Related papers: Local Geometry Inclusive Global Shape Representati…

3D Shape representation has substantial effects on 3D shape reconstruction. Primitive-based representations approximate a 3D shape mainly by a set of simple implicit primitives, but the low geometrical complexity of the primitives limits…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Guaranteeing that Fr\'echet means of object populations do not locally self-intersect or are thereby affected is a serious challenge for object representations because the objects' shape space typically includes elements corresponding to…

Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…

Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean…

Accurate surround-view depth estimation provides a competitive alternative to laser-based sensors and is essential for 3D scene understanding in autonomous driving. While empirical studies have proposed various approaches that primarily…

In this paper, we propose using curvatures in digital space for 3D object analysis and recognition. Since direct adjacency has only six types of digital surface points in local configurations, it is easy to determine and classify the…

Learning structures of 3D shapes is a fundamental problem in the field of computer graphics and geometry processing. We present a simple yet interpretable unsupervised method for learning a new structural representation in the form of 3D…

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment…

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…

Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…

Shape completion, i.e., predicting the complete geometry of an object from a partial observation, is highly relevant for several downstream tasks, most notably robotic manipulation. When basing planning or prediction of real grasps on…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…

In this paper we address the task of the comparison and the classification of 3D shape sequences of human. The non-linear dynamics of the human motion and the changing of the surface parametrization over the time make this task very…

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly…

We present a novel 3D shape completion method that operates directly on unstructured point clouds, thus avoiding resource-intensive data structures like voxel grids. To this end, we introduce KAPLAN, a 3D point descriptor that aggregates…

Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the…