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A method is proposed for decomposing morphological structuring elements based on integer linear programming. A decomposition problem is formulated into a set of linear constraints, and an optimal decomposition is a solution to the constraints, obtained by the cutting-plane simplex algorithm. The method has several advantages. It provides a systematic way of decomposing arbitrarily shaped structuring elements. For convex images, factors can be of any size, not restricted to 3 × 3; the candidate set can be freely assigned by the user; and the optimality criteria can be flexible.