Lucas-Kanade 20 Years On: Part 5

Image alignment is one of the most widely used techniques in computer vision. Applications range from optical flow, tracking and layered motion, to mosaic construction, medical image registration, and face model fitting. The original image alignment algorithm was the Lucas-Kanade algorithm. Since then, numerous extensions have been made to it. In particular, Baker and Matthews recently proposed the inverse compositional algorithm, an efficient algorithm applicable to most 2D image alignment problems. In this report, we investigate whether the 2D inverse compositional algorithm can be generalized to 2.5D and 3D. By 3D we mean volumetric data consisting of a dense 3D array of voxels. By 2.5D we mean a surface in 3D represented by a collection of 3D surface points. We show that the inverse compositional algorithm is easily generalized to 3D. On the other hand, while algebraically it appears as though the 2.5D case may be treated similarly, doing so violates one of the assumptions in the proof of equivalence of the two algorithms.

[1]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.

[2]  P. Anandan,et al.  Hierarchical Model-Based Motion Estimation , 1992, ECCV.

[3]  Gregory D. Hager,et al.  Efficient Region Tracking With Parametric Models of Geometry and Illumination , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Simon Baker,et al.  Equivalence and efficiency of image alignment algorithms , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[5]  Richard Szeliski,et al.  Construction of Panoramic Image Mosaics with Global and Local Alignment , 2001 .

[6]  Takeo Kanade,et al.  Shape-from-silhouette of articulated objects and its use for human body kinematics estimation and motion capture , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[7]  Takeo Kanade,et al.  Visual hull alignment and refinement across time: a 3D reconstruction algorithm combining shape-from-silhouette with stereo , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[8]  Sami Romdhani,et al.  Efficient, robust and accurate fitting of a 3D morphable model , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[9]  Jing Xiao,et al.  Real-time combined 2D+3D active appearance models , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[10]  Simon Baker,et al.  Lucas-Kanade 20 Years On: A Unifying Framework , 2004, International Journal of Computer Vision.

[11]  Simon Baker,et al.  Active Appearance Models Revisited , 2004, International Journal of Computer Vision.

[12]  Michael J. Black,et al.  EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation , 1996, International Journal of Computer Vision.