vpml(1)

PROGRAM
vpml - Estimates the Fractal Dimension of an image based on the P(m,L)

SYNTAX

vpml

-i  input image

-o1 resulting multiband fractal dimension output image

-o2 output image specifying the fractal dimension of each class

[-f1]
    output file for P(m,L) statistics

[-l]
    select the initial size of the sliding window

[-u]
    select the final size of the sliding window

[-s]
    select the window step size or interval

[-q]
    select the range of moments (-r/2 <= 0 >= r/2)

[-V]
    Gives the version for vpml

[-U]
    Gives the usage for vpml

[-P]
    Prompts for command line options

[-A [file1]]
    Creates the answer file called vpml.ans or file1

[-a [file1]]
    Uses vpml.ans or file1 as the answer file

DESCRIPTION
vpml estimates the fractal dimension of an image based on the probability that there are m pixels within a window of size L centered on a pixel from a particular class. For a selected range of window sizes (L), the window is centered on the first occurrence of the pixel belonging to a particular class. The number of pixels within a window of size L, belonging to a specific class are counted (including the center pixel of the window), and a "histogram" is formed as the window is moved over the image. This "histogram" represents the total number of occurrences, m, of a class of pixels in a window of size L. From this, a normalized histogram is formed, which yields an estimate of the probability density function, P(m,L), for each window size L.

All selected moments (q) of the P(m,L) distributions for each of the desired window sizes are determined, and a linear regression or "best fit line" is found for the moment generating function, log(M(L))^1/q, versus the log of the window size, log(L). The slope of the "best fit line" provides an estimate for the fractal dimension, D.

The center pixel of the largest window, Lmax, is replaced with the computed fractal dimension based on the probability density function, P(m,L). The largest window size, Lmax, determines the resulting size of the fractal dimension image. This results in a border of size (Lmax / 2) around the image, which is set to zero.

The input arguments are described as follows:

-i  specifies the input image, which must be of data type BYTE or INTEGER. The input image must be a single band image.

-o1 specifies the output image, which will be a multiband image representing the fractal dimension of the input image for each of the specified moments. The resulting output image will be of data storage type FLOAT, and will have a border of pixels of value zero. The size of the border will be determined by the size of the largest window specified. This can be determined from the following formulation, (Lmax -1) / 2 = border size. Where Lmax is the size of the largest window used. For example, if the largest window size is 9, then the border size will be (9 - 1) / 2 = 4 pixels.

-o2 specifies fractal dimension image, representing the fractal dimension vectors for each class and moment. This image will always have a row size of 1 and a column size determined by the number of classes in the input image. The number of data bands will be equal to the number of moments used in the estimation of the fractal dimension.

-f1 uses an ASCII file as output for the image information specifying the size of the input image, number of classes in the input image, and the range of moments used in the estimation of the fractal dimension. Also included is a listing of the fractal dimensions for each class and moment.

-l  specifies the initial or lower size of the sliding window. This MUST be an odd number resulting in a window with a center pixel. This means that the minimum size of the sliding window is 3 x 3. The default value is 3, resulting in an initial window size of 3 x 3.

-u  specifies the final or upper size of the sliding window. This MUST also be an odd number resulting in a window with a center pixel. The size of the upper window MUST be at least one step greater than the lower window size. That is, if the lower window is 3 x 3, then the minimum size of the upper window must be 5 x 5, or one step greater than the lower window. This is necessary, since there must be at least two points for a best fit line to be formed determining the slope and ultimately the fractal dimension.

-s  specifies the step size or interval used when specifying a range of window sizes. The default value is two, corresponding to the next odd window size with a center pixel. This may be helpful when a wide range of window sizes is required, as it will reduce the number of points generated for the best fit line and hence the number of calculations.

-q  specifies the range of moments to base the P(m,L) fractal dimension calculations on. This must be an odd number, corresponding to the number of moments centered on zero. For example, a value of 5 would result in the computation of the fractal dimension for the range of moments, -2, -1, 0, 1, 2. The default value is 3, resulting in the range of -1, 0, 1.

The input image MUST be of data storage type BYTE or INTEGER.

REQUIRED ARGUMENTS

-i  type: infile
    desc: input image

-o1 type: outfile
    desc: resulting multiband fractal dimension output image

-o2 type: outfile
    desc: output image specifying the fractal dimension of each class

OPTIONAL ARGUMENTS

-f1 type: outfile
    desc: output file for P(m,L) statistics

-l  type: integer
    desc: select the initial size of the sliding window
    default: 3
    bounds: 3 < [-l] < 10000

-u  type: integer
    desc: select the final size of the sliding window
    default: 5
    bounds: 5 < [-u] < 10000

-s  type: integer
    desc: select the window step size or interval
    default: 2
    bounds: 2 < [-s] < 10000

-q  type: integer
    desc: select the range of moments (-r/2 <= 0 >= r/2)
    default: 3
    bounds: 3 < [-q] < 1000

EXAMPLES

vpml -i in_img -o1 out_img1 -o2 out_img2 -f1 file1 -u 11 -s 4 -q 5

this will estimate the fractal dimension of the in_img using a range of sliding window sizes from 3 x 3 (default lower value of 3) to an upper size of 11 x 11, with a step size of 4. This means that windows of size 3 x 3, 7 x 7, and 11 x 11 will be used in the fractal dimension calculation. A value of 5 was selected for the number of moments to be calculated, meaning that the fractal dimension will be computed for the range of moments, -2, -1, 0, 1, 2. The resulting output image, out_img1 will consist of a five-band FLOAT image with each band representing the fractal dimension for a particular moment, q. The out_img2 will consist of a single row, five-band image specifying the fractal dimension for each class of the input image and moment, q. The ascii file1 will provide the user with information on the size of the input image, number of classes, and the resulting fractal dimensions for each class and moment.

SEE ALSO
intro(1), verror(3), vgparms(3), vutils(3), lvpml(3) vfractal(1)

RESTRICTIONS

The input image MUST be of data storage type BYTE or INTEGER. The output images are of data storage type FLOAT.

COPYRIGHT
Copyright 1991, University of New Mexico. All rights reserved.