What, Mathematically Speaking, are Images?
Dr Garry Newsam (Intelligence Surveillance & Reconnaissance Division, DSTO)
MSI Computational Maths SeminarDATE: 2010-12-06
TIME: 16:00:00 - 17:00:00
LOCATION: G35 John Dedman Building
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ABSTRACT:
Analysts have constructed a rich conceptual hierarchy of function spaces in which problems can be framed and solved, but have been less concerned as to where real world objects such as images might fit within it. (Statisticians have constructed alternative models, in which much more attention is given to tests whether the models fit the data, but analysis still provides most of the structure used to frame image processing problems and construct numerical solutions for them.) During the last decade, however, a surprising consensus has emerged among analysts working with images: contrary to intuition, images do not fall within the standard L^p spaces but rather are distributions possibly best placed in H^{-1} . This unexpected characterisation appears to be the only way to accommodate consistent empirical observations that key properties and statistics of images exhibit power law scaling. The talk will briefly review the evolution of various mathematical models for images of natural scenes (with credit to those who first appreciated their special structure), and give a quick intuitive explanation of how power law scaling can arise just through perspective projection. Finally it will touch on the implications of this finding for formulation of standard image processing problems, such as image segmentation.
BIO:
After completing a PhD on numerical solution of inverse problems at Harvard and a postdoc on inverse problems at Australian National University, in 1989 Garry joined DSTO to work on image analysis. Since then he has led a number of groups and programs in image and signal processing, mainly focussed on developing operational solutions for detecting objects in images or signals. Personal research interests in this time have included: fast multi-resolution methods for interpolation and analysis of scattered data; synthetic aperture imaging; simulating random processes; signal geolocation; and statistical decision theory. For the last few years, however, he has been mainly working on something completely different: supporting the long slow gestation of an Australian space policy and program.
