Higher-dimensional affine registration and vision applications

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Affine registration has a long and venerable history in computer vision literature, and in particular, extensive work has been done for affine registration in IR2 and IR3. This paper studies affine registration in IRm with m typically ranging from 4 to 12. To justify breaking of this dimension barrier, the first part of the paper describes three novel matching problems that can be formulated and solved as affine point-set registration problems in dimensions greater than three: stereo correspondence under motion, image set matching, and covariant point-set matching, problems that are not only interesting in their own right but also have potential for important vision applications. Unfortunately, most of the existing affine registration algorithms do not generalize easily to higher dimensions due to their inefficiency. Therefore, the second part of this paper develops a novel algorithm for estimating the affine transform between two point sets in IR m. Specifically, the algorithm follows the common approach of iteratively solving the correspondences and transform. The initial correspondences are determined using the novel notion of local spectral features, features constructed from local distance matrices. Unlike many correspondence-based methods, the proposed algorithm is capable of registering point sets of different size, and the use of local features provides some degree of robustness against noise and outliers. The proposed algorithm is validated on a variety of synthetic point sets in different dimensions with varying degrees of deformation and noise, and the paper also shows experimentally that several instances of the aforementioned three matching problems can indeed be solved satisfactorily using the proposed affine registration algorithm.

Original languageEnglish
Article number5661788
Pages (from-to)1324-1338
Number of pages15
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number7
Publication statusPublished - 2011

Bibliographical note

Funding Information:
The authors thank one of the reviewers for providing many invaluable comments and suggestions. S.M. Shahed Nejhum, Y.-T. Chi, and J. Ho are partially supported by a US National Science Foundation (NSF) grant IIS-0916001. M.-H. Yang is supported in part by a Google faculty award and University of California Merced faculty start-up fund.

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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