This paper proposes a dictionary learning framework that combines the proposed block/group (BGSC) or reconstructed block/group (R-BGSC) sparse coding schemes with the novel Intra-block Coherence Suppression Dictionary Learning (ICS-DL) algorithm. An important and distinguishing feature of the proposed framework is that all dictionary blocks are trained simultaneously with respect to each data group while the intra-block coherence being explicitly minimized as an important objective. We provide both empirical evidence and heuristic support for this feature that can be considered as a direct consequence of incorporating both the group structure for the input data and the block structure for the dictionary in the learning process. The optimization problems for both the dictionary learning and sparse coding can be solved efficiently using block-gradient descent, and the details of the optimization algorithms are presented. We evaluate the proposed methods using well-known datasets, and favorable comparisons with state-of-the-art dictionary learning methods demonstrate the viability and validity of the proposed framework.

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Abstract. Estimating planar projective transform (homography) from a pair of images is a classical problem in computer vision. In this paper, we propose a novel algorithm for direct registering two point sets in R 2 using projective transform without using intensity values. In this very general context, there is no easily established correspondences that can be used to estimate the projective transform, and most of the existing techniques become either inadequate or inappropriate. While the planar projective transforms form an eight-dimensional Lie group, we show that for registering 2D point sets, the search space for the homographies can be effectively reduced to a three-dimensional space. To further improve on the running time without significantly reducing the accuracy of the registration, we propose a matching cost function constructed using local polynomial moments of the point sets and a coarse to fine approach. The resulting registration algorithm has linear time complexity with respect to the number of input points. We have validated the algorithm using points sets collected from real images. Preliminary experimental results are encouraging and they show that the proposed method is both efficient and accurate.

Abstract-Affine registration has a long and venerable history in computer vision literature, and in particular, extensive work has been done for affine registration in IR 2 and IR 3 . This paper studies affine registration in IR 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 IR 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.

Abstract-Affine registration has a long and venerable history in computer vision literature, and in particular, extensive work has been done for affine registration in IR 2 and IR 3 . This paper studies affine registration in IR 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 IR 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.