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

Chapter 1: Introduction 6We then perform region-growing segmentation and save the patch adjacencyinformation as illustrated in Figure 1.3(c).Now that we have segmented surface patches that make the object, we compute thecurvature variation measure on each of these patches (Figure 1.3(d)). We haveborrowed concepts from Shannon’s idea [Shannon, 1948] of measuring information ona probabilistic framework. We hence define the curvature variation measure as theentropy of curvature along that surface. We present a brief analysis on variouscurvature estimation methods on triangle meshes and reiterate the importance ofbandwidth optimized density estimation to stabilize the information measure. Ourmodification of Shannon’s definition of entropy is normalized and invariant to scale.The normalized resolution invariant measure attempts to quantify the complexity ofthe surface by a single number. Similar shapes at different scales will have equalmeasures.1.3 Document OrganizationThe remainder of this thesis documents the theory and results of our data collectionand CVM algorithm. Chapter 2 presents a survey of the literature on the shape analysisand description of 2D images and 3D models. Here we explain why methods in 2Dcannot be extended to 3D and discuss the scope for extending the state of the art.Then, we present our experience with the data acquisition using a laser-based scannerfor creating 3D models of automotive components and scenes under the vehicle inChapter 3. Chapter 4 documents the theory that supports our shape analysis algorithm.We test our algorithm on the acquired data and present our results in Chapter 5. Theseexperimental results demonstrate capabilities of our algorithm and its scope as anobject recognition system. Finally, we conclude with possible extensions in Chapter 6.