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Morphological image regularization using adaptive structuring functions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. (Centre)
(English)Manuscript (preprint) (Other academic)
National Category
Other Mathematics
URN: urn:nbn:se:uu:diva-221161OAI: oai:DiVA.org:uu-221161DiVA: diva2:707888
Available from: 2014-03-25 Created: 2014-03-25 Last updated: 2014-04-29
In thesis
1. Distance Functions and Their Use in Adaptive Mathematical Morphology
Open this publication in new window or tab >>Distance Functions and Their Use in Adaptive Mathematical Morphology
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the main problems in image analysis is a comparison of different shapes in images. It is often desirable to determine the extent to which one shape differs from another. This is usually a difficult task because shapes vary in size, length, contrast, texture, orientation, etc. Shapes can be described using sets of points, crisp of fuzzy. Hence, distance functions between sets have been used for comparing different shapes.

Mathematical morphology is a non-linear theory related to the shape or morphology of features in the image, and morphological operators are defined by the interaction between an image and a small set called a structuring element. Although morphological operators have been extensively used to differentiate shapes by their size, it is not an easy task to differentiate shapes with respect to other features such as contrast or orientation. One approach for differentiation on these type of features is to use data-dependent structuring elements.

In this thesis, we investigate the usefulness of various distance functions for: (i) shape registration and recognition; and (ii) construction of adaptive structuring elements and functions.

We examine existing distance functions between sets, and propose a new one, called the Complement weighted sum of minimal distances, where the contribution of each point to the distance function is determined by the position of the point within the set. The usefulness of the new distance function is shown for different image registration and shape recognition problems. Furthermore, we extend the new distance function to fuzzy sets and show its applicability to classification of fuzzy objects.

We propose two different types of adaptive structuring elements from the salience map of the edge strength: (i) the shape of a structuring element is predefined, and its size is determined from the salience map; (ii) the shape and size of a structuring element are dependent on the salience map. Using this salience map, we also define adaptive structuring functions. We also present the applicability of adaptive mathematical morphology to image regularization. The connection between adaptive mathematical morphology and Lasry-Lions regularization of non-smooth functions provides an elegant tool for image regularization.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 88 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1137
Image analysis, Distance functions, Mathematical morphology, Adaptive mathematical morphology, Image regularization
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Processing
urn:nbn:se:uu:diva-221568 (URN)978-91-554-8923-6 (ISBN)
Public defence
2014-05-23, Room 2347, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 13:15 (English)
Available from: 2014-04-28 Created: 2014-04-01 Last updated: 2014-07-21

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