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Empirical mode decomposition was proposed recently as a time frequency analysis tool for nonlinear and nonstationary signals. Despite from its many advantages, problems such as “uniqueness” problem have been discovered which limit the application. Although this problem has been addressed to some extent by various extensions of the original algorithm, the solution is far from satisfactory in some scenarios. In this work we propose two variants of the original algorithm, with emphasis on providing unified representations. R-EMD makes use of a set of reference signals to guide the decomposition therefore guarantees unified representation for multiple 1D signals. 2D- BEMD takes advantage of a projection procedure and is capable of providing unified representation between a pair of 2D signals. Application of the proposed algorithms on different problems in biometric and image processing demonstrates promising results and indicates the effectiveness of the proposed framework.

Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n_c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n_c + 1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods given in the Princeton Shape Benchmark.

Thesis (Ph.D.)--Tufts University, 2000. / Adviser: Joseph P. Noonan. Submitted to the Dept. of Electrical Engineering. Includes bibliographical references (leaves 83-87). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (M.Sc.)--Victoria University of Wellington, 2008. / Includes bibliographical references and index.

Rozprawa habilitacyjna--Warsaw. / Bibliography: p. [111]-114.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 70-72).

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Yu, Xingxing; Committee Member: Duke, Richard; Committee Member: Tetali, Prasad; Committee Member: Thomas, Robin; Committee Member: Vigoda, Eric. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 107-108). Also available on the World Wide Web.