Decomposition of geometric-shaped structuring elements and optimization on euclidean distance transformation using morphology

Thesis

5-31-1992

Degree Name

Master of Science in Computer and Information Science - (M.S.)

Department

Computer and Information Science

Frank Y. Shih

Abstract

Mathematical morphology which is based on geometric shape, provides an approach to the processing and analysis of digital images. Several widely-used geometric-shaped structuring elements can be used to explore the shape characteristics of an object. In first chapter, we present a unified technique to simplify the decomposition of various types of big geometric-shaped structuring elements into dilations of smaller structuring components by the use of a mathematical transformation. Hence, the desired morphological erosion and dilation are equivalent to a simple inverse transformation over the result of operations on the transformed decomposable structuring elements. We also present a strategy to decompose a large cyclic cosine structuring element. The technique of decomposing a two-dimensional convex structuring element into one-dimensional ones is also developed.

A distance transformation converts a digital binary image which consists of object (foreground) and non-object (background) pixels, into a gray-level image in which all object pixels have a value corresponding to the minimum distance from the background. Computing the distance from a pixel to a set of background pixels is in principle a global operation, that is often prohibitively costly. The Euclidean distance measurement is very useful in object recognition and inspection because of the metric accuracy and rotation invariance. However, its global operation is difficult to decompose into small neighborhood operations because of the nonlinearity of Euclidean distance computation. In second chapter presents three algorithms to the Euclidean distance transformation in digital images by the use of the grayscale morphological erosion with the squared Euclidean distance structuring element. The optimal algorithm only requires four erosions by small structuring components and is independent of the object size. It can be implemented in parallel and is very efficient in computation because only the integer is used until the last step of a square-root operation.

Feature extraction and object recognition can be achieved by mathematical morphology. An object is analyzed by using a set of primitive shapes. Primitive shapes are designed in binary templete. To detect each matching pattern, mapping of a set of templetes on the unknown object need to be performed. The templetes along with morphological operations and weights corresponding to each matching pattern are designed priorily and stored in database. During recognition, we get several sub-result according to its templetes. These results combined with their weights will produce a final matching probability. In third chapter, a new feature selection criterion based on mathematical morphology is proposed.

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