ABSTRACT
This chapter investigates a multifaceted suboptimal design meth-odology for binary filters based on the imposition of various constraints and small libraries, the goal being to facilitate computationally tractable design. It discusses general aspects of the three constraints: limiting the number of terms in the Matheron expansion, constraining the size of the observation window, and employing structuring-element libraries. The chapter describes the effect of window constraint and library constraint in detail, and discusses the effect on filter properties and design tractability. It presents a probabilistic analysis of the binary morphological filter that leads to a mean-square error (MSE) theorem that can be employed to search efficiently for a minimum MSE filter. A striking feature of the optimal mean-square erosion filter is that, relative to the entire image, it is not a morphological filter. Because filtering is considered as point- wise estimation, each pixel possesses its own optimal basis.
