Conclusion

Conclusion and Future Work

Aims Restated
Conclusion
Future Work

Aims Restated

One aim of this research was to examine the use of mixture modelling as an approximation to an image's histogram in greater detail using an iterative approach, and so examine the suitability of the Kullback-Leibler information measure for use as a possible relative or objective criterion for assessment of threshold selection. The other aim was to test the classification program Snob to find the appropriate number of classes in an image's histogram (and so find the best segmentation of the image), while also assessing the suitability of the Minimum Message Length criterion as an objective measure for assessing the quality of thresholding results.

Conclusion

Were the aims of this project achieved? In part, yes. Due to unexpected results from Snob, the Minimum Message Length criterion was not assessed for its suitability as an objective criterion. A deeper investigation into Snob's classification of greyscale images needs to be undertaken, specifically to isolate the problem of overfitting, but also to clarify the discrepancy seen between the entropy of the image's histogram and message length given for some classifications.

With respect to the investigation of the mixture modelling as an approximation to an image's histogram, it was shown that mixture modelling provides a strong and flexible solution, and one which generalises gracefully to multiple thresholds. During the course of this research the strengths and also some potential weaknesses of the iterative approach were isolated. The ability of the two parameter distributions to adequately model the histogram's pdf by way of their shape parameters is clear, although this feature was also shown to be a drawback in some instances, notably when irregularities and discontinuities are present in the histogram. Evidence suggesting that the skewed shape of the Rayleigh distribution better models the movement of the pdf from the object regions to the boundary regions was presented. Obvious parallels between the Gaussian and Rayleigh mixture models were also highlighted by this research, which open this approach to the possibility of using mixture models comprising different components, each with the same complexity. Incorporating different components would potentially increase the accuracy of the model representing the histogram, and so produce more precise segmentation results.

The Kullback-Leibler measure may yet be suitable as a relative criterion to assess thresholding results. The information measures examined suggested a distinction between the success and failure of segmentation, however, further testing needs to be done before any numerical values can assigned.

For the unsupervised mixture modelling approach with Snob as the tool for classification, mixed results were obtained. Snob correctly classified two of the Gaussian synthetic images, but for the synthetic image with the most overlap and also for the natural images, the number of classes found was deemed too high to be considered useful for the task of thresholding. The discrete nature of the data as the possible cause of this problem was ruled out by further testing, using floating point values to emulate the true continuous nature of an image. Randomly sampling the data points at very small rates produced exceptionally good classifications, more in line with the desired results. These results clearly need to be examined further. The conclusion from this is that some measure of similarity of the pixels needs to be found before the data is presented to Snob for classification, and so avoid the problem of overfitting.

The unusual result of the message length falling below the entropy of the image's histogram suggests that information is being lost during classification. The principle of Minimum Message Length states that the receiver must be able to decode the message exactly, hence this apparent loss of information violates this precondition. To fully understand why this loss of information is occurring, significant work needs to be done which is currently outside the scope of this thesis.

Future Work

The iterative mixture modelling approach implemented provided excellent results and should therefore be extended. The addition of extra distributions of differing complexities would enable further examination of the Kullback-Leibler measure as a possible relative criterion. Work could be done to improve the sensitivity of the Gaussian and, to a lesser extent the Rayleigh distributions, to irregularities in the histogram.

The use of Snob to classify images has previously not been examined in any great detail. This research has highlighted issues that need to be addressed before successful results are obtained. A better way of representing the histogram could well produce the desired results, perhaps by finding an initial measure of similarity of the pixels before the data is presented to Snob. More importantly, the issue of the message length falling below the entropy of the histogram should be further investigated.