Shape : representation, description, similarity and recognition

Arıca, Nafiz
In this thesis, we study the shape analysis problem and propose new methods for shape description, similarity and recognition. Firstly, we introduce a new shape descriptor in a two-step method. In the first step, the 2-D shape information is mapped into a set of 1-D functions. The mapping is based on the beams, which are originated from a boundary point, connecting that point with the rest of the points on the boundary. At each point, the angle between a pair of beams is taken as a random variable to define the statistics of the topological structure of the boundary. The third order statistics of all the beam angles is used to construct 1-D Beam Angle Statistics (BAS) functions. In the second step, we apply a set of feature extraction methods on BAS functions in order to describe it in a more compact form. BAS functions eliminate the context-dependency of the representation to the data set. BAS function is invariant to translation, rotation and scale. It is insensitive to distortions. No predefined resolution or threshold is required to define the BAS functions. Secondly, we adopt three different similarity distance methods defined on the BAS feature space, namely, Optimal Correspondence of String Subsequences, Dynamic Warping and Cyclic Sequence Matching algorithms. Main goal in these algorithms is to minimize the distance between two BAS features by allowing deformations. Thirdly, we propose a new Hidden Markov Model (HMM)topology for boundary based shape recognition. The proposed topology called Circular HMM is both ergodic and temporal. Therefore, the states can be revisited in finite time intervals while keeping the sequential information in the string, which represents the shape. It is insensitive to size changes. Since it has no starting and terminating state, it is insensitive to the starting point of the shape boundary. Experiments are done on the dataset of


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Citation Formats
N. Arıca, “Shape : representation, description, similarity and recognition,” Ph.D. - Doctoral Program, Middle East Technical University, 2003.