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Titlebook: Mathematical Morphology and Its Applications to Image and Signal Processing; John Goutsias,Luc Vincent,Dan S. Bloomberg Book 2000 Springer

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Decomposition of Separable Concave Structuring Functionsr instance, distance transforms and morphological scale space. In the continuous domain, the size of the structuring elements resulting from the decomposition, can be chosen arbitrarily small. For functions from the mentioned class, that can be separated along the standard image axes, a discrete decomposition in 3 × 3 elements can be guaranteed.
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Topological Properties of Hausdorff Discretizations 4-connected, and a Hausdorff discretization “preserves” the homotopy for a class of closed sets and a class of homogeneous metrics. Under some general condition, a Hausdorff discretization is “homeomorphic” to the original set.
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A Lattice Control Model of Fuzzy Dynamical Systems in State-Space, transformations are represented as lattice dilations or erosions. The state and output responses are computed via supremal convolutions based on fuzzy norms. Causality and stability issues are studied. Finally, solutions to the controllability and observability problem are found using lattice adjunctions.
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Affine Invariant Mathematical Morphology Applied to A Generic Shape Recognition Algorithmmage. Their number can be drastically reduced by using affine and contrast invariant smoothing Matheron operators, which we describe as alternate affine erosions-dilations. We then discuss an efficient local encoding of the shape elements. We finally show experiments. Applications aimed at include image registration, image indexing, optical flow.
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