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2009
Habilitation Thesis
Titel
Deep structure, singularities, and computer vision
Abstract
Since several decades computers are obtaining a more and more prominent place in society. Increasing computational possibilities combined with expanding storage potentialities in the field of computer vision urge for methods that can perform the tasks of identifying, comparing, and classifying objects in digital data automatically. In order to be highly user-independent and trustworthy stable for cost and time saving purposes, many methods combine sophisticated knowledge of different areas of mathematics, computer science, and human perception. In this work the mathematical concept of Singularities takes a prominent role. It describes situations that are special in some sense. A simple example is given by a topographical map with height lines describing a mountain landscape. Almost all lines are simply connected, but there are some special cases: at certain positions the lines reduce to a point, for instance at a mountain top, while at other locations (at passes) they intersect themselves. Furthermore, the height lines can have sharp corners and shown maximal and minimal bending. These features involve so-called critical points, the locally special points. A second concept used in this work is the reduction of structure. Again (topographic) maps serve as an example. The larger the scales on which they are drawn, the less the details are visible, but the more the main structure is kept. This effect is known as scale space. Instead of considering the image at one particular scale, or even a set of scales, the continuum of images at all scales, the Deep Structure, is taken.
ThesisNote
Graz, TU, Habil.-Schrift, 2009
Verlagsort
Graz