Learning-based density-equalizing map

• URL: http://arxiv.org/abs/2506.10027v1
• Date: Tue, 10 Jun 2025 02:54:39 GMT
• Title: Learning-based density-equalizing map
• Authors: Yanwen Huang, Lok Ming Lui, Gary P. T. Choi,
• Abstract summary: We propose a novel learning-based density-equalizing mapping framework (LDEM) using deep neural networks.<n>Specifically, we introduce a loss function that enforces density uniformity and geometric regularity, and utilize a hierarchical approach to predict the transformations at both the coarse and dense levels.<n>Our method demonstrates superior density-equalizing and bijectivity properties compared to prior methods for a wide range of simple and complex density distributions.
• Score: 0.6008132390640294
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data visualization, geometry processing, and medical imaging. Traditional approaches to DEM primarily rely on iterative numerical solvers for diffusion equations or optimization-based methods that minimize handcrafted energy functionals. However, these conventional techniques often face several challenges: they may suffer from limited accuracy, produce overlapping artifacts in extreme cases, and require substantial algorithmic redesign when extended from 2D to 3D, due to the derivative-dependent nature of their energy formulations. In this work, we propose a novel learning-based density-equalizing mapping framework (LDEM) using deep neural networks. Specifically, we introduce a loss function that enforces density uniformity and geometric regularity, and utilize a hierarchical approach to predict the transformations at both the coarse and dense levels. Our method demonstrates superior density-equalizing and bijectivity properties compared to prior methods for a wide range of simple and complex density distributions, and can be easily applied to surface remeshing with different effects. Also, it generalizes seamlessly from 2D to 3D domains without structural changes to the model architecture or loss formulation. Altogether, our work opens up new possibilities for scalable and robust computation of density-equalizing maps for practical applications.

Related papers

• Geometric Operator Learning with Optimal Transport [77.16909146519227]
  We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries.<n>For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space.<n> Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses.
  arXiv  Detail & Related papers  (2025-07-26T21:28:25Z)
• ND-SDF: Learning Normal Deflection Fields for High-Fidelity Indoor Reconstruction [50.07671826433922]
  It is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with differing characteristics.<n>We propose ND-SDF, which learns a Normal Deflection field to represent the angular deviation between the scene normal and the prior normal.<n>Our method not only obtains smooth weakly textured regions such as walls and floors but also preserves the geometric details of complex structures.
  arXiv  Detail & Related papers  (2024-08-22T17:59:01Z)
• Towards Universal Mesh Movement Networks [13.450178050669964]
  We introduce the Universal Mesh Movement Network (UM2N)<n>UM2N can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures.<n>We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case.
  arXiv  Detail & Related papers  (2024-06-29T09:35:12Z)
• GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image [94.56927147492738]
  We introduce GeoWizard, a new generative foundation model designed for estimating geometric attributes from single images. We show that leveraging diffusion priors can markedly improve generalization, detail preservation, and efficiency in resource usage. We propose a simple yet effective strategy to segregate the complex data distribution of various scenes into distinct sub-distributions.
  arXiv  Detail & Related papers  (2024-03-18T17:50:41Z)
• Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis [70.40950409274312]
  We modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. We also develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices.
  arXiv  Detail & Related papers  (2024-02-19T18:59:41Z)
• Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models [83.35835521670955]
  Surf-D is a novel method for generating high-quality 3D shapes as Surfaces with arbitrary topologies. We use the Unsigned Distance Field (UDF) as our surface representation to accommodate arbitrary topologies. We also propose a new pipeline that employs a point-based AutoEncoder to learn a compact and continuous latent space for accurately encoding UDF.
  arXiv  Detail & Related papers  (2023-11-28T18:56:01Z)
• A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems [3.6184545598911724]
  We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller-Segal (KS) chemotaxis system in two and three space dimensions. We further develop DeepParticle (DP) method to learn and generate solutions under variations of physical parameters.
  arXiv  Detail & Related papers  (2022-08-31T20:52:01Z)
• Volume Rendering of Neural Implicit Surfaces [57.802056954935495]
  This paper aims to improve geometry representation and reconstruction in neural volume rendering. We achieve that by modeling the volume density as a function of the geometry. Applying this new density representation to challenging scene multiview datasets produced high quality geometry reconstructions.
  arXiv  Detail & Related papers  (2021-06-22T20:23:16Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)

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.