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Distance measures between digital fuzzy objects and their applicability in image processing
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. (Centre for Image Analysis)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis.
Faculty of Technical Sciences, University of Novi Sad, Serbia.
2011 (English)In: Combinatorial Image Analysis / [ed] Jake Aggarwal, Reneta Barneva, Valentin Brimkov, Kostadin Koroutchev, Elka Koroutcheva, Springer , 2011, 385-397 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Springer , 2011. 385-397 p.
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Analysis
Identifiers
URN: urn:nbn:se:uu:diva-157186OAI: oai:DiVA.org:uu-157186DiVA: diva2:435525
Conference
Internatiional Workshop on Combinatorial Image Analysis, IWCIA 2011
Note
We present two different extensions of the Sum of minimal distances and the Complement weighted sum of minimal distances to distances between fuzzy sets. We evaluate to what extent the proposed distances show monotonic behavior with respect to increasing translation and rotation of digital objects, in noise free, as well as in noisy conditions. Tests show that one of the extension approaches leads to distances exhibiting very good performance. Furthermore, we evaluate distance based classification of crisp and fuzzy representations of objects at a range of resolutions. We conclude that the proposed distances are able to utilize the additional information available in a fuzzy representation, thereby leading to improved performance of related image processing tasks. Available from: 2011-08-18 Created: 2011-08-18 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.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1137
Keyword
Image analysis, Distance functions, Mathematical morphology, Adaptive mathematical morphology, Image regularization
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Processing
Identifiers
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)
Opponent
Supervisors
Available from: 2014-04-28 Created: 2014-04-01 Last updated: 2014-07-21

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Lindblad, Joakim

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