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Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the…
Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the…
We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…
Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…
Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…
3D shape matching is a long-standing problem in computer vision and computer graphics. While deep neural networks were shown to lead to state-of-the-art results in shape matching, existing learning-based approaches are limited in the…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution…
We propose a novel unsupervised learning approach for non-rigid 3D shape matching. Our approach improves upon recent state-of-the art deep functional map methods and can be applied to a broad range of different challenging scenarios.…
We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface…
Manually authoring 3D shapes is difficult and time consuming; generative models of 3D shapes offer compelling alternatives. Procedural representations are one such possibility: they offer high-quality and editable results but are difficult…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many…
Establishing point-to-point correspondences across multiple 3D shapes is a fundamental problem in computer vision and graphics. In this paper, we introduce DcMatch, a novel unsupervised learning framework for non-rigid multi-shape matching.…
Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…
Real-time 3D navigation during minimally invasive procedures is an essential yet challenging task, especially when considerable tissue motion is involved. To balance image acquisition speed and resolution, only 2D images or low-resolution…
Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…