Research On Morphological Filter Algorithms Based On Mathematical Morphology

Morphological filters are a class of very important nonlinear filters based on algebraic theory of the geometrical structure of sets which called mathematical morphology. They have found wide applications in many research fields, such as image analysis and processing, computer vision and mode recognition. Their main design questions are the selection of structuring elements and morphological transformation. In this paper, some researches of two above aspects and the implementation of morphological filters have been made as fellow.At first, basic morphological transformations in mathematical morphology are introduced. The fundamental theory of digital morphological filters is systematically summarized. With the aid of positive Boolean function (PBF) descriptions, the connection of standard morphological filters and stack filters is established. The output statistical properties of standard filters are particularly analyzed.By the omnidrectional structuring elements introduced into morphological filters, on the basis of open-closing and clos-opening filters suggested by Maragos, an omnidrectional adaptive weighted combination morphological filter is proposed under the constrained mean-absolute-error criterion. The contradiction between detail-preserving and noise-removing is well resolved. the paper closely combines the statistical properties of speckle noise with the morphological filter, and proposes the multidirectional weighted-averaging morphological filter. The filter operates as follows: Firstly the image is filtered by morphological open-close and close-open algorithm. Because of speckle noise strongly corrupting the images, the multidirectional one-dimension structure elements are selected for reducing the noise existing probability. Then, according to the statistical distribution of speckle noise, the multidirectional filtered results are weighted averaged.