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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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