article

Preserving Topology by a Digitization Process

Authors:

Longin Jan Latecki,

Christopher Conrad,

Ari GrossAuthors Info & Claims

Journal of Mathematical Imaging and Vision, Volume 8, Issue 2

Pages 131 - 159

https://doi.org/10.1023/A:1008273227913

Published: 01 March 1998 Publication History

Abstract

The main task of digital image processing is to recognize properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and represented as finite sets of points that are assigned some value in a gray-level or color scale. Based on technical properties of sampling devices, these points are usually assumed to form a square grid and are modeled as finite subsets of Z ^2 . Therefore, a fundamental question in digital image processing is which features in the digital image correspond, under certain conditions, to properties of the underlying objects. In practical applications this question is mostly answered by visually judging the obtained digital images. In this paper we present a comprehensive answer to this question with respect to topological properties. In particular, we derive conditions relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. These conditions also imply that two digital images of a given object are topologically equivalent. This means, for example, that shifting or rotating an object or the camera cannot lead to topologically different images, i.e., topological properties of obtained digital images are invariant under shifting and rotation.

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Preserving Topology by a Digitization Process

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Published In

cover image Journal of Mathematical Imaging and Vision

Journal of Mathematical Imaging and Vision Volume 8, Issue 2

March, 1998

93 pages

ISSN:0924-9907

Editor:
Gehard X. Ritter
Univ. of Florida

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Copyright © Copyright © 1998 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 March 1998

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Cited By

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Le Quentrec ÉMazo LBaudrier ÉTajine M(2022)Monotonic Sampling of a Continuous Closed Curve with Respect to Its Gauss Digitization: Application to Length EstimationJournal of Mathematical Imaging and Vision10.1007/s10851-022-01098-864:8(869-891)Online publication date: 1-Oct-2022
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Ngo PPassat NKenmochi YDebled-Rennesson I(2019)Geometric Preservation of 2D Digital Objects Under Rigid MotionsJournal of Mathematical Imaging and Vision10.1007/s10851-018-0842-961:2(204-223)Online publication date: 1-Feb-2019
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