Related papers: Morphing of Triangular Meshes in Shape Space
The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers,…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
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…
Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology.…
The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…
Imitation learning of robot policies from few demonstrations is crucial in open-ended applications. We propose a new method, Interaction Warping, for learning SE(3) robotic manipulation policies from a single demonstration. We infer the 3D…
Sculptors often deviate from geometric accuracy in order to enhance the appearance of their sculpture. These subtle stylizations may emphasize anatomy, draw the viewer's focus to characteristic features of the subject, or symbolize textures…
Despite recent advances in geometric modeling, 3D mesh modeling still involves a considerable amount of manual labor by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one…
The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian…
We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored…
Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and…
We propose Differentiable Stereopsis, a multi-view stereo approach that reconstructs shape and texture from few input views and noisy cameras. We pair traditional stereopsis and modern differentiable rendering to build an end-to-end model…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
The isoperimetric problem is one of the oldest in geometry and it consists of finding a surface of minimum area that encloses a given volume $V$. It is particularly important in physics because of its strong relation with stability, and…
The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…
In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…
This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines…
Separable 3D reconstruction of multiple objects from multi-view RGB images -- resulting in two different 3D shapes for the two objects with a clear separation between them -- remains a sparsely researched problem. It is challenging due to…
In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…