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

Chapter 5: Analysis and Results 705.3 Results of our Informational ApproachIn Chapter 4 we discussed our CVM algorithm that quantifies surface shapecomplexity. We compute curvature based on the method suggested by [Abidi, 1995]and measure boundary complexity as the Shannon’s entropy of curvature on 2Dcontours. We have presented these results in [Page et al., 2003b]. We discuss someimportant results on X-ray and range images. We also analyze some limitations ofusing Shannon entropy and the need for a normalized information measure beforediscussing the results of our graph representation on automotive components.5.3.1 Intensity and Range ImagesIn Figure 5.8(a) we show results on simple curves. We have made a few importantassumptions with these curves. These curves are of the same resolution and areuniformly sampled. We have computed the Shannon entropy of the turning angle ateach point on the boundary as the shape complexity measure (SCM). We note thatSCM and CVM are similar measures but are not equivalent.SCM inspired thedevelopment of CVM, and CVM represents the evolution of SCM from lessonslearned on scaling and resolution We would like to emphasize in these results on howshape information behaves with symmetry and how important the assumption on sizeand resolution turns out to be. We would also like to note that the shape informationfrom the Shannon’s measure cannot be compared if the two images are not at the sameresolution and comparable size. Hence for the real data we have normalized thesegmented region of interest for size and resolution and then computed the curvaturebasedmeasure on the normalized boundary contour. We would like to recall fromChapter 2 and note that our method falls under the boundary-based descriptionmethods. In Figure 5.8(b) we show an example with an X-ray image of a baggage. Thebag contains a few objects that we have segmented manually. We take each of thesegmented objects and then compute the shape information on each of these contours.Our measure categorizes complex objects and simple ones with satisfactory ease.Next, we show some results on range images in Figure 5.8(c).We believe that we willbe able to distinguish between the man-made structures that have flat and nice edgeslike the building in Figure 5.8 (c) and natural vegetation that has rugged boundaries.5.3.2 Surface RuggednessIn terms of resolution we would like to present some results on synthetic DEMs(Digital Elevation Maps) of the same resolution. The Shannon’s entropy of curvaturegives a consistent ruggedness measure of the surface. But we still face inconsistencywith resolution. We formulate our algorithm on the heuristic that the variation in theshape characteristics of surfaces is mathematically the variation of curvature. Wedefine shape information as the entropy of the curvature density of the surface underconsideration.