Related papers: Compression for Smooth Shape Analysis
3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
In this paper, we propose a scalable image compression scheme, including the base layer for feature representation and enhancement layer for texture representation. More specifically, the base layer is designed as the deep learning feature…
In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
The eigenfunctions of the Laplace-Beltrami operator have widespread applications in a number of disciplines of engineering, computer vision/graphics, machine learning, etc. These eigenfunctions or manifold harmonics, provide the means to…
Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…
3D representations of highly deformable 3D models, such as dynamic 3D meshes, have recently become very popular due to their wide applicability in various domains. This trend inevitably leads to a demand for storage and transmission of…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
Surface topography refers to the geometric micro-structure of a surface and defines its tactile characteristics (typically in the sub-millimeter range). High-resolution 3D scanning techniques developed recently enable the 3D reconstruction…
Traditional machine learning (ML) algorithms, such as multiple regression, require human analysts to make decisions on how to treat the data. These decisions can make the model building process subjective and difficult to replicate for…
We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…
Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
Mesh processing pipelines are mature, but adapting them to newer non-mesh surface representations -- which enable fast rendering with compact file size -- requires costly meshing or transmitting bulky meshes, negating their core benefits…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…