Fred's ImageMagick Scripts



    Licensing:

    Copyright © Fred Weinhaus

    My scripts are available free of charge for non-commercial use, ONLY.

    For use of my scripts in commercial (for-profit) environments or non-free applications, please contact me (Fred Weinhaus) for licensing arrangements. My email address is fmw at alink dot net.

    If you: 1) redistribute, 2) incorporate any of these scripts into other free applications or 3) reprogram them in another scripting language, then you must contact me for permission, especially if the result might be used in a commercial or for-profit environment.

    Usage, whether stated or not in the script, is restricted to the above licensing arrangements. It is also subject, in a subordinate manner, to the ImageMagick license, which can be found at: http://www.imagemagick.org/script/license.php

FUZZYTHRESH


Automatically thresholds an image to binary (b/w) format using the fuzzy c-means technique.

Download Script

last modified: November 03, 2015



USAGE: fuzzythresh [-r radius] [-g graph] infile outfile
USAGE: fuzzythresh [-help]

-r ..... radius ......... radius for spatial correlation; float;
......................... radius>=0; the default=0 signifies to
......................... ignore spatial correlation
-g ..... graph .......... graph specifies whether to generate a
......................... histogram graph image displaying the
......................... location and value of the threshold;
......................... choices are: view or save;
......................... default is no graph

PURPOSE: To automatically thresholds an image to binary (b/w) format using the fuzzy c-means technique.

DESCRIPTION: FUZZYTHRESH automatically thresholds an image to binary (b/w) format. It assume the histogram is bimodal, i.e. is the composite of two bell-shaped distributions representing the foreground and background classes. The fuzzy c-means appoach iteratively thresholds the image, computes a weighted mean for the foreground (above threshold data) and background (at and below threshold value), computes a new threshold equal to the average of these two means and repeats until there is no change in threshold between successive iterations. The weighting factors are the normalized inverse square difference between each pixel in the foreground or background data sets and the corresponding mean. However, to allow for spatial correlation of the graylevels among neighboring pixels, a Gaussian filtered version of the weighting factors may be used. This script is similar to the isodatathresh script, except uses a weighted mean calculation.

ARGUMENTS:

-r radius ... RADIUS is the radius of a Gaussian (blur) filter to apply to the weighting factors for the mean calculation. This permits spatial correlation of the graylevels among neighboring pixels and is useful to remove noise from the result. The radius value should be set to the size of the features in the image. Values are floats greater than zero. The default=0 signifies to ignore spatial correlation.

-g graph ... GRAPH specifies whether to generate a graph (image) of the histogram, displaying the location and value of the threshold. The choices are: view, save and none. If graph=view is selected, the graph will be created and displayed automatically, but not saved. If graph=save is selected, then the graph will be created and saved to a file using the infile name, with "_histog_fuzzy.gif" appended, but the graph will not be displayed automatically. If -g option is not specified, then no graph will be created.

NOTE: It is highly recommended that the output not be specified as a JPG image as that will cause compression and potentially a non-binary (i.e. a graylevel) result. GIF is the recommended output format.

REFERENCES: see the following:
http://www.iiitmk.ac.in/wiki/images/d/d2/Fuzzy_CMeans.pdf
http://www.quantlet.com/mdstat/scripts/xag/html/xaghtmlframe149.html
http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/cmeans.html

CAVEAT: No guarantee that this script will work on all platforms, nor that trapping of inconsistent parameters is complete and foolproof. Use At Your Own Risk.


EXAMPLES


Fuzzy C-Means Thresholding Of Various Images -- Radius=0

Pictures Were Obtained from:
blood.jpg from http://www.istanbul.edu.tr/eng/ee/jeee/main/pages/issues/is62/62008.pdf
fingerprint.jpg from http://www.istanbul.edu.tr/eng/ee/jeee/main/pages/issues/is62/62008.pdf
flower.jpg from http://www.jhlabs.com/ip/blurring.html
house.jpg from http://en.wikipedia.org/wiki/Otsu's_method
kanji.jpg from http://www.measurement.sk/2004/S1/Yong.pdf
parts.gif from http://www.ph.tn.tudelft.nl/Courses/FIP/noframes/fip-Segmenta.html
rice.jpg from http://www.istanbul.edu.tr/eng/ee/jeee/main/pages/issues/is62/62008.pdf
tank.jpg from http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=ADA464347&Location=U2&doc=GetTRDoc.pdf
textsample.jpg from http://signal.ece.utexas.edu/seminars/dsp_seminars/01fall/211_seeger_mf.pdf
lena2g_edge1.jpg was created using the IM function -edge 1

Original Image

Thresholded Image

Histogram



Fuzzy C-Means Thresholding Of Various Images -- Radius>0

Pictures Were Obtained from:
kanji.jpg from http://www.measurement.sk/2004/S1/Yong.pdf
rice.jpg from http://www.istanbul.edu.tr/eng/ee/jeee/main/pages/issues/is62/62008.pdf
lena2g_edge1.jpg was created using the IM function -edge 1

Original Image

Thresholded Image

Histogram

radius=30

radius=3

radius=10



See A Comparison Of Each Image Against Each Thresholding Technique



What the script does is as follows:

  • Converts the image to grayscale
  • Thresholds the image at the average of the min and max image graylevels as a mask for the foreground data
  • Creates a negated version of the thresholded image for a mask for the background data
  • Computes a normalized inverse squared difference image relative to each mean for the weighting images
  • Multiplies the image by the foreground weighting image and the foreground mask image
  • Multiplies the image by the background weighting image and the background mask image
  • Gets the mean or average values from each of the two resulting product image
  • Gets the mean of each of the masks
  • Divides the means of the product images by the means of the mask images
    to compute a proper mean value for only the foreground or background pixels in each image
  • Computes a new threshold from the average of these two means
  • Repeats each step above until the threshold does not change between
    successive iterations