SGP

We introduce a novel method for non-rigid shape matching, designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries. Unlike the majority of existing methods which try to overcome this ambiguity by ...

In this paper we target the problem of textured 3D object retrieval. As a first contribution, we show how to include photometric information in the persistence homology setting, also proposing a novel theoretical result about multidimensional ...

We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly ...

We propose a new approach to automatically semantize complex objects in a 3D scene. For this, we define an expressive formalism combining the power of both attribute grammars and constraint. It offers a practical conceptual interface, which is crucial ...

We propose a connectivity editing framework for quad-dominant meshes. In our framework, the user can edit the mesh connectivity to control the location, type, and number of irregular vertices (with more or fewer than four neighbors) and irregular faces (...

Two-parameter families of straight lines (line congruences) are implicitly present in graphics and geometry processing in several important ways including lighting and shape analysis. In this paper we make them accessible to optimization and geometric ...

The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low-level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms -- ...

In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real ...

We propose a method that computes a piecewise constant approximation of a function defined on a mesh. The approximation is associated with the cells of a restricted Voronoï diagram. Our method optimizes an objective function measuring the quality of the ...

In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The ...

We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result ...

Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. ...

Mappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that ...

We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading ...

Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self-intersections. Volumetric processing of solid shapes then ...

We present an algorithm for obtaining a triangulation of multiple, non-planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a ...

Geometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point-to-point correspondence, and we automatically ...

Recent advances in shape matching have shown that jointly optimizing the maps among the shapes in a collection can lead to significant improvements when compared to estimating maps between pairs of shapes in isolation. These methods typically invoke a ...

Large datasets of 3D objects require an intuitive way to browse and quickly explore shapes from the collection. We present a dynamic map of shapes where similar shapes are placed next to each other. Similarity between 3D models exists in a high ...

Soft maps taking points on one surface to probability distributions on another are attractive for representing surface mappings in the presence of symmetry, ambiguity, and combinatorial complexity. Few techniques, however, are available to measure their ...

The emergence of laser/LiDAR sensors, reliable multi-view stereo techniques and more recently consumer depth cameras have brought point clouds to the forefront as a data format useful for a number of applications. Unfortunately, the point data from ...

The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise ...

We propose a noise-adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect-laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise-...