Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Steerable-Scalable Kernels for Edge Detection and Junction Analysis
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Scale-Space: Its Natural Operators and Differential Invariants
IPMI '91 Proceedings of the 12th International Conference on Information Processing in Medical Imaging
Optimal Local Weighted Averaging Methods in Contour Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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 ${\cal L}_1$ 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.