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Image Compression



MML and Image Processing: Peter TISCHER




Chris Wallace and David Boulton first developed MML to help decide whether a given body of data was homogeneous or whether items in the data could be grouped with other items in the data to form subpopulations. This is known in the statistical literature as mixture modelling. In image processing we are particularly interested in saying which pixels belong with other pixels and form meaningful subdivisions of a picture. Humans are very adept at immediately recognising which parts of a picture belong together, a fundamental step in discerning the content of the picture. The subdivisions are often called segments.

Wallace and Boulton developed a program called "snob" which was very successful in determining whether a body of data could be subdivided into clusters. However, they were unable to extend this work to images. A breakthrough occurred when Peter Tischer came up with what he calls the Tischer observation and realised that ideas from Data Compression could be used in conjunction with snob's two-part messages to taylor two-part messages for images and thus to apply MML to the problem of image segmentation.

Under Peter Tischers's supervision, a masters student, Tetra Lindarto, applied this to the question of how best to threshold a greyscale image. Thresholding an image divides it into 2 segments. Normally these are the foreground and the background.

Another PhD student under Peter Tischer's supervision, Torsten Seemann, also applied the MML principle to segmenting images. In low level image processing, the value of a picture element (pixel) is often combined with the values of neighbouring pixel values in order to improve the value of the pixel. This is successful because neighbouring pixels often have information in common. For example, if one pixel is a particular shade of green, its neighbouring pixels are often part of the same segment and have a very similar shade of green. However, if the neighbouring pixels belong to different segments, they actually do not share information and their values should never be combined. This happens at the borders between objects, say like the border between a black square and a green background.

In his PhD thesis, Torsten Seemann enunciated this principle, which he calls 'Local Segmentation', and used it to construct a variety of algorithms for low level image processing. He concentrated on one problem in particular, namely the removal of Gaussian noise, and showed that the application of the local segmentation principle leads to algorithms which are the best at performing this task. In carrying out local segmentation, Seemann considered both non-MML approaches and an MML approach and showed that the MML approach led to the best results. He also sketched out how MML and local segmentation could be applied to other low level image processing tasks.

Work is currently continuing on how to apply MML to the general problem of image segmentation.




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