Variational Barycentric Coordinates
- URL: http://arxiv.org/abs/2310.03861v1
- Date: Thu, 5 Oct 2023 19:45:06 GMT
- Title: Variational Barycentric Coordinates
- Authors: Ana Dodik, Oded Stein, Vincent Sitzmann, Justin Solomon
- Abstract summary: We propose a variational technique to optimize for generalized barycentric coordinates.
We directly parameterize the continuous function that maps any coordinate in a polytope's interior to its barycentric coordinates using a neural field.
- Score: 18.752506994498845
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We propose a variational technique to optimize for generalized barycentric
coordinates that offers additional control compared to existing models. Prior
work represents barycentric coordinates using meshes or closed-form formulae,
in practice limiting the choice of objective function. In contrast, we directly
parameterize the continuous function that maps any coordinate in a polytope's
interior to its barycentric coordinates using a neural field. This formulation
is enabled by our theoretical characterization of barycentric coordinates,
which allows us to construct neural fields that parameterize the entire
function class of valid coordinates. We demonstrate the flexibility of our
model using a variety of objective functions, including multiple smoothness and
deformation-aware energies; as a side contribution, we also present
mathematically-justified means of measuring and minimizing objectives like
total variation on discontinuous neural fields. We offer a practical
acceleration strategy, present a thorough validation of our algorithm, and
demonstrate several applications.
Related papers
- Shape-informed surrogate models based on signed distance function domain encoding [8.052704959617207]
We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs)
Our approach is based on the combination of two neural networks (NNs)
arXiv Detail & Related papers (2024-09-19T01:47:04Z) - A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures [0.138120109831448]
We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data.
We model the sought function as a sample function of a non-stationary Gaussian Process (GP), that nests within itself multiple other GPs.
We illustrate this new learning strategy on a real dataset.
arXiv Detail & Related papers (2024-04-18T19:21:28Z) - Mapping-to-Parameter Nonlinear Functional Regression with Novel B-spline
Free Knot Placement Algorithm [12.491024918270824]
We propose a novel approach to nonlinear functional regression.
The model is based on the mapping of function data from an infinite-dimensional function space to a finite-dimensional parameter space.
The performance of our knot placement algorithms is shown to be robust in both single-function approximation and multiple-function approximation contexts.
arXiv Detail & Related papers (2024-01-26T16:35:48Z) - Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching [42.0728900164228]
We propose a novel approach of combining the non-orthogonal extrinsic basis of eigenfunctions of the elastic thin-shell hessian with the intrinsic ones of the Laplace-Beltrami operator (LBO) eigenmodes.
We show extensive evaluations across various supervised and unsupervised settings and demonstrate significant improvements.
arXiv Detail & Related papers (2023-12-06T18:41:01Z) - NeuRBF: A Neural Fields Representation with Adaptive Radial Basis
Functions [93.02515761070201]
We present a novel type of neural fields that uses general radial bases for signal representation.
Our method builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals.
When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.
arXiv Detail & Related papers (2023-09-27T06:32:05Z) - Dynamic Kernel-Based Adaptive Spatial Aggregation for Learned Image
Compression [63.56922682378755]
We focus on extending spatial aggregation capability and propose a dynamic kernel-based transform coding.
The proposed adaptive aggregation generates kernel offsets to capture valid information in the content-conditioned range to help transform.
Experimental results demonstrate that our method achieves superior rate-distortion performance on three benchmarks compared to the state-of-the-art learning-based methods.
arXiv Detail & Related papers (2023-08-17T01:34:51Z) - Imitation of Manipulation Skills Using Multiple Geometries [20.21868546298435]
We propose a learning approach to extract the optimal representation from a dictionary of coordinate systems to represent an observed movement.
We apply our approach to grasping and box opening tasks in simulation and on a 7-axis Franka Emika robot.
arXiv Detail & Related papers (2022-03-02T15:19:33Z) - Multiway Non-rigid Point Cloud Registration via Learned Functional Map
Synchronization [105.14877281665011]
We present SyNoRiM, a novel way to register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds.
We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy.
arXiv Detail & Related papers (2021-11-25T02:37:59Z) - NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One
Go [109.88509362837475]
We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes.
NeuroMorph produces smooth and point-to-point correspondences between them.
It works well for a large variety of input shapes, including non-isometric pairs from different object categories.
arXiv Detail & Related papers (2021-06-17T12:25:44Z) - Model identification and local linear convergence of coordinate descent [74.87531444344381]
We show that cyclic coordinate descent achieves model identification in finite time for a wide class of functions.
We also prove explicit local linear convergence rates for coordinate descent.
arXiv Detail & Related papers (2020-10-22T16:03:19Z) - Fast Gravitational Approach for Rigid Point Set Registration with
Ordinary Differential Equations [79.71184760864507]
This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA)
In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field.
We show that the new method class has characteristics not found in previous alignment methods.
arXiv Detail & Related papers (2020-09-28T15:05:39Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.