In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space approach. Fourier transform formulas are provided and used for quick and efficient computations. A number of useful properties of the maximal set of kernels are derived. We also strengthen and generalize some previous results on the classification of Gaussian kernels. Finally, a new topologically invariant method of constructing trees is introduced.
@article{arxiv.2305.13350,
title = {A Multiple Parameter Linear Scale-Space for one dimensional Signal Classification},
author = {Leon A. Luxemburg and Steven B. Damelin},
journal= {arXiv preprint arXiv:2305.13350},
year = {2023}
}
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arXiv admin note: text overlap with arXiv:2305.13255