A generalized morphological filter

Jisheng Song, Purdue University

Abstract

Mathematical morphology is an important class of image transformations that have been studied extensively in image processing and analysis. Mathematical morphology is a set algebra developed to deal with the geometrical structures of objects. Basic morphological transformations are performed using a set, known as the structuring element, which specifies a geometrical structure with certain shape and size properties. Morphological transformations can be used to extract information relative to the distribution of the geometrical structure specified by the structuring element. They can also be used to transform an image into another image which contains the specified geometrical structure. One of the basic design requirements in image enhancement is to remove noise and minimize the blurring effect. A traditional morphological filter uses only one structuring element which is usually supported on a square or circular region. This filter can effectively remove impulsive noise with geometrical feature preservation if the image in consideration consists of large homogeneous regions. For an image that has fine details, the transformed image, resulting from the use of a single structuring element, has only the one geometrical structure specified by the structuring element in it and will not be visually pleasing. Morphological filters using multiple structuring elements are developed to address the difficulties of the traditional morphological filter. The goal is to preserve within an image multiple basic geometrical structures, as defined by the structuring elements, that can form fine details and also maintain noise suppression. Motivated by exploiting the merits of linear filtering and morphological filtering techniques, we have developed a new filter structure which is known as the Generalized Morphological Filter (GMF). The output of the GMF is the linear combination of the ordered outputs of multiple morphological operators using different structuring elements. The deterministic and statistical properties of GMF have been investigated. Optimal coefficients in the linear part of the GMF combination have also been derived. The quantitative evaluation of the performance of the GMF has shown superior performance in comparison with other popular filters such as averaging and median filters.

Degree

Ph.D.

Advisors

Delp, Purdue University.

Subject Area

Electrical engineering

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