Publication 1995 Issue No. 10 - October Abstract - Optimal L1${\cal L}_1$ Approximation of the Gaussian Kernel With Application to Scale-Space Construction
Optimal L1${\cal L}_1$ Approximation of the Gaussian Kernel With Application to Scale-Space Construction
October 1995 (vol. 17 no. 10)
pp. 1015-1019
 ASCII Text x 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 and Machine Intelligence, vol. 17, no. 10, pp. 1015-1019, October, 1995.
 BibTex x @article{ 10.1109/34.464565,author = {Xiaoping Li and Tongwen Chen},title = {Optimal L1${\cal L}_1$ Approximation of the Gaussian Kernel With Application to Scale-Space Construction},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {17},number = {10},issn = {0162-8828},year = {1995},pages = {1015-1019},doi = {http://doi.ieeecomputersociety.org/10.1109/34.464565},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - Optimal L1${\cal L}_1$ Approximation of the Gaussian Kernel With Application to Scale-Space ConstructionIS - 10SN - 0162-8828SP1015EP1019EPD - 1015-1019A1 - Xiaoping Li, A1 - Tongwen Chen, PY - 1995KW - Gaussian kernelKW - scale-spaceKW - total positivityKW - ${\cal L}_1$ approximation.VL - 17JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -

Abstract—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 $\left\{\cal L\right\}_1$ 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.

Index Terms:
Gaussian kernel, scale-space, total positivity, ${\cal L}_1$ approximation.
Citation:
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 and Machine Intelligence, vol. 17, no. 10, pp. 1015-1019, Oct. 1995, doi:10.1109/34.464565