Curve and polygon evolution techniques for image processing

The objective of this thesis is to develop image processing algorithms which are efficient, statistically robust and sufficiently general, in order to account for noise and textural variations in images, and which have the ability to extract and provide compact and useful descriptions of target objects in images, for object recognition and tracking purposes. The main contribution is the development of image processing algorithms, which are based on the theory of curve evolution with connections to information theory and probability theory. These connections form the basis for extracting a compact object description, in the form of a polygonal contour. One contribution is the development of a new class of curve evolutions designed to preserve prescribed polygonal structures in an image while removing noise. A local stochastic formulation of a geometric heat equation led to our proposal of its vanishing at pre-defined directions. Under these flows, the limiting shape of a curve is a polygon, pre-specified by the form and the parameters of the specific flow. The second contribution of the thesis is the development of a new active contour model which merges the desirable polygonal representation of an object directly to the image segmentation process by adapting an information-theoretic measure into an active contour framework with an unsupervised texture segmentation goal. The polygon-propagating models we develop can capture texture boundaries more reliably than the continuous active contour models because the evolution of an active polygon vertex depends on an overall speed function integrated along its two adjacent polygon edges rather than on pointwise measurements along continuous contour points. Thus, higher-order statistics which provide more adapted information than the first and second-order, are captured. Another contribution in this sequel is a new global polygon regularizer algorithm which uses electrostatics principles. The final contribution of the thesis is the development of a simple and efficient object tracking algorithm well-adapted to polygonal objects. This is an extension of the second contribution of the thesis, and the key idea here is centered around tracking a relatively few vertices together with their corresponding edges, which in turn yields a bookkeeping simplicity and hence efficiency.