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Abstract

There are two major formulations of image alignment using gradient descent. The first estimates an additive increment to the parameters (the additive approach), the second an incremental warp (the compositional approach). We first prove that these two formulations are equivalent. A very efficient algorithm was recently proposed by Hager and Belhumeur using the additive approach that unfortunately can only be applied to a very restricted class of warps. We show that using the compositional approach an equally efficient algorithm (the inverse compositional algorithm) can be derived that can be applied to any set of warps which form a group. While most warps used in computer vision form groups, there are a certain warps that do not. Perhaps most notable is the set of piecewise affine warps used in Flexible Appearance Models (FAMs). We end this paper by extending the inverse compositional algorithm to apply to FAMs.

Keywords

Image alignment, tracking, flexible appearance models, active blobs, non-rigid face modeling, efficiency.

Notes

Sponsor: U.S. Office of Naval Research

Grant ID: N00014-00-1-0915

Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Associated Lab(s) / Group(s): Vision for Safe Driving, People Image Analysis Consortium, Human Identification at a Distance, Face Group

Associated Project(s): Face Model Building and Fitting, Face and Facial Feature Tracking, AAM Fitting Algorithms

Number of pages: 8

Text Reference

Simon Baker and Iain Matthews, "Equivalence and Efficiency of Image Alignment Algorithms," Proceedings of the 2001 IEEE Conference on Computer Vision and Pattern Recognition, December, 2001, pp. 1090 - 1097.

BibTeX Reference

@inproceedings{Baker_2001_3805,
   author = "Simon Baker and Iain Matthews",
   title = "Equivalence and Efficiency of Image Alignment Algorithms",
   booktitle = "Proceedings of the 2001 IEEE Conference on Computer Vision and Pattern Recognition",
   pages = "1090 - 1097",
   month = "December",
   year = "2001",
   volume = "1",
}

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