Scale Space Implementation - Other Multi-scale Approaches

Other Multi-scale Approaches

For one-dimensional kernels, there is a well-developed theory of multi-scale approaches, concerning filters that do not create new local extrema or new zero-crossings with increasing scales. For continuous signals, filters with real poles in the s-plane are within this class, while for discrete signals the above-described recursive and FIR filters satisfy these criteria. Combined with the strict requirement of a continuous semi-group structure, the continuous Gaussian and the discrete Gaussian constitute the unique choice for continuous and discrete signals.

There are many other multi-scale signal processing, image processing and data compression techniques, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; that is, they do not depend on a coarser scale not generating a new extremum that was not present at a finer scale (in 1-D) or non-enhancement of local extrema between adjacent scale levels (in any number of dimensions).