Space-Variant Filtering Models for Recovering Depth

Abstract

The Fourier transform is a very useful tool for performing time-invariant filtering of signals. The filtering approach generally reduces to multiplying the Fourier transform of a signal by a function H(w), the transfer function of the filter, to obtain a filtered version of the signal. For time-variant filtering, it is necessary to look for other representations that play a similar role to that of the Fourier transform in the time-invariant case. In [Sub88], Subotic and Saleh suggested a new approach to time-variant filtering. The approach is based upon the generation of the time-frequency representation (TFR) of a signal, multiplication of that representation by a function H(w,t), which can be regarded as the time-varying transfer function, and obtaining a filtered output by an inverse operation, assuming that the inverse exists. This is an intuitive generalization of time-invariant filtering. The nature of the resultant time-variant filter depends on the type of the TFR chosen.