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<p><it>Abstract</it>—Scale-space construction based on Gaussian filtering requires convolving signals with a large bank of Gaussian filters with different widths. In this paper we propose an efficient way for this purpose by <math><tmath>${\cal L}_1$</tmath></math> 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 <it>continuum</it> 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.</p>
Gaussian kernel, scale-space, total positivity, ${\cal L}_1$ approximation.
Xiaoping Li, Tongwen Chen, "Optimal L1${\cal L}_1$ Approximation of the Gaussian Kernel With Application to Scale-Space Construction", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 1015-1019, October 1995, doi:10.1109/34.464565
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