Fractal

This module calculates the fractal dimension (D) of images using the grid-intercept method (Tatsumi et al. 1989). D is calculated by fitting a linear regression to the following equation:

where r = resolution of image (number of pixels per unit length), n = the number of pixels intersecting a portion of the image and K is a constant.   Ten separate resolutions are used to generate the values used in this regression.  Resolution values ranged from the maximum image resolution (rmax), that of the input image, to rmax * 10 at even intervals. 

Maximum resolution is taken as the value in the "Scale Size"  /  "# Pixels/Length" text field in the Preferences dialog (Figure 2).  The "Use Scale Bar" option is not available for this module.

BranChing outputs two values for each image processed, D and K.  

Example output from this module and details on different methods for preparing images for analysis are provided in Berntson (1994b).