Multiresolution decomposition and adaptive filtering with rank order based filters-application to defect detection

A class of nonlinear filters called rank order based filters, including, as special cases, rank order and morphological (with flat structuring element) filters, are dealt with. How they achieve size-sensitive multiresolution decompositions is described. The necessity of a special processing stage dedicated to shape preservation is shown, and a solution is proposed. The problem of filter mask (or structuring element) optimization to minimize a statistical criterion is also studied. The proposed algorithms are very simple, and their derivation is performed by using an implicit formulation of the filtering process. Both techniques are applied to a practical defect detection problem