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In this paper, polar and spherical Fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. The proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures. The theory is compactly presented with an emphasis...
The calculation of local features at points of interest is a vital part of many current image retrieval and object detection systems. The wavelet-based interest point detector by Loupias et al. was especially developed for image retrieval applications. We show how the detector can be extended by a Laplacian scale selection mechanism to provide scale information and compare it to other state of the...
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