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Optimal ℒ1 approximation of the Gaussian kernel with application to scale-space construction

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2 Author(s)
Xiaoping Li ; Dept. of Electr. Eng., Calgary Univ., Alta., Canada ; Tongwen Chen

Scale-space construction based on Gaussian filtering requires convolving signals with a large bank of Gaussian filters with different widths. We propose an efficient way for this purpose by L1 optimal approximation of the Gaussian kernel in terms of linear combinations of a small number of basis functions. Exploring total positivity of the Gaussian kernel, the method has the following properties: 1) the optimal basis functions are still Gaussian and can be obtained analytically; 2) scale-spaces for a continuum of scales can be computed easily; 3) a significant reduction in computation and storage costs is possible. Moreover, this work sheds light on some issues related to use of Gaussian models for multiscale image processing

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:17 ,  Issue: 10 )