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Characterization of Signals from Multiscale Edges
July 1992 (vol. 14 no. 7)
pp. 710-732

A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented.

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Index Terms:
1D signals; 2D signals; picture processing; multiscale Canny edge detection; local maxima; wavelet theory; pattern recognition; multiscale edge representation; image coding; pattern recognition; picture processing
S. Mallat, S. Zhong, "Characterization of Signals from Multiscale Edges," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 710-732, July 1992, doi:10.1109/34.142909
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