Basis decomposition of morphological operations

Promotes the use of basis decomposition of discrete gray-scale structuring elements to design and apply morphological filters. Matheron (1975) has proved that many morphologic operations can be expressed as a single maximum of erosions by a set of basis filters. A constructive relationship between certain morphological operations and their basis sets is derived. The paper discusses how a detailed comparison of basis decomposition set members for given structuring elements can be used to engineer filters with optimal characteristics.<
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