In this dissertation, we have presented three mesh processing techniques for dif-ferent 3-D graphics-related applications. The three mesh processing methods include the visual salience-guided mesh decomposition (Chapter 2), the cognitive psychology-based approach for 3-D shape retrieval (Chapter 3), and the fragile watermarking method for authenticating 3-D polygonal meshes (Chapter 4).
In Chapter 2, we analyzed and pointed out that the theory of part salience proposed by Hoffman and Singh [51] can be converted into computational pro-cesses for extracting significant components from 3-D meshes. More specifically, the protrusion and boundary strength are modeled as the degree of center on the surface and the total-area-of-border change, respectively. These visually salient features are incorporated into the mesh decomposition process based on two rules.
They are (1) the protrusion degree characterized over the entire surface can be used as a guide to choose the salient representatives of the parts and (2) the boundary strength characterized over the entire surface can be used as a guide to find the locale of a part’s boundary. Since the features used to guide the de-composition process are closely related to Hoffman and Singh’s theory of visual
Chapter 5. Conclusions and Future Work
salience, the proposed decomposition algorithm can not only appropriately mimic the function of a human visual system, but also efficiently decompose a 3-D mesh into parts. Moreover, the proposed decomposition method is robust against ran-domization of vertex coordinates. To the best of our knowledge, this is the first 3-D mesh decomposition scheme that not only identifies the part’s boundaries defined by the minima rule, but also associates the part with its visual salience.
In Chapter 3, we incorporate a set of cognitive psychology-based principles into the design of 3-D shape analysis and retrieval algorithms. In order to realize the conceptual rule of “recognition-by-components,” the proposed visual salience-guided mesh decomposition is adopted to decompose a 3-D mesh-based shape into parts. Next, the decomposed components are individually analyzed and quanti-fied according to the psychology theory of visual salience [51]. Using the above concept, one can label a D shape and then decide on which components on the 3-D shape are the most salient ones. In order to represent the geometrical relations among the parts of a 3-D shape, we propose the use of spherical parameterization to map the labeled 3-D mesh onto a unit sphere. In this way, a set of spherical domain-based shape descriptors, which encodes a part’s relation and salience, can be constructed such that comparing 3-D shapes can be done within a normal-ized sphere. Moreover, our system provides a coarse-to-fine search scheme: (1) a components strategy for coarse search and (2) a recognition-by-visually-salient-components strategy for fine search. More precisely, our
relation-based shape descriptor implements the recognition-by-components strategy to perform a coarse search. On the other hand, the visual salience-based shape de-scriptor realizes the recognition-by-visually-salient-components strategy to refine the results (up to the best m objects) retrieved in the coarse search stage.
Finally, in Chapter 4, we propose a fragile watermarking method for authen-ticating 3-D polygonal meshes. The proposed authentication scheme can tolerate unintentional modifications, such as vertex re-ordering and floating-point trun-cation. The robustness comes from the principle that the two hash functions can be designed to form binary state spaces particularly helpful for defining the ro-bustness. Another benefit of our scheme is that region-based tampering detection is achieved by our fragile watermarking method. To the best of our knowledge, this is the first 3-D mesh authentication scheme that can detect malicious attacks involving incidental modifications.
In future work, we shall establish a large 3-D model database for performance evaluation and present more quantitative results for comparison with the existing 3-D shape retrieval systems. Moreover, use of combined features to perform the retrieval task will be the main subject for our future work.
Chapter 5. Conclusions and Future Work
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