Metric Learning for Image Alignment

Learning quasi-convex cost function for image alignment 

Learning a metric for image alignment.
(d,f): error surface and contour plot of the PCA model; there are many local minima.
(e, g): our method learns a better error surface to fit PAMs; it has a global minimum in the expected location and no local minima in a given neighborhood.


Image alignment has been a long standing problem in computer vision. Parameterized Appearance Models (PAMs) such as the Lucas-Kanade method, Eigentracking, and Active Appearance Models are commonly used to align images with respect to a template or to a previously learned model. While PAMs have numerous advantages relative to alternate approaches, they have at least two drawbacks. First, they are especially prone to local minima in the registration process. Second, often few, if any, of the local minima of the cost function correspond to acceptable solutions. To overcome these problems, this paper proposes a method to learn a metric for PAMs that explicitly optimizes that local minima occur at and only at the places corresponding to the correct fitting parameters. To the best of our knowledge, this is the first paper to address the problem of learning a metric to explicitly model local properties of the PAMs’ error surface. Synthetic and real examples show improvement in alignment performance in comparison with traditional approaches. In addition, we show how the proposed criteria for a good metric can be used to select good features to track.


Minh Hoai Nguyen & Fernando de la Torre


  • Metric Learning for Image Alignment. Nguyen, M.H. & De la Torre, F. (2009)International Journal of Computer Vision, accepted. Paper.

  • Local Minima Free Parameterized Appearance Models. Nguyen, M.H. & De la Torre, F. (2008) Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. Paper.

  • Learning Image Alignment without Local Minima for Face Detection and Tracking. Nguyen, M.H. & De la Torre, F. (2008) Proceedings of the 8th IEEE International Conference on Automatic Face and Gesture Recognition. Paper


  • Local Minima Free Parameterized Appearance Models, Machine Learning Lunch, Carnegie Mellon University. Video.

  • Learning Image Alignment without Local Minima for Face Detection and Tracking, oral presentation, Face & Gesture 08. Slides.

Acknowledgments and funding

This material is based upon work supported by the U.S. Naval Research Laboratory under Contract No. N00173-07-C-2040 and National Institute of Health Grant R01 MH 051435. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the U.S. Naval Research Laboratory. The authors would like to thank General Motors Corporation for their continued support of this research.

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