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MacBinary | 1993-03-15 | 605.1 KB | [ ONLN/HLX2]
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MacBinary II, inited, Sun Mar 14 20:30:23 1993, modified Sun Mar 14 20:30:31 1993, creator 'HLX2', type 'ONLN', 616059 bytes "In Search of Optimal Palette" , at 0x966fb 3411 bytes resource
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file
data
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66%
TrID
SpeedScript document (C64)
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TrID
MacBinary 2
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siegfried
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MacBinary
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id metadata key value macFileType [ ONLN] macFileCreator [ HLX2]
hex view +--------+-------------------------+-------------------------+--------+--------+ |00000000| 00 1c 49 6e 20 53 65 61 | 72 63 68 20 6f 66 20 4f |..In Sea|rch of O| |00000010| 70 74 69 6d 61 6c 20 50 | 61 6c 65 74 74 65 00 00 |ptimal P|alette..| |00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000040| 00 4f 4e 4c 4e 48 4c 58 | 32 01 00 00 00 00 00 00 |.ONLNHLX|2.......| |00000050| 00 00 00 00 09 66 7b 00 | 00 0d 53 a7 c9 8c af a7 |.....f{.|..S.....| |00000060| c9 8c b7 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 23 d2 00 00 |........|....#...| |00000080| 49 4e 20 53 45 41 52 43 | 48 20 4f 46 20 54 48 45 |IN SEARC|H OF THE| |00000090| 20 4f 50 54 49 4d 41 4c | 20 50 41 4c 45 54 54 45 | OPTIMAL| PALETTE| |000000a0| 0d 44 41 56 45 20 47 4f | 4f 44 20 41 4e 44 20 4b |.DAVE GO|OD AND K| |000000b0| 4f 4e 53 54 41 4e 54 49 | 4e 20 4f 54 48 4d 45 52 |ONSTANTI|N OTHMER| |000000c0| 0d 57 68 65 6e 20 79 6f | 75 20 77 61 6e 74 20 74 |.When yo|u want t| |000000d0| 6f 20 64 69 73 70 6c 61 | 79 20 61 6e 20 69 6d 61 |o displa|y an ima| |000000e0| 67 65 20 74 68 61 74 20 | 63 6f 6e 74 61 69 6e 73 |ge that |contains| |000000f0| 20 6d 6f 72 65 20 63 6f | 6c 6f 72 20 69 6e 66 6f | more co|lor info| |00000100| 72 6d 61 74 69 6f 6e 20 | 74 68 61 6e 20 74 68 65 |rmation |than the| |00000110| 20 64 69 73 70 6c 61 79 | 20 64 65 76 69 63 65 20 | display| device | |00000120| 69 73 20 63 61 70 61 62 | 6c 65 20 6f 66 20 72 65 |is capab|le of re| |00000130| 6e 64 65 72 69 6e 67 2c | 20 68 6f 77 20 64 6f 20 |ndering,| how do | |00000140| 79 6f 75 20 70 69 63 6b | 20 74 68 65 20 62 65 73 |you pick| the bes| |00000150| 74 20 63 6f 6c 6f 72 73 | 20 74 6f 20 75 73 65 3f |t colors| to use?| |00000160| 20 54 68 65 20 50 69 63 | 74 75 72 65 20 55 74 69 | The Pic|ture Uti| |00000170| 6c 69 74 69 65 73 20 50 | 61 63 6b 61 67 65 2c 20 |lities P|ackage, | |00000180| 6e 65 77 20 69 6e 20 53 | 79 73 74 65 6d 20 37 2c |new in S|ystem 7,| |00000190| 20 70 72 6f 76 69 64 65 | 73 20 74 77 6f 20 6d 65 | provide|s two me| |000001a0| 74 68 6f 64 73 2c 20 77 | 68 69 63 68 20 77 65 20 |thods, w|hich we | |000001b0| 64 65 73 63 72 69 62 65 | 20 68 65 72 65 2e 20 59 |describe| here. 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On an| |000002f0| 20 69 6e 64 65 78 65 64 | 20 64 65 76 69 63 65 20 | indexed| device | |00000300| 28 32 35 36 20 6f 72 20 | 66 65 77 65 72 20 63 6f |(256 or |fewer co| |00000310| 6c 6f 72 73 29 2c 20 61 | 6e 20 61 70 70 6c 69 63 |lors), a|n applic| |00000320| 61 74 69 6f 6e 20 63 61 | 6e 20 63 68 6f 6f 73 65 |ation ca|n choose| |00000330| 2c 20 76 69 61 20 74 68 | 65 20 50 61 6c 65 74 74 |, via th|e Palett| |00000340| 65 20 4d 61 6e 61 67 65 | 72 2c 20 77 68 69 63 68 |e Manage|r, which| |00000350| 20 63 6f 6c 6f 72 73 20 | 74 6f 20 75 73 65 2e 20 | colors |to use. | |00000360| 42 75 74 20 68 6f 77 20 | 77 69 6c 6c 20 69 74 20 |But how |will it | |00000370| 6b 6e 6f 77 20 77 68 69 | 63 68 20 63 6f 6c 6f 72 |know whi|ch color| |00000380| 73 20 61 72 65 20 74 68 | 65 20 62 65 73 74 20 6f |s are th|e best o| |00000390| 6e 65 73 20 74 6f 20 63 | 68 6f 6f 73 65 2c 20 67 |nes to c|hoose, g| |000003a0| 69 76 65 6e 20 61 20 70 | 61 72 74 69 63 75 6c 61 |iven a p|articula| |000003b0| 72 20 69 6d 61 67 65 3f | 0d 54 6f 20 61 76 6f 69 |r image?|.To avoi| |000003c0| 64 20 74 68 69 73 20 69 | 73 73 75 65 20 61 6c 74 |d this i|ssue alt| |000003d0| 6f 67 65 74 68 65 72 2c | 20 79 6f 75 72 20 61 70 |ogether,| your ap| |000003e0| 70 6c 69 63 61 74 69 6f | 6e 20 63 61 6e 20 73 69 |plicatio|n can si| |000003f0| 6d 70 6c 79 20 64 72 61 | 77 20 74 68 65 20 69 6d |mply dra|w the im| |00000400| 61 67 65 20 61 6e 64 20 | 6c 65 74 20 51 75 69 63 |age and |let Quic| |00000410| 6b 44 72 61 77 20 75 73 | 65 20 69 74 73 20 64 65 |kDraw us|e its de| |00000420| 66 61 75 6c 74 20 63 6f | 6c 6f 72 20 70 61 6c 65 |fault co|lor pale| |00000430| 74 74 65 73 20 74 6f 20 | 6d 61 6b 65 20 74 68 65 |ttes to |make the| |00000440| 20 63 68 6f 69 63 65 2e | 20 42 65 63 61 75 73 65 | choice.| Because| |00000450| 20 74 68 65 73 65 20 70 | 61 6c 65 74 74 65 73 20 | these p|alettes | |00000460| 63 6f 6e 74 61 69 6e 20 | 61 20 77 65 6c 6c 2d 64 |contain |a well-d| |00000470| 69 73 70 65 72 73 65 64 | 20 73 65 74 20 6f 66 20 |ispersed| set of | |00000480| 63 6f 6c 6f 72 73 2c 20 | 6d 6f 73 74 20 69 6d 61 |colors, |most ima| |00000490| 67 65 73 20 6c 6f 6f 6b | 20 70 72 65 74 74 79 20 |ges look| pretty | |000004a0| 67 6f 6f 64 2e 20 48 6f | 77 65 76 65 72 2c 20 69 |good. 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In thi|s case, | |00000580| 79 6f 75 20 6d 75 73 74 | 20 74 61 63 6b 6c 65 20 |you must| tackle | |00000590| 74 68 65 20 69 73 73 75 | 65 20 6f 66 20 68 6f 77 |the issu|e of how| |000005a0| 20 74 6f 20 63 68 6f 6f | 73 65 20 74 68 65 20 6f | to choo|se the o| |000005b0| 70 74 69 6d 61 6c 20 70 | 61 6c 65 74 74 65 2e 20 |ptimal p|alette. | |000005c0| 54 68 61 74 d5 73 20 77 | 68 65 6e 20 74 68 65 20 |That.s w|hen the | |000005d0| 6e 65 77 20 50 69 63 74 | 75 72 65 20 55 74 69 6c |new Pict|ure Util| |000005e0| 69 74 69 65 73 20 50 61 | 63 6b 61 67 65 20 63 61 |ities Pa|ckage ca| |000005f0| 6e 20 68 65 6c 70 2e 0d | 50 69 63 74 75 72 65 20 |n help..|Picture | |00000600| 55 74 69 6c 69 74 69 65 | 73 20 70 72 6f 76 69 64 |Utilitie|s provid| |00000610| 65 73 20 74 77 6f 20 6d | 65 74 68 6f 64 73 d1 74 |es two m|ethods.t| |00000620| 68 65 20 70 6f 70 75 6c | 61 72 20 6d 65 74 68 6f |he popul|ar metho| |00000630| 64 20 61 6e 64 20 74 68 | 65 20 6d 65 64 69 61 6e |d and th|e median| |00000640| 20 6d 65 74 68 6f 64 d1 | 66 6f 72 20 64 65 74 65 | method.|for dete| |00000650| 72 6d 69 6e 69 6e 67 20 | 74 68 65 20 62 65 73 74 |rmining |the best| |00000660| 20 63 6f 6c 6f 72 73 2e | 20 54 68 69 73 20 61 72 | colors.| This ar| |00000670| 74 69 63 6c 65 20 64 65 | 73 63 72 69 62 65 73 20 |ticle de|scribes | |00000680| 74 68 65 73 65 20 74 77 | 6f 20 6d 65 74 68 6f 64 |these tw|o method| |00000690| 73 2e 20 49 6e 20 61 64 | 64 69 74 69 6f 6e 2c 20 |s. In ad|dition, | |000006a0| 69 74 20 64 65 73 63 72 | 69 62 65 73 20 61 20 74 |it descr|ibes a t| |000006b0| 68 69 72 64 20 6d 65 74 | 68 6f 64 d1 74 68 65 20 |hird met|hod.the | |000006c0| 6f 63 74 72 65 65 20 6d | 65 74 68 6f 64 d1 77 68 |octree m|ethod.wh| |000006d0| 69 63 68 2c 20 69 6e 20 | 61 64 64 69 74 69 6f 6e |ich, in |addition| |000006e0| 20 74 6f 20 62 65 69 6e | 67 20 75 73 65 66 75 6c | to bein|g useful| |000006f0| 20 69 6e 20 69 74 73 65 | 6c 66 2c 20 6d 61 6b 65 | in itse|lf, make| |00000700| 73 20 61 20 63 6f 6e 76 | 65 6e 69 65 6e 74 20 73 |s a conv|enient s| |00000710| 74 61 72 74 69 6e 67 20 | 70 6f 69 6e 74 20 66 6f |tarting |point fo| |00000720| 72 20 79 6f 75 20 74 6f | 20 64 65 76 65 6c 6f 70 |r you to| develop| |00000730| 20 79 6f 75 72 20 6f 77 | 6e 20 61 6c 67 6f 72 69 | your ow|n algori| |00000740| 74 68 6d 20 66 6f 72 20 | 63 68 6f 6f 73 69 6e 67 |thm for |choosing| |00000750| 20 74 68 65 20 6f 70 74 | 69 6d 61 6c 20 63 6f 6c | the opt|imal col| |00000760| 6f 72 20 70 61 6c 65 74 | 74 65 2e 0d 44 45 43 49 |or palet|te..DECI| |00000770| 44 49 4e 47 20 57 48 49 | 43 48 20 4d 45 54 48 4f |DING WHI|CH METHO| |00000780| 44 20 54 4f 20 55 53 45 | 0d 49 74 20 77 6f 75 6c |D TO USE|.It woul| |00000790| 64 20 62 65 20 6e 69 63 | 65 20 69 66 20 6f 6e 65 |d be nic|e if one| |000007a0| 20 6d 65 74 68 6f 64 20 | 6f 66 20 73 65 6c 65 63 | method |of selec| |000007b0| 74 69 6e 67 20 63 6f 6c | 6f 72 73 20 77 6f 72 6b |ting col|ors work| |000007c0| 65 64 20 62 65 73 74 20 | 66 6f 72 20 61 6c 6c 20 |ed best |for all | |000007d0| 74 79 70 65 73 20 6f 66 | 20 69 6d 61 67 65 73 2e |types of| images.| |000007e0| 20 42 75 74 20 74 68 65 | 20 74 72 75 74 68 20 69 | But the| truth i| |000007f0| 73 20 74 68 61 74 20 74 | 68 65 20 6d 65 74 68 6f |s that t|he metho| |00000800| 64 73 20 70 72 6f 76 69 | 64 65 64 20 69 6e 20 50 |ds provi|ded in P| |00000810| 69 63 74 75 72 65 20 55 | 74 69 6c 69 74 69 65 73 |icture U|tilities| |00000820| 20 77 6f 72 6b 20 62 65 | 73 74 20 66 6f 72 20 73 | work be|st for s| |00000830| 6f 6d 65 0d 74 79 70 65 | 73 20 6f 66 20 69 6d 61 |ome.type|s of ima| |00000840| 67 65 73 20 28 73 75 63 | 68 20 61 73 20 74 68 6f |ges (suc|h as tho| |00000850| 73 65 20 77 68 6f 73 65 | 20 63 6f 6c 6f 72 73 20 |se whose| colors | |00000860| 61 72 65 20 61 6c 6c 20 | 63 6c 75 73 74 65 72 65 |are all |clustere| |00000870| 64 20 69 6e 20 6f 6e 65 | 20 73 6d 61 6c 6c 20 70 |d in one| small p| |00000880| 6f 72 74 69 6f 6e 20 6f | 66 20 74 68 65 20 52 47 |ortion o|f the RG| |00000890| 42 20 63 75 62 65 29 2c | 20 77 68 69 6c 65 20 51 |B cube),| while Q| |000008a0| 75 69 63 6b 44 72 61 77 | d5 73 20 73 74 61 6e 64 |uickDraw|.s stand| |000008b0| 61 72 64 20 6d 65 74 68 | 6f 64 20 77 6f 72 6b 73 |ard meth|od works| |000008c0| 20 62 65 73 74 20 66 6f | 72 20 6f 74 68 65 72 20 | best fo|r other | |000008d0| 74 79 70 65 73 2e 20 54 | 68 65 72 65 66 6f 72 65 |types. 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Th|e operat| |00002500| 69 6f 6e 20 6f 66 20 74 | 68 69 73 20 73 79 73 74 |ion of t|his syst| |00002510| 65 6d 20 6d 65 74 68 6f | 64 20 69 73 20 61 6c 6d |em metho|d is alm| |00002520| 6f 73 74 20 63 65 72 74 | 61 69 6e 20 74 6f 20 63 |ost cert|ain to c| |00002530| 68 61 6e 67 65 20 69 6e | 20 74 68 65 20 66 75 74 |hange in| the fut| |00002540| 75 72 65 2e 0d 4e 6f 77 | 20 74 68 61 74 20 79 6f |ure..Now| that yo| |00002550| 75 20 68 61 76 65 20 73 | 6f 6d 65 20 69 64 65 61 |u have s|ome idea| |00002560| 20 6f 66 20 68 6f 77 20 | 74 68 65 20 61 76 61 69 | of how |the avai| |00002570| 6c 61 62 6c 65 20 63 6f | 6c 6f 72 2d 70 69 63 6b |lable co|lor-pick| |00002580| 69 6e 67 20 6d 65 74 68 | 6f 64 73 20 63 6f 6d 70 |ing meth|ods comp| |00002590| 61 72 65 2c 20 77 65 20 | 74 75 72 6e 20 74 6f 20 |are, we |turn to | |000025a0| 64 65 74 61 69 6c 73 20 | 6f 66 20 68 6f 77 20 74 |details |of how t| |000025b0| 68 65 20 70 6f 70 75 6c | 61 72 2c 20 6d 65 64 69 |he popul|ar, medi| |000025c0| 61 6e 2c 20 61 6e 64 20 | 6f 63 74 72 65 65 20 6d |an, and |octree m| |000025d0| 65 74 68 6f 64 73 20 77 | 6f 72 6b 2e 0d 48 4f 57 |ethods w|ork..HOW| |000025e0| 20 54 48 45 20 50 4f 50 | 55 4c 41 52 20 4d 45 54 | THE POP|ULAR MET| |000025f0| 48 4f 44 20 57 4f 52 4b | 53 0d 54 68 65 20 70 6f |HOD WORK|S.The po| |00002600| 70 75 6c 61 72 20 6d 65 | 74 68 6f 64 20 6f 66 20 |pular me|thod of | |00002610| 63 6f 6c 6f 72 20 73 65 | 6c 65 63 74 69 6f 6e 20 |color se|lection | |00002620| 69 73 20 74 68 65 20 65 | 61 73 69 65 73 74 20 74 |is the e|asiest t| |00002630| 6f 20 75 6e 64 65 72 73 | 74 61 6e 64 20 61 6e 64 |o unders|tand and| |00002640| 20 69 6e 20 67 65 6e 65 | 72 61 6c 20 70 72 6f 64 | in gene|ral prod| |00002650| 75 63 65 73 20 74 68 65 | 20 6c 65 61 73 74 20 73 |uces the| least s| |00002660| 61 74 69 73 66 61 63 74 | 6f 72 79 20 72 65 73 75 |atisfact|ory resu| |00002670| 6c 74 73 2e 20 54 68 69 | 73 20 6d 65 74 68 6f 64 |lts. 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The o|peration| |000026d0| 20 69 73 20 70 65 72 66 | 6f 72 6d 65 64 20 62 79 | is perf|ormed by| |000026e0| 20 63 72 65 61 74 69 6e | 67 20 61 20 68 69 73 74 | creatin|g a hist| |000026f0| 6f 67 72 61 6d 20 28 61 | 20 66 72 65 71 75 65 6e |ogram (a| frequen| |00002700| 63 79 20 63 6f 75 6e 74 | 20 6f 66 20 65 61 63 68 |cy count| of each| |00002710| 20 63 6f 6c 6f 72 29 20 | 61 6e 64 20 74 68 65 6e | color) |and then| |00002720| 20 72 65 74 75 72 6e 69 | 6e 67 20 74 68 65 20 63 | returni|ng the c| |00002730| 6f 6c 6f 72 73 20 74 68 | 61 74 20 6f 63 63 75 72 |olors th|at occur| |00002740| 20 6d 6f 73 74 20 6f 66 | 74 65 6e 20 28 61 73 20 | most of|ten (as | |00002750| 73 68 6f 77 6e 20 69 6e | 20 46 69 67 75 72 65 20 |shown in| Figure | |00002760| 32 29 2c 20 75 70 20 74 | 6f 20 74 68 65 20 73 70 |2), up t|o the sp| |00002770| 65 63 69 66 69 65 64 20 | 6e 75 6d 62 65 72 20 6f |ecified |number o| |00002780| 66 20 63 6f 6c 6f 72 73 | 2e 20 49 66 20 74 68 65 |f colors|. If the| |00002790| 20 69 6d 61 67 65 20 63 | 6f 6e 74 61 69 6e 73 20 | image c|ontains | |000027a0| 6d 6f 72 65 20 74 68 61 | 6e 20 32 35 36 20 64 69 |more tha|n 256 di| |000027b0| 66 66 65 72 65 6e 74 20 | 63 6f 6c 6f 72 73 20 6f |fferent |colors o| |000027c0| 72 20 69 66 20 61 6e 79 | 20 6f 66 20 74 68 65 20 |r if any| of the | |000027d0| 73 6f 75 72 63 65 20 69 | 74 65 6d 73 20 61 72 65 |source i|tems are| |000027e0| 20 33 32 2d 62 69 74 20 | 70 69 78 4d 61 70 73 2c | 32-bit |pixMaps,| |000027f0| 20 50 69 63 74 75 72 65 | 20 55 74 69 6c 69 74 69 | Picture| Utiliti| |00002800| 65 73 20 6f 6e 6c 79 20 | 6d 61 69 6e 74 61 69 6e |es only |maintain| |00002810| 73 20 63 6f 6c 6f 72 20 | 69 6e 66 6f 72 6d 61 74 |s color |informat| |00002820| 69 6f 6e 20 74 6f 20 61 | 20 72 65 73 6f 6c 75 74 |ion to a| resolut| |00002830| 69 6f 6e 20 6f 66 20 66 | 69 76 65 20 62 69 74 73 |ion of f|ive bits| |00002840| 20 70 65 72 20 63 6f 6c | 6f 72 20 63 6f 6d 70 6f | per col|or compo| |00002850| 6e 65 6e 74 2e 20 54 68 | 75 73 2c 20 63 6f 6c 6f |nent. Th|us, colo| |00002860| 72 73 20 6d 75 73 74 20 | 64 69 66 66 65 72 20 69 |rs must |differ i| |00002870| 6e 20 74 68 65 20 68 69 | 67 68 65 73 74 20 66 69 |n the hi|ghest fi| |00002880| 76 65 20 62 69 74 73 20 | 6f 66 20 61 6e 79 20 6f |ve bits |of any o| |00002890| 66 20 74 68 65 20 74 68 | 72 65 65 20 63 6f 6c 6f |f the th|ree colo| |000028a0| 72 20 63 6f 6d 70 6f 6e | 65 6e 74 73 20 28 72 65 |r compon|ents (re| |000028b0| 64 2c 20 67 72 65 65 6e | 2c 20 61 6e 64 20 62 6c |d, green|, and bl| |000028c0| 75 65 29 20 74 6f 20 62 | 65 20 63 6f 6e 73 69 64 |ue) to b|e consid| |000028d0| 65 72 65 64 20 64 69 73 | 74 69 6e 63 74 2e 0d 46 |ered dis|tinct..F| |000028e0| 69 67 75 72 65 20 32 0d | 50 69 63 6b 69 6e 67 20 |igure 2.|Picking | |000028f0| 46 6f 75 72 20 43 6f 6c | 6f 72 73 20 55 73 69 6e |Four Col|ors Usin| |00002900| 67 20 74 68 65 20 50 6f | 70 75 6c 61 72 20 4d 65 |g the Po|pular Me| |00002910| 74 68 6f 64 0d 49 6e 20 | 46 69 67 75 72 65 20 32 |thod.In |Figure 2| |00002920| 2c 20 74 68 65 20 78 2d | 61 78 69 73 20 72 65 70 |, the x-|axis rep| |00002930| 72 65 73 65 6e 74 73 20 | 65 61 63 68 20 70 6f 73 |resents |each pos| |00002940| 73 69 62 6c 65 20 52 47 | 42 20 63 6f 6c 6f 72 20 |sible RG|B color | |00002950| 74 6f 20 61 20 72 65 73 | 6f 6c 75 74 69 6f 6e 20 |to a res|olution | |00002960| 6f 66 20 66 69 76 65 20 | 62 69 74 73 20 70 65 72 |of five |bits per| |00002970| 20 63 6f 6d 70 6f 6e 65 | 6e 74 2e 20 54 68 65 73 | compone|nt. Thes| |00002980| 65 20 63 6f 6c 6f 72 73 | 20 72 61 6e 67 65 20 66 |e colors| range f| |00002990| 72 6f 6d 20 30 2d 30 2d | 30 20 28 30 20 72 65 64 |rom 0-0-|0 (0 red| |000029a0| 2c 20 30 20 67 72 65 65 | 6e 2c 20 30 20 62 6c 75 |, 0 gree|n, 0 blu| |000029b0| 65 29 20 74 6f 20 33 32 | 2d 33 32 2d 33 32 20 28 |e) to 32|-32-32 (| |000029c0| 33 32 20 72 65 64 2c 20 | 33 32 20 67 72 65 65 6e |32 red, |32 green| |000029d0| 2c 20 33 32 20 62 6c 75 | 65 29 20 69 6e 20 74 68 |, 32 blu|e) in th| |000029e0| 65 20 68 69 67 68 20 66 | 69 76 65 20 62 69 74 73 |e high f|ive bits| |000029f0| 20 6f 66 20 74 68 65 20 | 72 65 64 2d 67 72 65 65 | of the |red-gree| |00002a00| 6e 2d 62 6c 75 65 20 63 | 6f 6c 6f 72 20 63 6f 6d |n-blue c|olor com| |00002a10| 70 6f 6e 65 6e 74 73 2c | 20 66 6f 72 20 61 20 74 |ponents,| for a t| |00002a20| 6f 74 61 6c 20 6f 66 20 | 32 31 35 20 6f 72 20 61 |otal of |215 or a| |00002a30| 72 6f 75 6e 64 20 33 32 | 2c 30 30 30 20 65 6e 74 |round 32|,000 ent| |00002a40| 72 69 65 73 2e 20 54 68 | 65 20 79 2d 61 78 69 73 |ries. Th|e y-axis| |00002a50| 20 6d 65 61 73 75 72 65 | 73 20 74 68 65 20 66 72 | measure|s the fr| |00002a60| 65 71 75 65 6e 63 79 20 | 6f 66 20 65 61 63 68 20 |equency |of each | |00002a70| 6f 66 20 74 68 65 20 63 | 6f 6c 6f 72 73 2c 20 75 |of the c|olors, u| |00002a80| 70 20 74 6f 20 61 20 6d | 61 78 69 6d 75 6d 20 6f |p to a m|aximum o| |00002a90| 66 20 33 32 2c 37 36 37 | 20 6f 63 63 75 72 72 65 |f 32,767| occurre| |00002aa0| 6e 63 65 73 2e 20 54 68 | 75 73 2c 20 74 68 69 73 |nces. Th|us, this| |00002ab0| 20 74 61 62 6c 65 20 63 | 6f 6e 74 61 69 6e 73 20 | table c|ontains | |00002ac0| 32 31 35 20 65 6e 74 72 | 69 65 73 20 6f 66 20 6f |215 entr|ies of o| |00002ad0| 6e 65 20 77 6f 72 64 20 | 65 61 63 68 20 61 6e 64 |ne word |each and| |00002ae0| 20 6f 63 63 75 70 69 65 | 73 20 36 34 4b 20 6f 66 | occupie|s 64K of| |00002af0| 20 6d 65 6d 6f 72 79 2e | 0d 46 6f 72 20 63 75 73 | memory.|.For cus| |00002b00| 74 6f 6d 20 6d 65 74 68 | 6f 64 73 2c 20 50 69 63 |tom meth|ods, Pic| |00002b10| 74 75 72 65 20 55 74 69 | 6c 69 74 69 65 73 20 63 |ture Uti|lities c| |00002b20| 61 6e 20 67 65 6e 65 72 | 61 74 65 20 74 68 69 73 |an gener|ate this| |00002b30| 20 68 69 73 74 6f 67 72 | 61 6d 20 6f 66 20 63 6f | histogr|am of co| |00002b40| 6c 6f 72 20 75 73 61 67 | 65 20 66 6f 72 20 79 6f |lor usag|e for yo| |00002b50| 75 2e 20 49 66 20 79 6f | 75 72 20 63 75 73 74 6f |u. If yo|ur custo| |00002b60| 6d 20 6d 65 74 68 6f 64 | 20 77 61 6e 74 73 20 74 |m method| wants t| |00002b70| 68 69 73 2c 20 69 74 73 | 20 69 6e 69 74 69 61 6c |his, its| initial| |00002b80| 69 7a 61 74 69 6f 6e 20 | 73 75 62 72 6f 75 74 69 |ization |subrouti| |00002b90| 6e 65 20 6d 75 73 74 20 | 72 65 74 75 72 6e 20 74 |ne must |return t| |00002ba0| 68 65 20 76 61 6c 75 65 | 20 43 6f 6c 6f 72 42 61 |he value| ColorBa| |00002bb0| 6e 6b 49 73 35 35 35 20 | 66 6f 72 20 74 68 65 20 |nkIs555 |for the | |00002bc0| 63 6f 6c 6f 72 20 62 61 | 6e 6b 20 70 61 72 61 6d |color ba|nk param| |00002bd0| 65 74 65 72 2e 20 54 68 | 65 20 6f 63 74 72 65 65 |eter. Th|e octree| |00002be0| 20 6d 65 74 68 6f 64 20 | 64 65 73 63 72 69 62 65 | method |describe| |00002bf0| 64 20 6c 61 74 65 72 20 | 69 6e 20 74 68 69 73 20 |d later |in this | |00002c00| 61 72 74 69 63 6c 65 20 | 64 6f 65 73 20 6e 6f 74 |article |does not| |00002c10| 20 75 73 65 20 61 20 68 | 69 73 74 6f 67 72 61 6d | use a h|istogram| |00002c20| 2e 20 49 6e 73 74 65 61 | 64 2c 20 69 74 20 75 73 |. Instea|d, it us| |00002c30| 65 73 20 69 74 73 20 6f | 77 6e 20 63 75 73 74 6f |es its o|wn custo| |00002c40| 6d 20 63 6f 6c 6f 72 20 | 62 61 6e 6b 20 61 6e 64 |m color |bank and| |00002c50| 20 74 68 75 73 20 72 65 | 74 75 72 6e 73 20 43 6f | thus re|turns Co| |00002c60| 6c 6f 72 42 61 6e 6b 49 | 73 43 75 73 74 6f 6d 20 |lorBankI|sCustom | |00002c70| 61 73 20 69 74 73 20 63 | 6f 6c 6f 72 20 62 61 6e |as its c|olor ban| |00002c80| 6b 20 70 61 72 61 6d 65 | 74 65 72 2e 0d 48 4f 57 |k parame|ter..HOW| |00002c90| 20 54 48 45 20 4d 45 44 | 49 41 4e 20 4d 45 54 48 | THE MED|IAN METH| |00002ca0| 4f 44 20 57 4f 52 4b 53 | 0d 54 68 65 20 6d 65 64 |OD WORKS|.The med| |00002cb0| 69 61 6e 20 6d 65 74 68 | 6f 64 20 69 73 20 61 6e |ian meth|od is an| |00002cc0| 20 69 74 65 72 61 74 69 | 76 65 20 61 6c 67 6f 72 | iterati|ve algor| |00002cd0| 69 74 68 6d 20 74 68 61 | 74 20 76 69 65 77 73 20 |ithm tha|t views | |00002ce0| 74 68 65 20 63 6f 6c 6f | 72 73 20 69 6e 20 61 6e |the colo|rs in an| |00002cf0| 20 69 6d 61 67 65 20 61 | 73 20 69 66 20 74 68 65 | image a|s if the| |00002d00| 79 20 77 65 72 65 20 61 | 72 72 61 6e 67 65 64 20 |y were a|rranged | |00002d10| 69 6e 20 61 20 63 75 62 | 65 20 77 69 74 68 20 61 |in a cub|e with a| |00002d20| 78 65 73 20 72 65 70 72 | 65 73 65 6e 74 69 6e 67 |xes repr|esenting| |00002d30| 20 74 68 65 20 72 65 64 | 2c 20 67 72 65 65 6e 2c | the red|, green,| |00002d40| 20 61 6e 64 20 62 6c 75 | 65 20 63 6f 6d 70 6f 6e | and blu|e compon| |00002d50| 65 6e 74 73 2e 20 49 74 | 20 73 74 61 72 74 73 20 |ents. It| starts | |00002d60| 62 79 20 67 65 6e 65 72 | 61 74 69 6e 67 20 61 20 |by gener|ating a | |00002d70| 68 69 73 74 6f 67 72 61 | 6d 20 6f 66 20 74 68 65 |histogra|m of the| |00002d80| 20 73 6f 75 72 63 65 20 | 63 6f 6c 6f 72 73 2c 20 | source |colors, | |00002d90| 6a 75 73 74 20 61 73 20 | 74 68 65 20 70 6f 70 75 |just as |the popu| |00002da0| 6c 61 72 20 6d 65 74 68 | 6f 64 20 64 6f 65 73 2e |lar meth|od does.| |00002db0| 20 48 6f 77 65 76 65 72 | 2c 20 77 68 69 6c 65 20 | However|, while | |00002dc0| 74 68 65 20 70 6f 70 75 | 6c 61 72 20 6d 65 74 68 |the popu|lar meth| |00002dd0| 6f 64 20 69 73 20 70 72 | 65 74 74 79 20 6d 75 63 |od is pr|etty muc| |00002de0| 68 20 64 6f 6e 65 20 61 | 66 74 65 72 20 74 68 69 |h done a|fter thi| |00002df0| 73 2c 20 74 68 65 20 6d | 65 64 69 61 6e 20 6d 65 |s, the m|edian me| |00002e00| 74 68 6f 64 d5 73 20 72 | 65 61 6c 20 77 6f 72 6b |thod.s r|eal work| |00002e10| 20 68 61 73 20 6f 6e 6c | 79 20 6a 75 73 74 20 62 | has onl|y just b| |00002e20| 65 67 75 6e 2e 0d 54 68 | 65 20 66 69 72 73 74 20 |egun..Th|e first | |00002e30| 72 65 61 6c 20 73 74 65 | 70 20 69 73 20 74 6f 20 |real ste|p is to | |00002e40| 64 65 74 65 72 6d 69 6e | 65 20 74 68 65 20 73 6d |determin|e the sm| |00002e50| 61 6c 6c 65 73 74 20 52 | 47 42 20 63 75 62 65 20 |allest R|GB cube | |00002e60| 74 68 61 74 20 77 69 6c | 6c 20 68 6f 6c 64 20 61 |that wil|l hold a| |00002e70| 6c 6c 20 74 68 65 20 63 | 6f 6c 6f 72 73 20 69 6e |ll the c|olors in| |00002e80| 20 74 68 65 20 69 6d 61 | 67 65 2e 20 41 66 74 65 | the ima|ge. Afte| |00002e90| 72 20 66 69 6e 64 69 6e | 67 20 74 68 65 20 6d 65 |r findin|g the me| |00002ea0| 64 69 61 6e 20 63 6f 6c | 6f 72 20 61 6c 6f 6e 67 |dian col|or along| |00002eb0| 20 74 68 65 20 6c 6f 6e | 67 65 73 74 20 63 6f 6c | the lon|gest col| |00002ec0| 6f 72 20 61 78 69 73 2c | 20 69 74 20 74 68 65 6e |or axis,| it then| |00002ed0| 20 70 75 74 73 20 61 6c | 6c 20 74 68 65 20 63 6f | puts al|l the co| |00002ee0| 6c 6f 72 73 20 6f 6e 20 | 6f 6e 65 20 73 69 64 65 |lors on |one side| |00002ef0| 20 6f 66 20 74 68 61 74 | 20 63 6f 6c 6f 72 20 69 | of that| color i| |00002f00| 6e 74 6f 20 6f 6e 65 20 | 62 6f 78 20 61 6e 64 20 |nto one |box and | |00002f10| 74 68 65 20 72 65 6d 61 | 69 6e 69 6e 67 20 63 6f |the rema|ining co| |00002f20| 6c 6f 72 73 20 69 6e 74 | 6f 20 61 6e 6f 74 68 65 |lors int|o anothe| |00002f30| 72 20 62 6f 78 2e 20 49 | 74 20 63 6f 6e 74 69 6e |r box. I|t contin| |00002f40| 75 65 73 20 74 68 69 73 | 20 6d 65 61 73 75 72 69 |ues this| measuri| |00002f50| 6e 67 20 61 6e 64 20 73 | 70 6c 69 74 74 69 6e 67 |ng and s|plitting| |00002f60| 20 70 72 6f 63 65 73 73 | 20 75 6e 74 69 6c 20 74 | process| until t| |00002f70| 68 65 20 63 6f 6c 6f 72 | 73 20 68 61 76 65 20 62 |he color|s have b| |00002f80| 65 65 6e 20 61 73 73 69 | 67 6e 65 64 20 74 6f 20 |een assi|gned to | |00002f90| 61 73 20 6d 61 6e 79 20 | 62 6f 78 65 73 20 61 73 |as many |boxes as| |00002fa0| 20 63 6f 6c 6f 72 73 20 | 72 65 71 75 65 73 74 65 | colors |requeste| |00002fb0| 64 2e 20 54 68 65 6e 20 | 74 68 65 20 77 65 69 67 |d. Then |the weig| |00002fc0| 68 74 65 64 20 61 76 65 | 72 61 67 65 20 63 6f 6c |hted ave|rage col| |00002fd0| 6f 72 20 6f 66 20 65 61 | 63 68 20 6f 66 20 74 68 |or of ea|ch of th| |00002fe0| 65 20 62 6f 78 65 73 20 | 69 73 20 72 65 74 75 72 |e boxes |is retur| |00002ff0| 6e 65 64 20 61 73 20 74 | 68 65 20 63 6f 6c 6f 72 |ned as t|he color| |00003000| 20 73 65 74 20 74 6f 20 | 75 73 65 2e 0d 53 69 6e | set to |use..Sin| |00003010| 63 65 20 74 68 65 20 61 | 6c 67 6f 72 69 74 68 6d |ce the a|lgorithm| |00003020| 20 69 73 20 6d 75 63 68 | 20 65 61 73 69 65 72 20 | is much| easier | |00003030| 74 6f 20 76 69 73 75 61 | 6c 69 7a 65 20 69 6e 20 |to visua|lize in | |00003040| 74 77 6f 20 64 69 6d 65 | 6e 73 69 6f 6e 73 2c 20 |two dime|nsions, | |00003050| 77 65 d5 6c 6c 20 69 6c | 6c 75 73 74 72 61 74 65 |we.ll il|lustrate| |00003060| 20 68 6f 77 20 69 74 20 | 77 6f 72 6b 73 20 69 6e | how it |works in| |00003070| 20 74 68 65 20 72 65 64 | 2d 67 72 65 65 6e 20 70 | the red|-green p| |00003080| 6c 61 6e 65 20 6f 6e 6c | 79 2e 20 45 78 74 65 6e |lane onl|y. Exten| |00003090| 64 69 6e 67 20 74 68 65 | 20 61 6c 67 6f 72 69 74 |ding the| algorit| |000030a0| 68 6d 20 74 6f 20 74 68 | 72 65 65 20 64 69 6d 65 |hm to th|ree dime| |000030b0| 6e 73 69 6f 6e 73 20 69 | 73 20 73 74 72 61 69 67 |nsions i|s straig| |000030c0| 68 74 66 6f 72 77 61 72 | 64 2e 20 49 6e 20 46 69 |htforwar|d. In Fi| |000030d0| 67 75 72 65 20 33 2c 20 | 65 69 67 68 74 20 63 6f |gure 3, |eight co| |000030e0| 6c 6f 72 73 20 61 72 65 | 20 70 72 65 73 65 6e 74 |lors are| present| |000030f0| 20 69 6e 20 74 68 65 20 | 72 65 64 2d 67 72 65 65 | in the |red-gree| |00003100| 6e 20 63 6f 6c 6f 72 20 | 70 6c 61 6e 65 20 28 74 |n color |plane (t| |00003110| 68 65 20 62 6c 75 65 20 | 63 6f 6d 70 6f 6e 65 6e |he blue |componen| |00003120| 74 20 69 73 20 74 61 6b | 65 6e 20 61 73 20 30 20 |t is tak|en as 0 | |00003130| 66 6f 72 20 61 6c 6c 20 | 63 6f 6c 6f 72 73 29 2e |for all |colors).| |00003140| 20 49 6e 20 74 68 69 73 | 20 73 69 6d 70 6c 69 66 | In this| simplif| |00003150| 69 65 64 20 65 78 61 6d | 70 6c 65 2c 20 65 61 63 |ied exam|ple, eac| |00003160| 68 20 63 6f 6c 6f 72 20 | 6f 63 63 75 72 73 20 6f |h color |occurs o| |00003170| 6e 6c 79 20 6f 6e 63 65 | 2e 20 49 6e 20 74 68 65 |nly once|. In the| |00003180| 20 67 65 6e 65 72 61 6c | 20 63 61 73 65 2c 20 69 | general| case, i| |00003190| 66 20 61 20 63 6f 6c 6f | 72 20 6f 63 63 75 72 73 |f a colo|r occurs| |000031a0| 20 6d 6f 72 65 20 74 68 | 61 6e 20 6f 6e 63 65 2c | more th|an once,| |000031b0| 20 74 68 61 74 20 63 6f | 6c 6f 72 20 69 73 20 77 | that co|lor is w| |000031c0| 65 69 67 68 74 65 64 20 | 61 63 63 6f 72 64 69 6e |eighted |accordin| |000031d0| 67 6c 79 20 69 6e 20 74 | 68 65 20 66 69 6e 61 6c |gly in t|he final| |000031e0| 20 73 74 65 70 20 77 68 | 65 6e 20 74 68 65 20 63 | step wh|en the c| |000031f0| 6f 6c 6f 72 73 20 69 6e | 20 65 61 63 68 20 62 6f |olors in| each bo| |00003200| 78 20 61 72 65 20 61 76 | 65 72 61 67 65 64 2e 0d |x are av|eraged..| |00003210| 54 68 65 20 66 69 72 73 | 74 20 64 69 76 69 73 69 |The firs|t divisi| |00003220| 6f 6e 20 69 73 20 61 6c | 6f 6e 67 20 74 68 65 20 |on is al|ong the | |00003230| 67 72 65 65 6e 20 61 78 | 69 73 20 73 69 6e 63 65 |green ax|is since| |00003240| 20 74 68 65 20 64 69 66 | 66 65 72 65 6e 63 65 20 | the dif|ference | |00003250| 62 65 74 77 65 65 6e 20 | 74 68 65 20 6d 6f 73 74 |between |the most| |00003260| 20 67 72 65 65 6e 20 61 | 6e 64 20 74 68 65 20 6c | green a|nd the l| |00003270| 65 61 73 74 20 67 72 65 | 65 6e 20 63 6f 6c 6f 72 |east gre|en color| |00003280| 20 69 73 20 73 6c 69 67 | 68 74 6c 79 20 6c 61 72 | is slig|htly lar| |00003290| 67 65 72 20 74 68 61 6e | 20 74 68 65 20 64 69 66 |ger than| the dif| |000032a0| 66 65 72 65 6e 63 65 20 | 62 65 74 77 65 65 6e 20 |ference |between | |000032b0| 74 68 65 20 6d 6f 73 74 | 20 72 65 64 20 61 6e 64 |the most| red and| |000032c0| 20 74 68 65 20 6c 65 61 | 73 74 20 72 65 64 20 63 | the lea|st red c| |000032d0| 6f 6c 6f 72 2e 20 54 68 | 69 73 20 64 69 76 69 73 |olor. Th|is divis| |000032e0| 69 6f 6e 20 72 65 73 75 | 6c 74 73 20 69 6e 20 74 |ion resu|lts in t| |000032f0| 68 65 20 74 77 6f 20 62 | 6f 78 65 73 20 73 68 6f |he two b|oxes sho| |00003300| 77 6e 20 69 6e 20 73 74 | 65 70 20 32 20 6f 66 20 |wn in st|ep 2 of | |00003310| 46 69 67 75 72 65 20 33 | 2e 20 54 68 65 20 6c 61 |Figure 3|. The la| |00003320| 72 67 65 73 74 20 64 69 | 66 66 65 72 65 6e 63 65 |rgest di|fference| |00003330| 20 69 6e 20 63 6f 6c 6f | 72 73 20 61 6c 6f 6e 67 | in colo|rs along| |00003340| 20 6f 6e 65 20 61 78 69 | 73 20 69 73 20 6e 6f 77 | one axi|s is now| |00003350| 20 61 6c 6f 6e 67 20 74 | 68 65 20 72 65 64 20 61 | along t|he red a| |00003360| 78 69 73 20 6f 66 20 74 | 68 65 20 74 6f 70 20 62 |xis of t|he top b| |00003370| 6f 78 2e 20 54 68 75 73 | 2c 20 74 68 69 73 20 62 |ox. Thus|, this b| |00003380| 6f 78 20 69 73 20 64 69 | 76 69 64 65 64 20 69 6e |ox is di|vided in| |00003390| 74 6f 20 74 77 6f 20 61 | 6c 6f 6e 67 20 74 68 65 |to two a|long the| |000033a0| 20 72 65 64 20 61 78 69 | 73 2c 20 6c 65 61 76 69 | red axi|s, leavi| |000033b0| 6e 67 20 75 73 20 77 69 | 74 68 20 74 68 72 65 65 |ng us wi|th three| |000033c0| 20 62 6f 78 65 73 20 61 | 73 20 73 68 6f 77 6e 20 | boxes a|s shown | |000033d0| 69 6e 20 73 74 65 70 20 | 33 2e 20 54 68 69 73 20 |in step |3. 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In tw| |00003e40| 6f 20 64 69 6d 65 6e 73 | 69 6f 6e 73 20 77 65 d5 |o dimens|ions we.| |00003e50| 72 65 20 77 6f 72 6b 69 | 6e 67 20 77 69 74 68 20 |re worki|ng with | |00003e60| 61 20 71 75 61 64 74 72 | 65 65 20 69 6e 73 74 65 |a quadtr|ee inste| |00003e70| 61 64 20 6f 66 20 61 6e | 20 6f 63 74 72 65 65 2e |ad of an| octree.| |00003e80| 20 41 20 71 75 61 64 74 | 72 65 65 20 68 61 73 20 | A quadt|ree has | |00003e90| 66 6f 75 72 20 62 72 61 | 6e 63 68 65 73 20 61 74 |four bra|nches at| |00003ea0| 20 65 61 63 68 20 6e 6f | 64 65 2c 20 61 73 20 69 | each no|de, as i| |00003eb0| 6c 6c 75 73 74 72 61 74 | 65 64 20 69 6e 20 46 69 |llustrat|ed in Fi| |00003ec0| 67 75 72 65 20 34 2e 20 | 28 4e 6f 74 65 20 74 68 |gure 4. |(Note th| |00003ed0| 61 74 20 62 65 6c 6f 77 | 20 6c 65 76 65 6c 20 31 |at below| level 1| |00003ee0| 20 6f 6e 6c 79 20 6f 6e | 65 20 62 72 61 6e 63 68 | only on|e branch| |00003ef0| 20 70 65 72 20 6e 6f 64 | 65 20 69 73 20 66 6f 6c | per nod|e is fol| |00003f00| 6c 6f 77 65 64 20 74 6f | 20 61 20 64 65 65 70 65 |lowed to| a deepe| |00003f10| 72 20 6c 65 76 65 6c 2c | 20 66 6f 72 20 74 68 65 |r level,| for the| |00003f20| 20 73 61 6b 65 20 6f 66 | 20 73 69 6d 70 6c 69 66 | sake of| simplif| |00003f30| 79 69 6e 67 20 74 68 65 | 20 64 72 61 77 69 6e 67 |ying the| drawing| |00003f40| 2e 20 49 6e 20 72 65 61 | 6c 69 74 79 2c 20 65 61 |. In rea|lity, ea| |00003f50| 63 68 20 6e 6f 64 65 20 | 73 70 72 6f 75 74 73 20 |ch node |sprouts | |00003f60| 66 6f 75 72 20 62 72 61 | 6e 63 68 65 73 2c 20 65 |four bra|nches, e| |00003f70| 61 63 68 20 6f 66 20 77 | 68 69 63 68 20 69 6e 20 |ach of w|hich in | |00003f80| 74 75 72 6e 20 73 70 72 | 6f 75 74 73 20 66 6f 75 |turn spr|outs fou| |00003f90| 72 20 6d 6f 72 65 2c 20 | 61 6e 64 20 73 6f 20 6f |r more, |and so o| |00003fa0| 6e 20 74 6f 20 74 68 65 | 20 64 65 65 70 65 73 74 |n to the| deepest| |00003fb0| 20 6c 65 76 65 6c 2e 29 | 20 43 6f 6c 6f 72 73 20 | level.)| Colors | |00003fc0| 61 72 65 20 69 6e 73 65 | 72 74 65 64 20 69 6e 74 |are inse|rted int| |00003fd0| 6f 20 74 68 65 20 71 75 | 61 64 74 72 65 65 20 6d |o the qu|adtree m| |00003fe0| 75 63 68 20 61 73 20 74 | 68 65 79 20 77 6f 75 6c |uch as t|hey woul| |00003ff0| 64 20 62 65 20 69 6e 20 | 61 6e 20 6f 63 74 72 65 |d be in |an octre| |00004000| 65 2c 20 65 78 63 65 70 | 74 20 74 68 61 74 20 74 |e, excep|t that t| |00004010| 68 65 20 62 6c 75 65 20 | 63 6f 6d 70 6f 6e 65 6e |he blue |componen| |00004020| 74 20 69 73 20 6d 69 73 | 73 69 6e 67 2e 20 46 6f |t is mis|sing. Fo| |00004030| 72 20 69 6e 73 74 61 6e | 63 65 2c 20 74 68 65 20 |r instan|ce, the | |00004040| 30 2d 30 20 28 72 65 64 | 2d 67 72 65 65 6e 29 20 |0-0 (red|-green) | |00004050| 63 6f 6c 6f 72 20 69 73 | 20 74 68 65 20 66 69 72 |color is| the fir| |00004060| 73 74 20 65 6e 74 72 79 | 20 69 6e 20 74 68 65 20 |st entry| in the | |00004070| 6e 6f 64 65 2c 20 74 68 | 65 20 30 2d 31 20 63 6f |node, th|e 0-1 co| |00004080| 6c 6f 72 20 69 73 20 74 | 68 65 20 73 65 63 6f 6e |lor is t|he secon| |00004090| 64 20 65 6e 74 72 79 2c | 20 61 6e 64 20 74 68 65 |d entry,| and the| |000040a0| 20 31 2d 31 20 63 6f 6c | 6f 72 20 69 73 20 74 68 | 1-1 col|or is th| |000040b0| 65 20 66 6f 75 72 74 68 | 20 65 6e 74 72 79 2e 20 |e fourth| entry. | |000040c0| 54 68 75 73 2c 20 74 68 | 65 20 74 77 6f 2d 64 69 |Thus, th|e two-di| |000040d0| 6d 65 6e 73 69 6f 6e 61 | 6c 20 63 6f 6c 6f 72 20 |mensiona|l color | |000040e0| 76 61 6c 75 65 20 63 61 | 6e 20 73 74 69 6c 6c 20 |value ca|n still | |000040f0| 62 65 20 75 73 65 64 20 | 61 73 20 61 20 7a 65 72 |be used |as a zer| |00004100| 6f 2d 62 61 73 65 64 20 | 69 6e 64 65 78 20 69 6e |o-based |index in| |00004110| 74 6f 20 74 68 65 20 6e | 6f 64 65 2e 0d 57 65 20 |to the n|ode..We | |00004120| 74 68 69 6e 6b 20 6f 66 | 20 74 68 69 73 20 71 75 |think of| this qu| |00004130| 61 64 74 72 65 65 20 61 | 73 20 63 6f 72 72 65 73 |adtree a|s corres| |00004140| 70 6f 6e 64 69 6e 67 20 | 74 6f 20 61 20 63 6f 6f |ponding |to a coo| |00004150| 72 64 69 6e 61 74 65 20 | 70 6c 61 6e 65 20 66 6f |rdinate |plane fo| |00004160| 72 6d 65 64 20 62 79 20 | 74 77 6f 20 63 6f 6c 6f |rmed by |two colo| |00004170| 72 20 61 78 65 73 3b 20 | 65 61 63 68 20 62 72 61 |r axes; |each bra| |00004180| 6e 63 68 20 74 68 65 6e | 20 63 6f 72 72 65 73 70 |nch then| corresp| |00004190| 6f 6e 64 73 20 74 6f 20 | 61 20 71 75 61 64 72 61 |onds to |a quadra| |000041a0| 6e 74 20 6f 66 20 74 68 | 65 20 73 70 61 63 65 20 |nt of th|e space | |000041b0| 63 6f 76 65 72 65 64 20 | 62 79 20 74 68 65 20 70 |covered |by the p| |000041c0| 61 72 65 6e 74 20 6e 6f | 64 65 2e 20 46 6f 72 20 |arent no|de. For | |000041d0| 69 6e 73 74 61 6e 63 65 | 2c 20 69 66 20 61 20 71 |instance|, if a q| |000041e0| 75 61 64 74 72 65 65 20 | 69 73 20 62 65 69 6e 67 |uadtree |is being| |000041f0| 20 75 73 65 64 20 74 6f | 20 72 65 70 72 65 73 65 | used to| represe| |00004200| 6e 74 20 74 68 65 20 72 | 65 64 2d 67 72 65 65 6e |nt the r|ed-green| |00004210| 20 70 6c 61 6e 65 20 6f | 66 20 61 6e 20 52 47 42 | plane o|f an RGB| |00004220| 20 63 75 62 65 20 77 69 | 74 68 20 65 61 63 68 20 | cube wi|th each | |00004230| 61 78 69 73 20 72 61 6e | 67 69 6e 67 20 66 72 6f |axis ran|ging fro| |00004240| 6d 20 30 20 74 6f 20 38 | 2c 20 74 68 65 20 66 6f |m 0 to 8|, the fo| |00004250| 75 72 20 6c 65 76 65 6c | 2d 31 20 6e 6f 64 65 73 |ur level|-1 nodes| |00004260| 20 72 65 70 72 65 73 65 | 6e 74 20 74 68 65 20 66 | represe|nt the f| |00004270| 6f 75 72 20 71 75 61 64 | 72 61 6e 74 73 20 6f 66 |our quad|rants of| |00004280| 20 74 68 69 73 20 70 6c | 61 6e 65 20 64 65 66 69 | this pl|ane defi| |00004290| 6e 65 64 20 62 79 20 28 | 72 65 64 20 30 2d 34 2c |ned by (|red 0-4,| |000042a0| 20 67 72 65 65 6e 20 30 | 2d 34 29 2c 20 28 72 65 | green 0|-4), (re| |000042b0| 64 20 34 2d 38 2c 20 67 | 72 65 65 6e 20 30 2d 34 |d 4-8, g|reen 0-4| |000042c0| 29 2c 20 28 72 65 64 20 | 30 2d 34 2c 20 67 72 65 |), (red |0-4, gre| |000042d0| 65 6e 20 34 2d 38 29 2c | 20 61 6e 64 20 28 72 65 |en 4-8),| and (re| |000042e0| 64 20 34 2d 38 2c 20 67 | 72 65 65 6e 20 34 2d 38 |d 4-8, g|reen 4-8| |000042f0| 29 2e 20 54 68 65 20 6c | 65 76 65 6c 2d 32 20 6e |). The l|evel-2 n| |00004300| 6f 64 65 73 20 6f 66 20 | 74 68 65 20 28 72 65 64 |odes of |the (red| |00004310| 20 30 2d 34 2c 20 67 72 | 65 65 6e 20 30 2d 34 29 | 0-4, gr|een 0-4)| |00004320| 20 71 75 61 64 72 61 6e | 74 20 72 65 70 72 65 73 | quadran|t repres| |00004330| 65 6e 74 20 74 68 65 20 | 66 6f 75 72 20 71 75 61 |ent the |four qua| |00004340| 72 74 65 72 73 20 6f 66 | 20 74 68 69 73 20 70 61 |rters of| this pa| |00004350| 72 74 69 63 75 6c 61 72 | 20 71 75 61 64 72 61 6e |rticular| quadran| |00004360| 74 2c 20 61 6e 64 20 73 | 6f 20 6f 6e 20 64 6f 77 |t, and s|o on dow| |00004370| 6e 20 74 6f 20 74 68 65 | 20 64 65 65 70 65 73 74 |n to the| deepest| |00004380| 20 6c 65 76 65 6c 2e 20 | 4f 66 20 63 6f 75 72 73 | level. |Of cours| |00004390| 65 2c 20 69 6e 20 74 68 | 65 20 63 61 73 65 20 6f |e, in th|e case o| |000043a0| 66 20 74 68 65 20 6f 63 | 74 72 65 65 20 28 74 68 |f the oc|tree (th| |000043b0| 65 20 73 74 72 75 63 74 | 75 72 65 20 74 68 61 74 |e struct|ure that| |000043c0| 20 6f 75 72 20 0d 0d 46 | 69 67 75 72 65 20 34 0d | our ..F|igure 4.| |000043d0| 41 20 46 69 76 65 2d 4c | 65 76 65 6c 20 51 75 61 |A Five-L|evel Qua| |000043e0| 64 74 72 65 65 0d 61 6c | 67 6f 72 69 74 68 6d 20 |dtree.al|gorithm | |000043f0| 61 63 74 75 61 6c 6c 79 | 20 75 73 65 73 29 2c 20 |actually| uses), | |00004400| 74 68 65 20 65 69 67 68 | 74 20 62 72 61 6e 63 68 |the eigh|t branch| |00004410| 65 73 20 63 6f 6e 74 61 | 69 6e 65 64 20 62 79 20 |es conta|ined by | |00004420| 61 20 6e 6f 64 65 20 63 | 6f 72 72 65 73 70 6f 6e |a node c|orrespon| |00004430| 64 20 74 6f 20 74 68 65 | 20 65 69 67 68 74 20 73 |d to the| eight s| |00004440| 75 62 63 75 62 65 73 20 | 6f 66 20 74 68 65 20 73 |ubcubes |of the s| |00004450| 70 61 63 65 20 72 65 70 | 72 65 73 65 6e 74 65 64 |pace rep|resented| |00004460| 20 62 79 20 74 68 65 20 | 65 6e 74 69 72 65 20 6e | by the |entire n| |00004470| 6f 64 65 2e 0d 54 68 65 | 20 6f 63 74 72 65 65 20 |ode..The| octree | |00004480| 61 6c 67 6f 72 69 74 68 | 6d 20 66 69 72 73 74 20 |algorith|m first | |00004490| 61 64 64 73 20 63 6f 6c | 6f 72 73 20 28 6c 65 61 |adds col|ors (lea| |000044a0| 76 65 73 29 20 74 6f 20 | 74 68 65 20 74 72 65 65 |ves) to |the tree| |000044b0| 20 75 6e 74 69 6c 20 74 | 68 65 72 65 20 69 73 20 | until t|here is | |000044c0| 6f 6e 65 20 6d 6f 72 65 | 20 63 6f 6c 6f 72 20 28 |one more| color (| |000044d0| 6c 65 61 66 29 20 74 68 | 61 6e 20 72 65 71 75 65 |leaf) th|an reque| |000044e0| 73 74 65 64 2e 20 54 68 | 65 6e 20 74 68 65 20 74 |sted. 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T| |00004640| 68 65 73 65 20 6c 65 61 | 76 65 73 20 61 72 65 20 |hese lea|ves are | |00004650| 74 68 65 6e 20 72 65 64 | 75 63 65 64 20 74 6f 20 |then red|uced to | |00004660| 74 68 65 20 70 61 72 65 | 6e 74 20 6e 6f 64 65 2e |the pare|nt node.| |00004670| 20 54 68 65 20 70 72 6f | 63 65 73 73 20 63 6f 6e | The pro|cess con| |00004680| 74 69 6e 75 65 73 20 75 | 6e 74 69 6c 20 74 68 65 |tinues u|ntil the| |00004690| 20 74 72 65 65 20 63 6f | 6e 74 61 69 6e 73 20 6e | tree co|ntains n| |000046a0| 6f 20 6d 6f 72 65 20 74 | 68 61 6e 20 74 68 65 20 |o more t|han the | |000046b0| 6e 75 6d 62 65 72 20 6f | 66 20 63 6f 6c 6f 72 73 |number o|f colors| |000046c0| 20 28 6c 65 61 76 65 73 | 29 20 72 65 71 75 65 73 | (leaves|) reques| |000046d0| 74 65 64 20 61 6e 64 20 | 6e 6f 20 6d 6f 72 65 20 |ted and |no more | |000046e0| 63 6f 6c 6f 72 73 20 72 | 65 6d 61 69 6e 20 74 6f |colors r|emain to| |000046f0| 20 62 65 20 61 64 64 65 | 64 2e 20 54 68 65 20 66 | be adde|d. 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The di| |000049a0| 73 61 64 76 61 6e 74 61 | 67 65 20 6f 66 20 74 68 |sadvanta|ge of th| |000049b0| 69 73 20 63 68 6f 69 63 | 65 20 69 73 20 74 68 61 |is choic|e is tha| |000049c0| 74 20 74 68 65 20 6f 63 | 74 72 65 65 20 6d 65 74 |t the oc|tree met| |000049d0| 68 6f 64 20 6d 75 73 74 | 20 6d 61 6b 65 20 64 65 |hod must| make de| |000049e0| 63 69 73 69 6f 6e 73 20 | 6f 6e 20 77 68 69 63 68 |cisions |on which| |000049f0| 20 63 6f 6c 6f 72 73 20 | 74 6f 20 74 68 72 6f 77 | colors |to throw| |00004a00| 20 6f 75 74 20 62 61 73 | 65 64 20 6f 6e 20 69 6e | out bas|ed on in| |00004a10| 63 6f 6d 70 6c 65 74 65 | 20 69 6e 66 6f 72 6d 61 |complete| informa| |00004a20| 74 69 6f 6e 2e 41 6e 6f | 74 68 65 72 20 69 6e 74 |tion.Ano|ther int| |00004a30| 65 72 65 73 74 69 6e 67 | 20 64 69 66 66 65 72 65 |eresting| differe| |00004a40| 6e 63 65 20 69 73 20 74 | 68 61 74 20 74 68 65 20 |nce is t|hat the | |00004a50| 6f 63 74 72 65 65 20 61 | 6c 67 6f 72 69 74 68 6d |octree a|lgorithm| |00004a60| 20 63 61 6e 20 61 63 74 | 75 61 6c 6c 79 20 72 65 | can act|ually re| |00004a70| 74 75 72 6e 20 66 65 77 | 65 72 20 63 6f 6c 6f 72 |turn few|er color| |00004a80| 73 20 74 68 61 6e 20 72 | 65 71 75 65 73 74 65 64 |s than r|equested| |00004a90| 2c 20 69 6e 73 74 65 61 | 64 20 6f 66 20 61 6c 77 |, instea|d of alw| |00004aa0| 61 79 73 20 72 65 74 75 | 72 6e 69 6e 67 20 74 68 |ays retu|rning th| |00004ab0| 65 20 65 78 61 63 74 20 | 6e 75 6d 62 65 72 2e 20 |e exact |number. | |00004ac0| 54 68 65 6f 72 65 74 69 | 63 61 6c 6c 79 2c 20 74 |Theoreti|cally, t| |00004ad0| 68 69 73 20 63 61 6e 20 | 72 65 64 75 63 65 20 74 |his can |reduce t| |00004ae0| 68 65 20 61 63 63 75 72 | 61 63 79 20 6f 66 20 74 |he accur|acy of t| |00004af0| 68 65 20 72 65 74 75 72 | 6e 65 64 20 63 6f 6c 6f |he retur|ned colo| |00004b00| 72 20 73 65 74 2c 20 73 | 69 6e 63 65 20 74 68 65 |r set, s|ince the| |00004b10| 72 65 20 61 72 65 20 66 | 65 77 65 72 20 63 6f 6c |re are f|ewer col| |00004b20| 6f 72 73 20 74 6f 20 72 | 65 70 72 65 73 65 6e 74 |ors to r|epresent| |00004b30| 20 74 68 65 20 66 75 6c | 6c 20 72 61 6e 67 65 20 | the ful|l range | |00004b40| 61 6e 64 20 64 65 74 61 | 69 6c 20 6f 66 20 74 68 |and deta|il of th| |00004b50| 65 20 70 69 63 74 75 72 | 65 2e 20 48 6f 77 65 76 |e pictur|e. Howev| |00004b60| 65 72 2c 20 77 65 20 68 | 61 76 65 20 66 6f 75 6e |er, we h|ave foun| |00004b70| 64 20 74 68 61 74 20 6d | 6f 73 74 20 69 6d 61 67 |d that m|ost imag| |00004b80| 65 73 20 64 6f 20 72 65 | 74 75 72 6e 20 65 69 74 |es do re|turn eit| |00004b90| 68 65 72 20 74 68 65 20 | 66 75 6c 6c 20 6e 75 6d |her the |full num| |00004ba0| 62 65 72 20 6f 66 20 63 | 6f 6c 6f 72 73 20 72 65 |ber of c|olors re| |00004bb0| 71 75 65 73 74 65 64 20 | 6f 72 20 6f 6e 6c 79 20 |quested |or only | |00004bc0| 6f 6e 65 20 6f 72 20 74 | 77 6f 20 66 65 77 65 72 |one or t|wo fewer| |00004bd0| 2e 0d 46 6f 72 20 70 75 | 72 70 6f 73 65 73 20 6f |..For pu|rposes o| |00004be0| 66 20 63 6f 6d 70 61 72 | 69 73 6f 6e 2c 20 77 65 |f compar|ison, we| |00004bf0| d5 6c 6c 20 64 69 73 63 | 75 73 73 20 68 6f 77 20 |.ll disc|uss how | |00004c00| 74 68 65 20 6f 63 74 72 | 65 65 20 6d 65 74 68 6f |the octr|ee metho| |00004c10| 64 20 70 69 63 6b 73 20 | 74 68 65 20 62 65 73 74 |d picks |the best| |00004c20| 20 66 6f 75 72 20 63 6f | 6c 6f 72 73 20 69 6e 20 | four co|lors in | |00004c30| 61 20 63 6f 6c 6f 72 20 | 70 6c 61 6e 65 20 77 68 |a color |plane wh| |00004c40| 65 6e 20 67 69 76 65 6e | 20 74 68 65 20 73 61 6d |en given| the sam| |00004c50| 65 20 65 69 67 68 74 20 | 63 6f 6c 6f 72 73 20 61 |e eight |colors a| |00004c60| 73 20 75 73 65 64 20 69 | 6e 20 74 68 65 20 65 78 |s used i|n the ex| |00004c70| 61 6d 70 6c 65 20 66 6f | 72 20 74 68 65 20 6d 65 |ample fo|r the me| |00004c80| 64 69 61 6e 20 6d 65 74 | 68 6f 64 2e 20 54 68 65 |dian met|hod. The| |00004c90| 20 70 72 6f 63 65 73 73 | 20 69 73 20 69 6c 6c 75 | process| is illu| |00004ca0| 73 74 72 61 74 65 64 20 | 69 6e 20 46 69 67 75 72 |strated |in Figur| |00004cb0| 65 20 35 2e 20 4e 6f 74 | 65 20 74 68 61 74 20 74 |e 5. 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Un| |000058a0| 66 6f 72 74 75 6e 61 74 | 65 6c 79 2c 20 62 6f 74 |fortunat|ely, bot| |000058b0| 68 20 61 6c 67 6f 72 69 | 74 68 6d 73 20 66 61 6c |h algori|thms fal| |000058c0| 6c 20 73 6f 6d 65 77 68 | 61 74 20 73 68 6f 72 74 |l somewh|at short| |000058d0| 20 6f 66 20 74 68 69 73 | 20 67 6f 61 6c 2c 20 65 | of this| goal, e| |000058e0| 73 70 65 63 69 61 6c 6c | 79 20 77 69 74 68 20 69 |speciall|y with i| |000058f0| 6d 61 67 65 73 20 74 68 | 61 74 20 68 61 76 65 20 |mages th|at have | |00005900| 61 20 66 61 69 72 6c 79 | 20 77 65 6c 6c 20 64 69 |a fairly| well di| |00005910| 73 70 65 72 73 65 64 20 | 73 65 74 20 6f 66 20 63 |spersed |set of c| |00005920| 6f 6c 6f 72 73 2e 0d 57 | 65 20 63 61 6e 20 74 68 |olors..W|e can th| |00005930| 69 6e 6b 20 6f 66 20 73 | 65 76 65 72 61 6c 20 61 |ink of s|everal a| |00005940| 72 65 61 73 20 77 68 65 | 72 65 20 62 6f 74 68 20 |reas whe|re both | |00005950| 63 6f 75 6c 64 20 62 65 | 20 69 6d 70 72 6f 76 65 |could be| improve| |00005960| 64 2e 20 46 69 72 73 74 | 2c 20 62 6f 74 68 20 61 |d. 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Whi|le this | |00005bd0| 70 72 6f 64 75 63 65 73 | 20 74 68 65 20 63 6f 6c |produces| the col| |00005be0| 6f 72 20 74 68 61 74 20 | 6d 6f 73 74 20 61 63 63 |or that |most acc| |00005bf0| 75 72 61 74 65 6c 79 20 | 72 65 70 72 65 73 65 6e |urately |represen| |00005c00| 74 73 20 65 61 63 68 20 | 62 6f 78 2c 20 69 74 20 |ts each |box, it | |00005c10| 6e 65 63 65 73 73 61 72 | 69 6c 79 20 6c 65 61 76 |necessar|ily leav| |00005c20| 65 73 20 73 6f 6d 65 20 | 63 6f 6c 6f 72 73 20 75 |es some |colors u| |00005c30| 6e 72 65 61 63 68 61 62 | 6c 65 2c 20 65 76 65 6e |nreachab|le, even| |00005c40| 20 62 79 20 64 69 74 68 | 65 72 69 6e 67 2e 20 41 | by dith|ering. A| |00005c50| 20 62 65 74 74 65 72 20 | 63 68 6f 69 63 65 20 6f | better |choice o| |00005c60| 66 20 63 6f 6c 6f 72 20 | 6d 69 67 68 74 20 62 65 |f color |might be| |00005c70| 20 74 68 65 20 63 6f 72 | 6e 65 72 20 6f 66 20 74 | the cor|ner of t| |00005c80| 68 65 20 66 69 6e 61 6c | 20 62 6f 78 20 74 68 61 |he final| box tha| |00005c90| 74 d5 73 20 66 61 72 74 | 68 65 73 74 20 61 77 61 |t.s fart|hest awa| |00005ca0| 79 20 66 72 6f 6d 20 74 | 68 65 20 63 65 6e 74 65 |y from t|he cente| |00005cb0| 72 20 6f 66 20 74 68 65 | 20 52 47 42 20 63 75 62 |r of the| RGB cub| |00005cc0| 65 2e 20 54 68 69 73 20 | 77 6f 75 6c 64 20 61 73 |e. 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A goo|d genera| |00006300| 6c 20 61 6c 67 6f 72 69 | 74 68 6d 20 77 6f 75 6c |l algori|thm woul| |00006310| 64 20 70 72 6f 62 61 62 | 6c 79 20 74 72 79 20 74 |d probab|ly try t| |00006320| 6f 20 69 6e 63 6f 72 70 | 6f 72 61 74 65 20 62 6f |o incorp|orate bo| |00006330| 74 68 20 6f 66 20 74 68 | 65 73 65 20 65 66 66 65 |th of th|ese effe| |00006340| 63 74 73 20 62 79 20 68 | 61 76 69 6e 67 20 61 6e |cts by h|aving an| |00006350| 20 6f 63 63 75 72 72 65 | 6e 63 65 20 74 68 72 65 | occurre|nce thre| |00006360| 73 68 6f 6c 64 3b 20 63 | 6f 6c 6f 72 73 20 74 68 |shold; c|olors th| |00006370| 61 74 20 6f 63 63 75 72 | 20 66 65 77 65 72 20 74 |at occur| fewer t| |00006380| 68 61 6e 20 61 20 63 65 | 72 74 61 69 6e 20 6e 75 |han a ce|rtain nu| |00006390| 6d 62 65 72 20 6f 66 20 | 74 69 6d 65 73 20 77 6f |mber of |times wo| |000063a0| 75 6c 64 20 62 65 20 63 | 6f 6e 73 69 64 65 72 65 |uld be c|onsidere| |000063b0| 64 20 6e 6f 69 73 65 20 | 61 6e 64 20 65 69 74 68 |d noise |and eith| |000063c0| 65 72 20 74 68 72 6f 77 | 6e 20 6f 75 74 20 63 6f |er throw|n out co| |000063d0| 6d 70 6c 65 74 65 6c 79 | 20 6f 72 20 72 65 64 75 |mpletely| or redu| |000063e0| 63 65 64 20 62 65 66 6f | 72 65 20 6d 6f 72 65 20 |ced befo|re more | |000063f0| 73 69 67 6e 69 66 69 63 | 61 6e 74 20 63 6f 6c 6f |signific|ant colo| +--------+-------------------------+-------------------------+--------+--------+ Only 25.0 KB of data is shown above.