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In this paper we study the scale-space classification of signals via themaximal set of kernels. We use a geometric approach which arises naturally whenwe consider parameter variations in scale-space. We derive the Fouriertransform formulas for quick and efficient computation of zero-crossings andthe corresponding classifying trees. General theory of convergence forconvolutions is developed, and practically useful properties of scale-spaceclassification are derived as a consequence also give a complete topologicaldescription of level curves for convolutions of signals with the maximal set ofkernels. We use these results to develop a bifurcation theory for the curvesunder the parameter changes. This approach leads to a novel set of integerinvariants for arbitrary signals.

The Geometric Approach to the Classification of Signals via a Maximal Set of Signals