We approach recognition in the framework of deformable shape matching, relying on a new algorithm for finding correspondences between feature points. This algorithm sets up correspondence as an integer quadratic programming problem, where the cost function has terms based on similarity of corresponding geometric blur point descriptors as well as the geometric distortion between pairs of corresponding feature points. The algorithm handles outliers, and thus enables matching of exemplars to query images in the presence of occlusion and clutter. Given the correspondences, we estimate an aligning transform, typically a regularized thin plate spline, resulting in a dense correspondence between the two shapes. Object recognition is then handled in a nearest neighbor framework where the distance between exemplar and query is the matching cost between corresponding points. We show results on two datasets. One is the Caltech 101 dataset (Fei-Fei, Fergus and Perona), an extremely challenging dataset with large intraclass variation. Our approach yields a 48 % correct classification rate, compared to Fei-Fei et al’s 16%. We also show results for localizing frontal and profile faces that are comparable to special purpose approaches tuned to faces. 1.

We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. The algorithm registers two meshes by optimizing a joint probabilistic model over all point-topoint correspondences between them. This model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs. The algorithm applies even when one of the meshes is an incomplete range scan; thus, it can be used to automatically fill in the remaining surfaces for this partial scan, even if those surfaces were previously only seen in a different configuration. We evaluate the algorithm on several real-world datasets, where we demonstrate good results in the presence of significant movement of articulated parts and non-rigid surface deformation. Finally, we show that the output of the algorithm can be used for compelling computer graphics tasks such as interpolation between two scans of a non-rigid object and automatic recovery of articulated object models. 1

We propose using the inner-distance between landmark points to build shape descriptors. The inner-distance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that the innerdistance is articulation insensitive and more effective at capturing complex shapes with part structures than Euclidean distance. To demonstrate this idea, it is used to build a new shape descriptor based on shape contexts. After that, we design a dynamic programming based method for shape matching and comparison. We have tested our approach on a variety of shape databases including an articulated shape dataset, MPEG7 CE-Shape-1, Kimia silhouettes, a Swedish leaf database and a human motion silhouette dataset. In all the experiments, our method demonstrates effective performance compared with other algorithms. 1

We present a real-time method for detecting deformable surfaces, with no need whatsoever for a priori pose knowledge. Our method starts from a set of wide baseline point matches between an undeformed image of the object and the image in which it is to be detected. The matches are used not only to detect but also to compute a precise mapping from one to the other. The algorithm is robust to large deformations, lighting changes, motion blur, and occlusions. It runs at 10 frames per second on a 2.8 GHz PC and we are not aware of any other published technique that produces similar results. Introducing deformable meshes, along with a well designed robust estimator, is the key to dealing with the large number of parameters involved in modeling deformable surfaces and rejecting erroneous matches for error rates of up to 95%, which is considerably more than what is required in practice. 1

Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3-dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms. We impose a Hilbert space structure on currents, whose norm gives a convenient and practical way to define a matching functional. Using this Hilbert space norm, we also derive and implement a surface matching algorithm under the large deformation framework, guaranteeing that the optimal solution is a one-to-one regular map of the entire ambient space. We detail an implementation of this algorithm for triangular meshes and present results on 3D face and medical image data. 1

In the paper, we study the problem of optimal matching of two generalized functions (distributions) via a diffeomorphic transformation of the ambient space. In the particular case of discrete distributions (weighted sums of Dirac measures), we provide a new algorithm to compare two arbitrary unlabelled sets of points, and show that it behaves properly in limit of continuous distributions on submanifolds. As a consequence, the algorithm may apply to various matching problems, such as curve or surface matching (via a sub-sampling), or mixings of landmark and curve data. As the solution forbids high energy solutions, it is also robust towards addition of noise and the technique can be used for nonlinear projection of datasets. We present 2D and 3D experiments. 1.

The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has low-dimensionality – six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closed-form after a mid-edge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportation-type distance between corresponding points in that plane. Motivated by these observations, we have developed a Möbius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Möbius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces “votes” for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.

The iterative closest point (ICP) algorithm [2] is a popular method for modeling 3D objects from range data. The classical ICP algorithm rests on a rigid surface assumption. Building on recent work on nonrigid object models [5, 16, 9] , this paper presents an ICP algorithm capable of modeling nonrigid objects, where individual scans may be subject to local deformations. We describe an integrated mathematical framework for simultaneously registering scans and recovering the surface configuration. To tackle the resulting...

Registering images of a deforming surface is a well-studied problem. Solutions include computing optic flow or estimating a parameterized motion model. In the case of optic flow it is necessary to include some regularization. We propose an approach based on representing the induced transformation between images using Radial Basis Functions (RBF). The approach can be viewed as a direct, i.e. intensity-based, method, or equivalently, as a way of using RBFs as non-linear regularizers on the optic flow field. The approach is demonstrated on several image sequences of deforming surfaces. It is shown that the computed registrations are sufficiently accurate to allow convincing augmentations of the images. 1

Geometric flows are ubiquitous in mesh processing. Curve and surface evolutions based on functional minimization have been used in the context of surface diffusion, denoising, shape optimization, minimal surfaces, and geodesic paths to mention a few. Such gradient flows are nearly always, yet often implicitly, based on the canonical L 2 inner product of vector fields. In this paper, we point out that changing this inner product provides a simple, powerful, and untapped approach to extend current flows. We demonstrate the value of such a norm alteration for regularization and volume-preservation purposes and in the context of shape matching, where deformation priors (ranging from rigid motion to articulated motion) can be incorporated into a gradient flow to drastically improve results. Implementation details, including a differentiable approximation of the Hausdorff distance between irregular meshes, are presented.