Multiscale recursive medians, scale-space, and transforms with applications to image processing

A cascade of increasing scale, 1-D, recursive median filters produces a sieve, termed an X-sieve, has a number of properties important to image processing. In particular, it 1) simplifies signals without introducing new extrema or edges, that is, it preserves scale-space. It shares this property with Gaussian filters, but has the advantage of being significantly more robust. 2) The differences between successive stages of the sieve yield a transform, to the granularity domain. Patterns and shapes can be recognized in this domain using idempotent matched sieves and the result transformed back to the spatial domain. The R-sieve is very fast to compute and has a close relationship to 1-D alternating sequential filters with flat structuring elements. They are useful for machine vision applications.