Solution of morphological operator relations with invariance boundary conditions

摘要

The present paper formulates increasing, translation-invariant filter design for the subtractive-noise restoration problem in terms of the classical boundary-value-problem paradigm. The boundary-value problem involves both operator relations and invariant (fixed-point) boundary conditions. A design approach is formulated that derives the morphological basis expansion directly from the statement of the boundary-value problem. Solutions are found that possess both minimal bases and minimal structuring elements.