This paper proposes a novel image-retargeting algorithm that can retarget images to a large family of non-rectangular shapes. Specifically, we study image retargeting from a broader perspective that includes the content as well as the shape of an image, and the proposed content and shape-aware image-retargeting (CASAIR) algorithm is driven by the dual objectives of image content preservation and image domain transformation, with the latter defined by an application-specific target shape. The algorithm is based on the idea of seam segment carving that successively removes low-cost seam segments from the image to simultaneously achieve the two objectives, with the selection of seam segments determined by a cost function incorporating inputs from image content and target shape. To provide a complete characterization of shapes that can be obtained using CASAIR, we introduce the notion of bhv-convex shapes, and we show that bhv-convex shapes are precisely the family of shapes that can be retargeted to by CASAIR. The proposed algorithm is simple in both its design and implementation, and in practice, it offers an efficient and effective retargeting platform that provides its users with considerable flexibility in choosing target shapes. To demonstrate the potential of CASAIR for broadening the application scope of image retargeting, this paper also proposes a smart camera-projector system that incorporates CASAIR. In the context of ubiquitous display, CASAIR equips the camera-projector system with the capability of retargeting images online in order to maximize the quality and fidelity of the displayed images whenever the situation demands.

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 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.

This paper proposes a novel approach for sparse coding that further improves upon the sparse representation-based classification (SRC) framework. The proposed framework, Affine-Constrained Group Sparse Coding (ACGSC), extends the current SRC framework to classification problems with multiple input samples. Geometrically, the affineconstrained group sparse coding essentially searches for the vector in the convex hull spanned by the input vectors that can best be sparse coded using the given dictionary. The resulting objective function is still convex and can be efficiently optimized using iterative block-coordinate descent scheme that is guaranteed to converge. Furthermore, we provide a form of sparse recovery result that guarantees, at least theoretically, that the classification performance of the constrained group sparse coding should be at least as good as the group sparse coding. We have evaluated the proposed approach using three different recognition experiments that involve illumination variation of faces and textures, and face recognition under occlusions. Preliminary experiments have demonstrated the effectiveness of the proposed approach, and in particular, the results from the recognition/occlusion experiment are surprisingly accurate and robust.

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.