A Multiple Parameter Linear Scale-Space for one dimensional Signal Classification

Scale-space filtering provides a powerful framework for the structural feature extraction, and classification and recognition of waveforms. It is based on convolving a signal with a one-parametric family of kernels and the convolutions can be used to construct certain trees to correspond to the original signal ([5,17,23,26,28]). In this article we solve the following important problems: (I) We construct a maximal set of kernels that allows us to construct trees and have the property that the signals with the same shape result in equivalent trees. It turns out that this maximal set of kernels is a set of pth frac tional derivatives of a Gaussian.