A Multiple Parameter Linear Scale-Space for one dimensional Signal Classification
This work addresses signal classification for domains like audio or time-series analysis, but it appears incremental as it builds on existing Gaussian scale-space approaches.
The authors tackled the problem of classifying one-dimensional continuous signals by constructing a maximal set of kernels for a multi-parameter linear scale-space, enabling efficient computation and introducing a new topologically invariant tree construction method.
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.