To the Graduate Council: I am submitting herewith a thesis written by ...

Chapter 4: Algorithm Overview 404.1.1 Informational Approach to Shape Description – Curvature VariationMeasureWe would like to formulate our algorithm on the basis that shape information isdirectly proportional to the variation in curvature (curvature of the boundary for 2Dcurves and curvature of surfaces on 3D surfaces) and inversely proportional tosymmetry. We propose to extract shape information from the images and analyze aprocedure to discriminate objects based on a single number that is a measure of itsvisual complexity.To understand the basis of our algorithm better, let us start with a small and simpleexample. In Figure 4.1, we show a circle and an arbitrary contour. Visually, the moreappealing of the two is the circle while the complex of the two contours is the arbitrarycontour. We propose that smoothly varying curvature conveys very little informationwhile sharp variation in curvature increases the complexity for shape description. Inthis context, we would like to refresh the fact that more likely an event is, lesser theinformation it conveys. The circle has uniformly varying curvature; that is there is nouncertainty involved in the variation of its curvature, which means it has the leastshape information. Figure 4.2 is the block diagram of our algorithm for 2D silhouettesand segmented boundary contours. The block diagram represents the CVM algorithmfor 2D contours. We get back to the example of the circle again. The curvature of acircle is uniformly distributed. The density of curvature hence is a Kronecker deltafunction of strength one. The entropy of a Kronecker delta function is zero. This resultimplies that circular and linear contours convey no significant shape information. Wenote that circles of different radii will also have zero shape information. We argue thatchange in scale (radius) adds no extra shape information. On the other hand, the broaderthe curvature density, the higher the entropy and more complex the shape is. The mostcomplex shape hence would be the one that has randomly varying curvature at everypoint on the boundary.Figure 4.1: A circle and an arbitrary object.