20 April 2015 Fourier transform-based method for pattern matching: affine invariance and beyond
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Several pattern-matching techniques have focused on affine invariant pattern matching, mainly because rotation, scale, translation, and shear are common image transformations. In some situations, other transformations may be modeled as a small deformation on top of an affine transformation. This work presents an algorithm which aims at improving existing Fourier Transform (FT)-based pattern matching techniques in such a situation. The pattern is first decomposed into non-overlapping concentric circular rings, which are centered in middle of the pattern. Then, the FT of each ring is computed. Essentially, adding the individual complex-valued FTs provides the overall FT of the pattern. Past techniques used the overall FT to identify the parameters of the affine transformation between two patterns. In this work, it is assumed that the rings may be rotated with respect to each other, thus, parameters of transformations beyond the affine ones can be computed. The proposed method determines this variable angle of rotation starting from the FT of the outermost ring and moving inwards to the FT of the innermost ring. The variable angle of rotation provides information about the directional properties of a pattern. Two methods are investigated, namely a dynamic programming algorithm and a greedy algorithm, in order to determine the variable angle of rotation. The intuition behind this approach is that since the rings are not necessarily aligned in the same manner for different patterns, their ring FTs may also be rotated with respect to each other. Simulations demonstrate the effectiveness of the proposed technique.
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Madhuri Gundam, Madhuri Gundam, Dimitrios Charalampidis, Dimitrios Charalampidis, } "Fourier transform-based method for pattern matching: affine invariance and beyond", Proc. SPIE 9477, Optical Pattern Recognition XXVI, 94770I (20 April 2015); doi: 10.1117/12.2176969; https://doi.org/10.1117/12.2176969


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