ADAPTIVE RECONSTRUCTIVE TAU-OPENINGS - CONVERGENCE AND THE STEADY-STATE DISTRIBUTION

A parameterized tau-opening is a filter defined as a union of openings by a collection of compact convex structuring elements, each scalar m ultiplied by the parameter. For a reconstructive tau-opening, the filt er is modified by fully passing any connected component not completely eliminated Applied to the signal-union-noise model. in which the reco nstructive filter is designed to sieve out clutter while passing the s ignal, the optimization problem is to find a parameter value that mini mizes the MAE between the filtered and ideal image processes. The pres ent study introduces an adaptation procedure for the design of reconst ructive tau-openings. The adaptive filter fits into the framework of M arkov processes, the adaptive parameter being the state of the process . There exists a stationary distribution governing the parameter in th e steady state and convergence is characterized via the steady-state d istribution. Key filter properties such as parameter mean, parameter v ariance, and expected error in the steady state are characterized via the stationary distribution. The Chapman-Kolmogorov equations are deve loped for various scanning modes and transient behavior is examined. ( C) 1996 SPIE and IS&T.