Higher dimensional affine registration and vision applications

Yu Tseh Chi, S. M.Nejhum Shahed, Jeffrey Ho, Ming Hsuan Yang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

Affine registration has a long and venerable history in computer vision literature, and extensive work have been done for affine registrations in ℝ2 and ℝ3. In this paper, we study affine registrations in ℝ m for m > 3, and to justify breaking this dimension barrier, we show two interesting types of matching problems that can be formulated and solved as affine registration problems in dimensions higher than three: stereo correspondence under motion and image set matching. More specifically, for an object undergoing non-rigid motion that can be linearly modelled using a small number of shape basis vectors, the stereo correspondence problem can be solved by affine registering points in ℝ3n . And given two collections of images related by an unknown linear transformation of the image space, the correspondences between images in the two collections can be recovered by solving an affine registration problem in ℝ m , where m is the dimension of a PCA subspace. The algorithm proposed in this paper estimates the affine transformation between two point sets in ℝ m . It does not require continuous optimization, and our analysis shows that, in the absence of data noise, the algorithm will recover the exact affine transformation for almost all point sets with the worst-case time complexity of O(mk 2), k the size of the point set. We validate the proposed algorithm on a variety of synthetic point sets in different dimensions with varying degrees of deformation and noise, and we also show experimentally that the two types of matching problems can indeed be solved satisfactorily using the proposed affine registration algorithm.

Original languageEnglish
Title of host publicationComputer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings
Pages256-269
Number of pages14
EditionPART 4
DOIs
Publication statusPublished - 2008 Dec 1
Event10th European Conference on Computer Vision, ECCV 2008 - Marseille, France
Duration: 2008 Oct 122008 Oct 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 4
Volume5305 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th European Conference on Computer Vision, ECCV 2008
CountryFrance
CityMarseille
Period08/10/1208/10/18

Fingerprint

Registration
High-dimensional
Point Sets
Linear transformations
Matching Problem
Affine transformation
Computer vision
Correspondence
Correspondence Problem
Image Space
Continuous Optimization
Motion
Linear transformation
Vision
Computer Vision
Justify
Time Complexity
Higher Dimensions
Linearly
Subspace

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Chi, Y. T., Shahed, S. M. N., Ho, J., & Yang, M. H. (2008). Higher dimensional affine registration and vision applications. In Computer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings (PART 4 ed., pp. 256-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5305 LNCS, No. PART 4). https://doi.org/10.1007/978-3-540-88693-8-19
Chi, Yu Tseh ; Shahed, S. M.Nejhum ; Ho, Jeffrey ; Yang, Ming Hsuan. / Higher dimensional affine registration and vision applications. Computer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings. PART 4. ed. 2008. pp. 256-269 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 4).
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Chi, YT, Shahed, SMN, Ho, J & Yang, MH 2008, Higher dimensional affine registration and vision applications. in Computer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings. PART 4 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 4, vol. 5305 LNCS, pp. 256-269, 10th European Conference on Computer Vision, ECCV 2008, Marseille, France, 08/10/12. https://doi.org/10.1007/978-3-540-88693-8-19

Higher dimensional affine registration and vision applications. / Chi, Yu Tseh; Shahed, S. M.Nejhum; Ho, Jeffrey; Yang, Ming Hsuan.

Computer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings. PART 4. ed. 2008. p. 256-269 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5305 LNCS, No. PART 4).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Chi YT, Shahed SMN, Ho J, Yang MH. Higher dimensional affine registration and vision applications. In Computer Vision - ECCV 2008 - 10th European Conference on Computer Vision, Proceedings. PART 4 ed. 2008. p. 256-269. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 4). https://doi.org/10.1007/978-3-540-88693-8-19