uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Adaptive Mathematical Morphology: a survey of the field
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. 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, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
2014 (English)In: Pattern Recognition Letters, ISSN 0167-8655, E-ISSN 1872-7344, Vol. 47, 18-28 p.Article in journal (Refereed) Published
Abstract [en]

We present an up-to-date survey on the topic of adaptive mathematical morphology. A broad review of research performed within the field is provided, as well as an in-depth summary of the theoretical advances within the field. Adaptivity can come in many different ways, based on different attributes, measures, and parameters. Similarities and differences between a few selected methods for adaptive structuring elements are considered, providing perspective on the consequences of different types of adaptivity. We also provide a brief analysis of perspectives and trends within the field, discussing possible directions for future studies.

Place, publisher, year, edition, pages
2014. Vol. 47, 18-28 p.
Keyword [en]
Overview, Mathematical morphology, Adaptive morphology, Adaptive structuring elements, Adjunction property
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:uu:diva-221159DOI: 10.1016/j.patrec.2014.02.022ISI: 000339999200003OAI: oai:DiVA.org:uu-221159DiVA: diva2:707886
Available from: 2014-03-18 Created: 2014-03-25 Last updated: 2017-12-05Bibliographically approved
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

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Curic, VladimirLuengo Hendriks, Cris L.

Search in DiVA

By author/editor
Curic, VladimirLuengo Hendriks, Cris L.
By organisation
Division of Visual Information and InteractionComputerized Image Analysis and Human-Computer Interaction
In the same journal
Pattern Recognition Letters
Computer Vision and Robotics (Autonomous Systems)

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 977 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf