Multivariate granulometric filters

Sinan Batman; Edward R. Dougherty

doi:10.1117/12.271129

4 April 1997 Multivariate granulometric filters

Sinan Batman, Edward R. Dougherty

Proceedings Volume 3026, Nonlinear Image Processing VIII; (1997) https://doi.org/10.1117/12.271129
Event: Electronic Imaging '97, 1997, San Jose, CA, United States

Abstract

As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element. The concept of granulometry has recently been extended in such a way that each structuring element has its own sizing parameter resulting in a filter (Psi) _t depending on the vector parameter t equals (t₁..., t_n). The present paper generalizes the concept of a parameterized reconstructive (tau) -opening to the multivariate setting, where the reconstructive filter (Lambda) _t fully passes any connected component not fully eliminated by (Psi) _t. The problem of minimizing the MAE between the filtered and ideal image processes becomes one of vector optimization in an n- dimensional search space. Unlike the univariate case, the MAE achieved by the optimum filter (Lambda) _t is global in the sense that it is independent of the relative sizes of structuring elements in the filter basis. As a consequence, multivariate granulometries provide a natural environment to study optimality of the choice of structuring elements. If the shapes of the structuring elements are themselves parameterized, the expected error is a deterministic function of the shape and size parameters and its minimization yields the optimal MAE filter.

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Sinan Batman and Edward R. Dougherty "Multivariate granulometric filters", Proc. SPIE 3026, Nonlinear Image Processing VIII, (4 April 1997); https://doi.org/10.1117/12.271129

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KEYWORDS

Interference (communication)

Image filtering

Optimal filtering

Error analysis

Image processing

Monte Carlo methods

Statistical modeling

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