Multiscale median and morphological filters for 2D pattern recognition

Abstract

Experiments demonstrate a multiscale decomposition that complements those using standard linear functions. It binds edges rather than waves to features of different scales. The configuration of non-linear median or alternating sequential filters, ‘morphological filters’, used for the decomposition is referred to as a ‘sieve’. Results suggest that whilst some sieves produce an invertible transform, others have better statistical behaviour. Sieves are appropriate for isolating and locating the position of objects with sharp edges arising from nonlinear events such as occlusion. They represent shape information in a way that is independent of spatial frequency, that has different uncertainty trade-offs, and can be used for signal analysis and pattern recognition. For example, by matching the granularity of an image with the granularity of a target pattern, a simple pattern selective system (matched sieve) can be implemented that outperforms its linear analogue, a matcher filter. A sieve is a good multiscale smoother that improves upon single step standard median and morphological filters and is particularly appropriate for discontinuous signals, such as images where edges must be preserved.