Testing

Testing

Since one aim of this research is the investigation of a possible criterion for threshold assessment, it was considered important to use a suitably wide set of test images, both natural and synthetic, in order to see any potential pattern emerge and so avoid drawing a conclusion based on one perhaps anomolous value. It was also deemed important to not only select images that were considered to be very well suited to the task of mixture modelling thresholding, but also to select images that may cause the method to possibly fail.

Implementation Details
Synthetic Images
Natural Images
Testing with Snob

Implementation Details

The code implemented for the iterative mixture modelling was based on code produced by Bertolo (2001) for his investigation into probabilistic distance criteria. He implemented Relative Entropy, and replaced the uniform distribution with Gaussian and Poisson distributions. One aim of this project is to extend this approach, and examine in greater detail the results within a mixture modelling framework.

For very large N the Poisson distribution approximates the binomial distribution, which itself is a discrete approximation to the Gaussian distribution. Due to the large number of pixels in an image, the usual decaying shape of the distribution is not present, and so the Rayleigh distribution was added, both right and left-skewed, to account for the decaying or skewed shape that is a common property in the histograms of natural images. The inclusion of the Rayleigh distribution also allows for a comparison of models of equivalent complexities. The calculation of the optimal threshold(s) was also implemented for the different distributions to more accurately classify the pixels into the most appropriate segments. An attempt was also made to account for overlapping of the tails of the Gaussian component distributions as described in Cho, Haralick & Yi (1989), although this produced a very minimal improvement on the results.

The current implementation of the mixture modelling method steps through each grey level, fitting the appropriate number of distributions to each side of the threshold(s). The best model is selected when the Kullback-Leibler measure is minimised. The threshold is set as the value at which the component distributions intersect.

For all of the formulas and derviations it is much easier for you to look at my thesis.

Synthetic Images

Synthetic images were created with specific distributions, namely, those implemented in the iterative mixture modelling approach. Each distribution has a set of three synthetic images for two and three components, with each set of the three images containing distributions with no overlap, slight overlap and heavy overlap of the components. The rationale behind the creation of synthetic images was twofold; to examine how well the parameters were being estimated for both non-overlapping and overlapping regions of the histogram, and to provide a lower bound for Kullback-Leibler measure assessment. All synthetic images are 8 bits per pixel greyscale GIF images. The synthetic images comprising two components are each 500 x 500, and the three component images are 600 x 600. The synthetic images can be downloaded from here. A full listing of the synthetic images and their histograms is in Appendix B of my thesis.

Natural Images

The natural images used came from three different sources. The images house.gif and hotel.gif were downloaded from Carnegie Mellon Image Database in PNG format. The images bubbles.gif, bottles.gif, headct.gif, fingerprint.gif, matches.gif, messy-matches.gif, moon.gif and tungsten.gif were downloaded from Gonzalez and Woods' Digital Image Processing book in JPEG format. All images were converted to GIF format to comply with the Monash Image Library functionality. The remaining images were downloaded from Monash Image Library in GIF format.

Testing with Snob

The Fortran version of Snob was used (Wallace & Dowe 1996). Control files were created for each image input file so each could be run numerous times, with the classification yielding the shortest message length taken.