Waveform recognition in the presence of domain and amplitude noise

In this paper, we discuss the problem of recognizing single-dimensional, real-valued, functions in the presence of domain noise (i.e., noise that affects the domain rather than the amplitude). This problem is inspired by the field of on-line character recognition where it is more natural to view the hand as deforming the domain of the character rather than adding noise to its amplitude. The results obtained illustrate the difficulties one faces when dealing with both domain and amplitude deformation of waveforms or images. Our major result is a set of sufficient conditions that a recognition metric has to satisfy. Examples of metrics that satisfy these conditions, and hence are appropriate for recognition when the deformation affects the domain rather than the amplitude, include the supnorm metric and the total variation metric. Furthermore, we extend the results to the case when a waveform is corrupted by both amplitude and domain deformation