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Equivalence and Efficiency of Image Alignment Algorithms

Simon Baker and Iain Matthews
Conference Paper, Proceedings of the 2001 IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1, pp. 1090 - 1097, December, 2001

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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.

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},
year = {2001},
month = {December},
volume = {1},
pages = {1090 - 1097},
keywords = {Image alignment, tracking, flexible appearance models, active blobs, non-rigid face modeling, efficiency.},
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