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In the present work, the geometric transformations referred to such as rotation, translation, and scaling, are two-dimensional transformations, i.e., transformations on the plane.
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85033316524
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note
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It is important to note that fast-Fourier transform (FFT) implementations lead to s=0...N-1, and that the corrections must be made in such a way that each frequency component is multiplied by its respective correct value of s.
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note
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Although traditional pyramid algorithms are based on a smoothing followed by subsampling, since no new information can be created by increasing the resolution of an already sampled signal, an oversampled version of the original shape was generated. This procedure makes sense under the shape analysis viewpoint, since the obtained image represents in fact a scaled version of the shape, presenting the characteristics of a real situation, such as differences due discrete sampling and the contour tracking algorithm.
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