We present a review of the correspondence problem targeted towards the computer graphics audience. This survey is motivated by recent developments such as advances in the correspondence of non-rigid or isometric shapes and methods that extract semantic information from the shapes ...

We introduce the notion of consensus skeletons for non-rigid space-time registration of a deforming shape. Instead of basing the registration on point features, which are local and sensitive to noise, we adopt the curve skeleton of the shape as a global and descriptive feature for the task. Our method uses no template and only assumes that the skeletal structure of the captured shape remains largely consistent over time ...

While many 3D objects around us exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized ... In this paper, we introduce algorithms to extract and utilize partial intrinsic reflectional symmetries (PIRS) of a 3D shape ...

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and interference between close-by surface sheets as a preprocess to surface generation ... First, we present a weighted locally optimal projection operator ... Next, we introduce an iterative framework for robust normal estimation, ...

We explore the use of salient curves in synthesizing natural-looking, shape-revealing textures on surfaces. Our synthesis is guided by two principles: matching the direction of the texture patterns to those of the salient curves, and aligning the prominent feature lines in the texture to the salient curves exactly ...

We address the problem of finding analogies between parts of 3D objects. By partitioning an object into meaningful parts and finding analogous parts in other objects, not necessarily of the same type, based on a contextual signature, many analysis and modeling tasks could be enhanced ...

We undertake a study of the local properties of 2-Gabriel meshes. We show that, under mild constraints on the dihedral angles, such meshes are Delaunay meshes. The analysis is done by means of the Delaunay edge flipping algorithm and it reveals the details of the distinction between these two mesh structures ...

We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of a point set with normals, via a variational formulation ...

We propose a method for fast updating of harmonic fields defined on polygonal meshes, enabling real-time insertion and deletion of constraints. Our approach utilizes the penalty method to enforce constraints in harmonic field computation. It maintains the symmetry of the Laplacian system ...

We present a face recognition method based on sparse representation for recognizing 3D face meshes under expressions using low-level geometric features ... To handle facial expressions, we design a feature pooling and ranking scheme to collect various types of low-level geometric features and rank them ...

We provide the first comprehensive survey on spectral mesh processing. Spectral methods for mesh processing and analysis rely on eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks ...

We define quality differential coordinates (QDC) for per-vertex encoding of the quality of a tetrahedral mesh. Our formulation allows the incorporation of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra ...

The notion of parts in a shape plays an important role in many geometry problems. At the same time, many such problems utilize a surface metric to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts ...

We introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We use four applications to illustrate the benefit of using the resulting TDF scalar field: view point selection, ...

We develop adaptive sampling criteria which guarantee a topologically faithful mesh and demonstrate an improvement and simplification over earlier results, albeit restricted to 2D surfaces. These sampling criteria are based on the strong convexity radius and the injectivity radius ...

We present an automatic feature correspondence algorithm capable of handling large, non-rigid shape variations, as well as partial matching ... The search is deformation-driven, prioritized by a self-distortion energy measured on meshes deformed according to a given correspondence ...

We look at a particular instance of the convex decomposition problem which arises from real-world game development. Given a collection of polyhedral surfaces (possibly with boundaries, holes, and complex interior structures) that model the scene geometry in a game environment, we wish to find a small set of convex hulls ...

We formulate contour correspondence as a Quadratic Assignment Problem (QAP), incorporating proximity information. By maintaining the neighborhood relation between points this way, we show that better matching results are obtained in practice. We propose the first Ant Colony Optimization (ACO) algorithm ...

We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometry-preserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a poorly sampled input mesh may yield unflippable edges necessitating refinement ...

Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. This state-of-the-art report aims to provide a comprehensive survey on the spectral approach ...

We propose a mesh segmentation algorithm where at each step, a sub-mesh embedded in 3D is first spectrally projected into the plane with a contour extracted from the planar embedding. Transforming the shape analysis problem to the 2D domain facilitates our segmentability analysis and sampling tasks ...

We investigate the use of multiple intrinsic geometric attributes, including angles, geodesic distances, and curvatures, for 3D face recognition ... As invariance to facial expressions holds the key to improving recognition performance, we propose to train for the component-wise weights ...

We define a Delaunay mesh to be a manifold triangle mesh whose edges form an intrinsic Delaunay triangulation or iDT of its vertices ... We show that meshes constructed from a smooth surface by taking an iDT or a restricted Delaunay triangulation, do not in general yield a Delaunay mesh ...

We present an algorithm for finding a meaningful correspondence between two triangle meshes, which is designed to handle general non-rigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling and rigid-body transformation.

We present an approach for robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigid-body transformations, shape articulation ...

We propose an algorithm for guaranteed nonobtuse remeshing and nonobtuse mesh decimation. Our strategy for the remeshing problem is to first convert an input mesh, using a modified Marching Cubes algorithm, into a rough approximate mesh that is guaranteed to be nonobtuse. We then apply iterative "deform-to-fit" ...

We present an efficient silhouette extractor for triangle meshes under perspective projection in the Hough space. The more favorable point distribution in Hough space allows us to obtain significant performance gains over the traditional dual-space based techniques ...

We present a spectral approach for robust shape retrieval from databases containing articulated 3D shapes. We show absolute improvement in retrieval performance when conventional shape descriptors are used in the spectral domain on the McGill database of articulated 3D shapes. We also propose a simple eigenvalue-based descriptor ...

In this paper, we treat optimal mesh layout generation as a problem of preserving graph distances and propose to use the subdominant eigenvector of a kernel (affinity) matrix for sequencing ...

We apply Nystrom method, a sub-sampling and reconstruction technique, to speed up spectral mesh processing. We first relate this method to Kernel Principal Component Analysis (KPCA). This enables us to derive a novel measure in the form of a matrix trace, based soly on sampled data, to quantify the quality of Nystrom approximation ...

We present an algorithm for finding a meaningful correspondence between two 3D shapes given as triangle meshes. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling, rigid-body transformation and shape bending ...

We present a novel approach for discretely optimizing contours on the surface of a triangle mesh. This is achieved through the use of a minimum ratio cycle (MRC) algorithm, where we compute a contour having the minimal ratio between a novel contour energy term and the length of the contour ...

Facial expression, which changes face geometry, usually has an adverse effect on the performance of a face recognition system. On the other hand, face geometry is a useful cue for recognition. Taking these into account, we utilize the idea of separating geometry and texture information in a face image ...

6. Jeff J. Yu and Hao Zhang, "A Prototype Sketch-Based Architectural Design System with Behavior Mode," Technical Report TR-2007-?, School of Computing Science, Simon Fraser University, November 2007. [PDF | AVI Video 1 | AVI Video 2]