Combinatorial structure of rigid transformations in 2D digital images

► We propose to study rigid transformations of digital images in a fully discrete process. ► We model the parameter space of digital rigid transformations on any subset of Z2 of size N×N by a combinatorial structure. ► We describe this structure which has a space complexity O(N9). ► We propose an (e...

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Bibliographic Details
Published in:Computer vision and image understanding Vol. 117; no. 4; pp. 393 - 408
Main Authors: Ngo, Phuc, Kenmochi, Yukiko, Passat, Nicolas, Talbot, Hugues
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2013
Elsevier
Subjects:
Algorithms
Combinatorial analysis
Combinatorial structure
Complexity
Computational Geometry
Computer Science
Computer vision
Digital
Digital rigid transformations
Discrete algorithm
Discrete Mathematics
Image Processing
Transformations
Digital rigid transformations
Discrete algorithm
Combinatorial structure
digital rigid transformations
discrete algorithm
combinatorial structure
ISSN:1077-3142, 1090-235X
Online Access:Get full text
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Summary:► We propose to study rigid transformations of digital images in a fully discrete process. ► We model the parameter space of digital rigid transformations on any subset of Z2 of size N×N by a combinatorial structure. ► We describe this structure which has a space complexity O(N9). ► We propose an (exact computation) algorithm to build this structure in linear time with respect to its size. Rigid transformations are involved in a wide range of digital image processing applications. When applied on discrete images, rigid transformations are usually performed in their associated continuous space, requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as fully discrete processes. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on arbitrary subset of Z2 of size N×N. We describe this combinatorial structure, which presents a space complexity O(N9) and we propose an algorithm enabling to construct it in linear time with respect to its space complexity. This algorithm, which handles real (i.e., non-rational) values related to the continuous transformations associated to the discrete ones, is however defined in a fully discrete form, leading to exact computation.
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ISSN:1077-3142
1090-235X
DOI:10.1016/j.cviu.2012.08.014