Affine registration has a long and venerable history in computer vision literature, and in particular, extensive work has been done for affine registration in R(2) and R(3). This paper studies affine registration in R(m) 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 R(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.

We propose an algorithm for accurate tracking of (articulated) objects using online update of appearance and shape. The challenge here is to model foreground appearance with histograms in a way that is both efficient and accurate. In this algorithm, the constantly changing foreground shape is modeled as a small number of rectangular blocks, whose positions within the tracking window are adaptively determined. Under the general assumption of stationary foreground appearance, we show that robust object tracking is possible by adaptively adjusting the locations of these blocks. Implemented in MATLAB without substantial optimization, our tracker runs already at 3.7 frames per second on a 3GHz machine. Experimental results have demonstrated that the algorithm is able to efficiently track articulated objects undergoing large variation in appearance and shape.