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.

翻译：本文构建了多参数线性尺度空间的最大核集，该核集允许我们构建用于一维连续信号分类与识别的树结构，其方法类似于高斯线性尺度空间方法。文中给出了傅里叶变换公式，并用于快速高效的计算。推导了最大核集的一些有用性质。我们还强化并推广了先前关于高斯核分类的一些结果。最后，引入了一种新的拓扑不变树构建方法。