74 65 63 68 6e 69 |mpressio|n.techni|
|00004410| 71 75 65 73 20 64 65 73 | 63 72 69 62 65 64 20 69 |ques des|cribed i|
|00004420| 6e 20 74 68 69 73 20 70 | 61 70 65 72 2c 20 77 65 |n this p|aper, we|
|00004430| 20 70 6c 61 6e 20 74 6f | 20 64 69 73 74 72 69 62 | plan to| distrib|
|00004440| 75 74 65 20 6f 75 72 20 | 64 69 67 69 74 61 6c 0a |ute our |digital.|
|00004450| 73 6b 79 20 73 75 72 76 | 65 79 20 6f 6e 20 43 44 |sky surv|ey on CD|
|00004460| 2d 52 4f 4d 73 3b 20 20 | 61 62 6f 75 74 20 31 30 |-ROMs; |about 10|
|00004470| 30 20 43 44 2d 52 4f 4d | 73 20 77 69 6c 6c 20 62 |0 CD-ROM|s will b|
|00004480| 65 20 72 65 71 75 69 72 | 65 64 20 69 66 20 74 68 |e requir|ed if th|
|00004490| 65 0a 73 75 72 76 65 79 | 20 69 73 20 63 6f 6d 70 |e.survey| is comp|
|000044a0| 72 65 73 73 65 64 20 62 | 79 20 61 20 66 61 63 74 |ressed b|y a fact|
|000044b0| 6f 72 20 6f 66 20 31 30 | 2e 0a 0a 54 68 65 20 61 |or of 10|...The a|
|000044c0| 6c 67 6f 72 69 74 68 6d | 20 64 65 73 63 72 69 62 |lgorithm| describ|
|000044d0| 65 64 20 69 6e 20 74 68 | 69 73 20 70 61 70 65 72 |ed in th|is paper|
|000044e0| 20 68 61 73 20 62 65 65 | 6e 20 73 68 6f 77 6e 20 | has bee|n shown |
|000044f0| 74 6f 20 62 65 20 63 61 | 70 61 62 6c 65 20 6f 66 |to be ca|pable of|
|00004500| 0a 70 72 6f 64 75 63 69 | 6e 67 20 68 69 67 68 6c |.produci|ng highl|
|00004510| 79 20 63 6f 6d 70 72 65 | 73 73 65 64 20 69 6d 61 |y compre|ssed ima|
|00004520| 67 65 73 20 74 68 61 74 | 20 61 72 65 20 76 65 72 |ges that| are ver|
|00004530| 79 20 66 61 69 74 68 66 | 75 6c 20 74 6f 20 74 68 |y faithf|ul to th|
|00004540| 65 0a 6f 72 69 67 69 6e | 61 6c 2e 20 20 41 6c 67 |e.origin|al. Alg|
|00004550| 6f 72 69 74 68 6d 73 20 | 64 65 73 69 67 6e 65 64 |orithms |designed|
|00004560| 20 74 6f 20 77 6f 72 6b | 20 6f 6e 20 74 68 65 20 | to work| on the |
|00004570| 6f 72 69 67 69 6e 61 6c | 20 69 6d 61 67 65 73 20 |original| images |
|00004580| 63 61 6e 20 67 69 76 65 | 0a 63 6f 6d 70 61 72 61 |can give|.compara|
|00004590| 62 6c 65 20 72 65 73 75 | 6c 74 73 20 6f 6e 20 6f |ble resu|lts on o|
|000045a0| 62 6a 65 63 74 20 64 65 | 74 65 63 74 69 6f 6e 2c |bject de|tection,|
|000045b0| 20 61 73 74 72 6f 6d 65 | 74 72 79 2c 20 61 6e 64 | astrome|try, and|
|000045c0| 20 70 68 6f 74 6f 6d 65 | 74 72 79 20 77 68 65 6e | photome|try when|
|000045d0| 0a 61 70 70 6c 69 65 64 | 20 74 6f 20 74 68 65 20 |.applied| to the |
|000045e0| 69 6d 61 67 65 73 20 63 | 6f 6d 70 72 65 73 73 65 |images c|ompresse|
|000045f0| 64 20 62 79 20 61 20 66 | 61 63 74 6f 72 20 6f 66 |d by a f|actor of|
|00004600| 20 31 30 20 6f 72 20 70 | 6f 73 73 69 62 6c 79 20 | 10 or p|ossibly |
|00004610| 6d 6f 72 65 2e 0a 46 75 | 72 74 68 65 72 20 65 78 |more..Fu|rther ex|
|00004620| 70 65 72 69 6d 65 6e 74 | 73 20 77 69 6c 6c 20 64 |periment|s will d|
|00004630| 65 74 65 72 6d 69 6e 65 | 20 6d 6f 72 65 20 70 72 |etermine| more pr|
|00004640| 65 63 69 73 65 6c 79 20 | 6a 75 73 74 20 77 68 61 |ecisely |just wha|
|00004650| 74 20 65 72 72 6f 72 73 | 20 61 72 65 0a 69 6e 74 |t errors| are.int|
|00004660| 72 6f 64 75 63 65 64 20 | 69 6e 20 74 68 65 20 63 |roduced |in the c|
|00004670| 6f 6d 70 72 65 73 73 65 | 64 20 64 61 74 61 3b 20 |ompresse|d data; |
|00004680| 69 74 20 69 73 20 70 6f | 73 73 69 62 6c 65 20 74 |it is po|ssible t|
|00004690| 68 61 74 20 63 65 72 74 | 61 69 6e 20 6b 69 6e 64 |hat cert|ain kind|
|000046a0| 73 20 6f 66 0a 61 6e 61 | 6c 79 73 69 73 20 77 69 |s of.ana|lysis wi|
|000046b0| 6c 6c 20 67 69 76 65 20 | 6d 6f 72 65 20 61 63 63 |ll give |more acc|
|000046c0| 75 72 61 74 65 20 72 65 | 73 75 6c 74 73 20 6f 6e |urate re|sults on|
|000046d0| 20 74 68 65 20 63 6f 6d | 70 72 65 73 73 65 64 20 | the com|pressed |
|000046e0| 64 61 74 61 20 74 68 61 | 6e 20 6f 6e 0a 74 68 65 |data tha|n on.the|
|000046f0| 20 6f 72 69 67 69 6e 61 | 6c 20 62 65 63 61 75 73 | origina|l becaus|
|00004700| 65 20 6f 66 20 74 68 65 | 20 61 64 61 70 74 69 76 |e of the| adaptiv|
|00004710| 65 20 66 69 6c 74 65 72 | 69 6e 67 20 6f 66 20 74 |e filter|ing of t|
|00004720| 68 65 20 5c 68 74 2f 20 | 28 43 61 70 61 63 63 69 |he \ht/ |(Capacci|
|00004730| 6f 6c 69 0a 5c 65 74 61 | 6c 5c 20 31 39 38 38 29 |oli.\eta|l\ 1988)|
|00004740| 2e 0a 0a 54 68 69 73 20 | 63 6f 6d 70 72 65 73 73 |...This |compress|
|00004750| 69 6f 6e 20 61 6c 67 6f | 72 69 74 68 6d 20 63 61 |ion algo|rithm ca|
|00004760| 6e 20 62 65 20 61 70 70 | 6c 69 65 64 20 74 6f 20 |n be app|lied to |
|00004770| 61 6e 79 20 69 6d 61 67 | 65 2c 20 6e 6f 74 20 6a |any imag|e, not j|
|00004780| 75 73 74 20 74 6f 0a 64 | 69 67 69 74 69 7a 65 64 |ust to.d|igitized|
|00004790| 20 70 68 6f 74 6f 67 72 | 61 70 68 69 63 20 70 6c | photogr|aphic pl|
|000047a0| 61 74 65 73 2e 20 20 45 | 78 70 65 72 69 6d 65 6e |ates. E|xperimen|
|000047b0| 74 73 20 6f 6e 20 43 43 | 44 20 69 6d 61 67 65 73 |ts on CC|D images|
|000047c0| 20 69 6e 64 69 63 61 74 | 65 20 74 68 61 74 0a 6c | indicat|e that.l|
|000047d0| 6f 73 73 6c 65 73 73 20 | 63 6f 6d 70 72 65 73 73 |ossless |compress|
|000047e0| 69 6f 6e 20 66 61 63 74 | 6f 72 73 20 6f 66 20 33 |ion fact|ors of 3|
|000047f0| 2d 2d 33 30 20 63 61 6e | 20 62 65 20 61 63 68 69 |--30 can| be achi|
|00004800| 65 76 65 64 20 64 65 70 | 65 6e 64 69 6e 67 20 6f |eved dep|ending o|
|00004810| 6e 20 74 68 65 0a 43 43 | 44 20 63 68 61 72 61 63 |n the.CC|D charac|
|00004820| 74 65 72 69 73 74 69 63 | 73 20 28 5c 65 67 20 74 |teristic|s (\eg t|
|00004830| 68 65 20 72 65 61 64 6f | 75 74 20 6e 6f 69 73 65 |he reado|ut noise|
|00004840| 29 2e 20 20 41 20 73 6c | 69 67 68 74 6c 79 20 6d |). A sl|ightly m|
|00004850| 6f 64 69 66 69 65 64 0a | 61 6c 67 6f 72 69 74 68 |odified.|algorith|
|00004860| 6d 20 63 75 73 74 6f 6d | 69 7a 65 64 20 74 6f 20 |m custom|ized to |
|00004870| 74 68 65 20 6e 6f 69 73 | 65 20 63 68 61 72 61 63 |the nois|e charac|
|00004880| 74 65 72 69 73 74 69 63 | 73 20 6f 66 20 74 68 65 |teristic|s of the|
|00004890| 20 43 43 44 20 77 69 6c | 6c 20 64 6f 0a 62 65 74 | CCD wil|l do.bet|
|000048a0| 74 65 72 2e 20 20 54 68 | 69 73 20 61 70 70 6c 69 |ter. Th|is appli|
|000048b0| 63 61 74 69 6f 6e 20 77 | 69 6c 6c 20 62 65 20 65 |cation w|ill be e|
|000048c0| 78 70 6c 6f 72 65 64 20 | 69 6e 20 64 65 74 61 69 |xplored |in detai|
|000048d0| 6c 20 69 6e 20 74 68 65 | 20 66 75 74 75 72 65 2e |l in the| future.|
|000048e0| 0a 0a 57 65 20 67 72 61 | 74 65 66 75 6c 6c 79 20 |..We gra|tefully |
|000048f0| 61 63 6b 6e 6f 77 6c 65 | 64 67 65 20 67 72 61 6e |acknowle|dge gran|
|00004900| 74 20 66 72 6f 6d 20 4e | 41 47 57 2d 32 31 36 36 |t from N|AGW-2166|
|00004910| 20 66 72 6f 6d 20 74 68 | 65 20 53 63 69 65 6e 63 | from th|e Scienc|
|00004920| 65 0a 4f 70 65 72 61 74 | 69 6f 6e 73 20 42 72 61 |e.Operat|ions Bra|
|00004930| 6e 63 68 20 6f 66 20 4e | 41 53 41 20 68 65 61 64 |nch of N|ASA head|
|00004940| 71 75 61 72 74 65 72 73 | 20 77 68 69 63 68 20 73 |quarters| which s|
|00004950| 75 70 70 6f 72 74 65 64 | 20 74 68 69 73 20 77 6f |upported| this wo|
|00004960| 72 6b 2e 0a 54 68 65 20 | 53 70 61 63 65 20 54 65 |rk..The |Space Te|
|00004970| 6c 65 73 63 6f 70 65 20 | 53 63 69 65 6e 63 65 20 |lescope |Science |
|00004980| 49 6e 73 74 69 74 75 74 | 65 20 69 73 20 6f 70 65 |Institut|e is ope|
|00004990| 72 61 74 65 64 20 62 79 | 20 41 55 52 41 20 77 69 |rated by| AURA wi|
|000049a0| 74 68 20 66 75 6e 64 69 | 6e 67 0a 66 72 6f 6d 20 |th fundi|ng.from |
|000049b0| 4e 41 53 41 20 61 6e 64 | 20 45 53 41 2e 0a 0a 5c |NASA and| ESA...\|
|000049c0| 73 65 63 74 69 6f 6e 20 | 52 65 66 65 72 65 6e 63 |section |Referenc|
|000049d0| 65 73 0a 0a 7b 5c 70 61 | 72 73 6b 69 70 3d 30 70 |es..{\pa|rskip=0p|
|000049e0| 74 20 5c 66 72 65 6e 63 | 68 73 70 61 63 69 6e 67 |t \frenc|hspacing|
|000049f0| 20 5c 61 64 76 61 6e 63 | 65 5c 6c 65 66 74 73 6b | \advanc|e\leftsk|
|00004a00| 69 70 20 62 79 5c 70 61 | 72 69 6e 64 65 6e 74 20 |ip by\pa|rindent |
|00004a10| 5c 70 61 72 69 6e 64 65 | 6e 74 3d 2d 5c 70 61 72 |\parinde|nt=-\par|
|00004a20| 69 6e 64 65 6e 74 0a 0a | 42 6c 75 6d 65 2c 20 48 |indent..|Blume, H|
|00004a30| 2e 2c 20 61 6e 64 20 46 | 61 6e 64 2c 20 41 2e 20 |., and F|and, A. |
|00004a40| 20 31 39 38 39 2c 20 7b | 5c 73 6c 20 53 50 49 45 | 1989, {|\sl SPIE|
|00004a50| 20 56 6f 6c 2e 20 31 30 | 39 31 2c 0a 4d 65 64 69 | Vol. 10|91,.Medi|
|00004a60| 63 61 6c 20 49 6d 61 67 | 69 6e 67 20 49 49 49 3a |cal Imag|ing III:|
|00004a70| 20 49 6d 61 67 65 20 43 | 61 70 74 75 72 65 20 61 | Image C|apture a|
|00004a80| 6e 64 20 44 69 73 70 6c | 61 79 7d 2c 20 70 2e 20 |nd Displ|ay}, p. |
|00004a90| 32 2e 0a 0a 43 61 70 61 | 63 63 69 6f 6c 69 2c 20 |2...Capa|ccioli, |
|00004aa0| 4d 2e 2c 20 48 65 6c 64 | 2c 20 45 2e 20 56 2e 2c |M., Held|, E. V.,|
|00004ab0| 20 4c 6f 72 65 6e 7a 2c | 20 48 2e 2c 20 52 69 63 | Lorenz,| H., Ric|
|00004ac0| 68 74 65 72 2c 20 47 2e | 20 4d 2e 2c 20 61 6e 64 |hter, G.| M., and|
|00004ad0| 20 5a 69 65 6e 65 72 2c | 20 52 2e 0a 31 39 38 38 | Ziener,| R..1988|
|00004ae0| 2c 20 7b 5c 73 6c 20 41 | 73 74 72 6f 6e 6f 6d 69 |, {\sl A|stronomi|
|00004af0| 73 63 68 65 20 4e 61 63 | 68 72 69 63 68 74 65 6e |sche Nac|hrichten|
|00004b00| 7d 2c 20 7b 5c 62 66 20 | 33 30 39 7d 2c 20 36 39 |}, {\bf |309}, 69|
|00004b10| 2e 0a 0a 44 61 75 62 65 | 63 68 69 65 73 2c 20 49 |...Daube|chies, I|
|00004b20| 2e 20 31 39 38 38 2c 20 | 7b 5c 73 6c 20 43 6f 6d |. 1988, |{\sl Com|
|00004b30| 6d 2e 20 50 75 72 65 20 | 61 6e 64 20 41 70 70 6c |m. Pure |and Appl|
|00004b40| 2e 20 4d 61 74 68 2e 7d | 2c 20 7b 5c 62 66 20 34 |. Math.}|, {\bf 4|
|00004b50| 31 7d 2c 20 39 30 39 2e | 0a 0a 46 72 69 74 7a 65 |1}, 909.|..Fritze|
|00004b60| 2c 20 4b 2e 2c 20 4c 61 | 6e 67 65 2c 20 4d 2e 2c |, K., La|nge, M.,|
|00004b70| 20 4d 5c 22 6f 73 74 6c | 2c 20 47 2e 2c 20 4f 6c | M\"ostl|, G., Ol|
|00004b80| 65 61 6b 2c 20 48 2e 2c | 20 61 6e 64 20 52 69 63 |eak, H.,| and Ric|
|00004b90| 68 74 65 72 2c 20 47 2e | 20 4d 2e 20 31 39 37 37 |hter, G.| M. 1977|
|00004ba0| 2c 0a 7b 5c 73 6c 20 41 | 73 74 72 6f 6e 6f 6d 69 |,.{\sl A|stronomi|
|00004bb0| 73 63 68 65 20 4e 61 63 | 68 72 69 63 68 74 65 6e |sche Nac|hrichten|
|00004bc0| 7d 2c 0a 7b 5c 62 66 20 | 32 39 38 7d 2c 20 31 38 |},.{\bf |298}, 18|
|00004bd0| 39 2e 0a 0a 48 61 61 72 | 2c 20 41 2e 20 31 39 31 |9...Haar|, A. 191|
|00004be0| 30 2c 20 7b 5c 73 6c 20 | 4d 61 74 68 2e 20 41 6e |0, {\sl |Math. An|
|00004bf0| 6e 2e 7d 20 7b 5c 62 66 | 20 36 39 7d 2c 20 33 33 |n.} {\bf| 69}, 33|
|00004c00| 31 2e 0a 0a 48 75 61 6e | 67 2c 20 4c 2c 20 61 6e |1...Huan|g, L, an|
|00004c10| 64 20 42 69 6a 61 6f 75 | 69 2c 20 41 2e 20 20 31 |d Bijaou|i, A. 1|
|00004c20| 39 39 31 2c 20 7b 5c 73 | 6c 20 45 78 70 65 72 69 |991, {\s|l Experi|
|00004c30| 6d 65 6e 74 61 6c 20 41 | 73 74 72 6f 6e 6f 6d 79 |mental A|stronomy|
|00004c40| 7d 2c 20 7b 5c 62 66 20 | 31 7d 2c 20 33 31 31 2e |}, {\bf |1}, 311.|
|00004c50| 0a 0a 52 69 63 68 74 65 | 72 2c 20 47 2e 20 4d 2e |..Richte|r, G. M.|
|00004c60| 20 31 39 37 38 2c 0a 7b | 5c 73 6c 20 41 73 74 72 | 1978,.{|\sl Astr|
|00004c70| 6f 6e 6f 6d 69 73 63 68 | 65 20 4e 61 63 68 72 69 |onomisch|e Nachri|
|00004c80| 63 68 74 65 6e 7d 2c 0a | 7b 5c 62 66 20 32 39 39 |chten},.|{\bf 299|
|00004c90| 7d 2c 20 32 38 33 2e 0a | 0a 53 61 6d 65 74 2c 20 |}, 283..|.Samet, |
|00004ca0| 48 2e 20 31 39 38 34 2c | 20 7b 5c 73 6c 20 41 43 |H. 1984,| {\sl AC|
|00004cb0| 4d 20 43 6f 6d 70 75 74 | 69 6e 67 20 53 75 72 76 |M Comput|ing Surv|
|00004cc0| 65 79 73 7d 2c 20 7b 5c | 62 66 20 31 36 7d 2c 20 |eys}, {\|bf 16}, |
|00004cd0| 31 38 37 2e 0a 0a 57 68 | 69 74 65 2c 20 52 2e 20 |187...Wh|ite, R. |
|00004ce0| 4c 2e 2c 20 50 6f 73 74 | 6d 61 6e 2c 20 4d 2e 2c |L., Post|man, M.,|
|00004cf0| 20 61 6e 64 20 4c 61 74 | 74 61 6e 7a 69 2c 20 4d | and Lat|tanzi, M|
|00004d00| 2e 20 31 39 39 31 2c 20 | 69 6e 20 7b 5c 73 6c 20 |. 1991, |in {\sl |
|00004d10| 50 72 6f 63 65 65 64 69 | 6e 67 73 20 6f 66 20 74 |Proceedi|ngs of t|
|00004d20| 68 65 0a 20 20 20 45 64 | 69 6e 62 75 72 67 68 20 |he. Ed|inburgh |
|00004d30| 4d 65 65 74 69 6e 67 20 | 6f 6e 20 44 69 67 69 74 |Meeting |on Digit|
|00004d40| 61 6c 20 53 6b 79 20 53 | 75 72 76 65 79 73 7d 2c |al Sky S|urveys},|
|00004d50| 20 69 6e 20 70 72 65 73 | 73 2e 0a 0a 57 69 74 74 | in pres|s...Witt|
|00004d60| 65 6e 2c 20 49 2e 20 48 | 2e 2c 20 52 61 64 66 6f |en, I. H|., Radfo|
|00004d70| 72 64 2c 20 4d 2e 20 4e | 2e 2c 20 61 6e 64 20 43 |rd, M. N|., and C|
|00004d80| 6c 65 61 72 79 2c 20 4a | 2e 20 47 2e 20 31 39 38 |leary, J|. G. 198|
|00004d90| 37 2c 20 7b 5c 73 6c 20 | 43 6f 6d 6d 75 6e 69 63 |7, {\sl |Communic|
|00004da0| 61 74 69 6f 6e 73 20 6f | 66 0a 74 68 65 20 41 43 |ations o|f.the AC|
|00004db0| 4d 7d 2c 20 7b 5c 62 66 | 20 33 30 7d 2c 20 35 32 |M}, {\bf| 30}, 52|
|00004dc0| 30 2e 0a 0a 7d 0a 5c 62 | 79 65 0a |0...}.\b|ye. |
+--------+-------------------------+-------------------------+--------+--------+