Applications of matrix morphology

Stephen S. Wilson

doi:10.1117/12.23575

1 November 1990 Applications of matrix morphology

Stephen S. Wilson

Proceedings Volume 1350, Image Algebra and Morphological Image Processing; (1990) https://doi.org/10.1117/12.23575
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

The current concept of mathematical morphology involves erosions and dilations using structuring elements and will be called scalar morphology in this paper. Scalar morphology can be extended to a matrix morphology formalism by the unusual idea that each matrix element is a set in EN space. An image matrix is an array of separate images and a structuring element matrix is defined to be an array where each component is a structuring element. Dilations or erosions of a matrix of images by a matrix of structuring elements consist of a number of dilations or erosions of various image components with structuring element components. The rules of matrix operations will tell which image components are transformed by which structuring element components and how the results are combined into a new array. Set unions and intersections are analogous to matrix addition. All non-increasing transformations can be described as a matrix erosion followed by a dilation inner product. Applications using scalar morphology can consist of a sequence of operations where several intermediate images are generated and recombined in various ways to eventually give a final result. These intermediate images can represent different features. Specific combinations of features in certain configurations can provide an identification or location of an object. It turns out that sequences of this type that consist of a multiplicity of operations on a multiplicity of images fit very well into the

Citation Download Citation

Stephen S. Wilson "Applications of matrix morphology", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); https://doi.org/10.1117/12.23575

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