Efficient, sparse representation of manifold distance matrices for classical scaling

Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points. Thus for large point sets it is common to use a low-rank approximation to the distance matrix, which fits in memory and can be efficiently analyzed using methods such as multidimensional scaling (MDS). In this paper we present a novel sparse method for efficiently representing geodesic distance matrices using biharmonic interpolation. This method exploits knowledge of the data manifold to learn a sparse interpolation operator that approximates distances using a subset of points. We show that our method is 2x faster and uses 20x less memory than current leading methods for solving MDS on large point sets, with similar quality. This enables analyses of large point sets that were previously infeasible.Comment: Conference CVPR 201

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach

We investigate the problem of estimating the 3D shape of an object, given a set of 2D landmarks in a single image. To alleviate the reconstruction ambiguity, a widely-used approach is to confine the unknown 3D shape within a shape space built upon existing shapes. While this approach has proven to be successful in various applications, a challenging issue remains, i.e., the joint estimation of shape parameters and camera-pose parameters requires to solve a nonconvex optimization problem. The existing methods often adopt an alternating minimization scheme to locally update the parameters, and consequently the solution is sensitive to initialization. In this paper, we propose a convex formulation to address this problem and develop an efficient algorithm to solve the proposed convex program. We demonstrate the exact recovery property of the proposed method, its merits compared to alternative methods, and the applicability in human pose and car shape estimation.Comment: In Proceedings of CVPR 201