2D Gaussians Spatial Transport for Point-supervised Density Regression

• URL: http://arxiv.org/abs/2511.14477v2
• Date: Mon, 24 Nov 2025 07:16:18 GMT
• Title: 2D Gaussians Spatial Transport for Point-supervised Density Regression
• Authors: Miao Shang, Xiaopeng Hong,
• Abstract summary: This paper introduces a novel framework that leverages Gaussian splatting to facilitate transport from the probability measure in the image coordinate space to the annotation map.<n>We propose a method to estimate pixel-annotation correspondence, which is then used to compute a transport plan derived from Bayesian probability.<n>Experiments on representative computer vision tasks, including crowd counting and landmark detection, validate the effectiveness of our approach.
• Score: 32.39131587673642
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces Gaussian Spatial Transport (GST), a novel framework that leverages Gaussian splatting to facilitate transport from the probability measure in the image coordinate space to the annotation map. We propose a Gaussian splatting-based method to estimate pixel-annotation correspondence, which is then used to compute a transport plan derived from Bayesian probability. To integrate the resulting transport plan into standard network optimization in typical computer vision tasks, we derive a loss function that measures discrepancy after transport. Extensive experiments on representative computer vision tasks, including crowd counting and landmark detection, validate the effectiveness of our approach. Compared to conventional optimal transport schemes, GST eliminates iterative transport plan computation during training, significantly improving efficiency. Code is available at https://github.com/infinite0522/GST.

Related papers

• Efficient Transferable Optimal Transport via Min-Sliced Transport Plans [25.845827856681492]
  We study the min-Sliced Transport Plan (min-STP) framework and investigate the transferability of optimized slicers.<n>We show that optimized slicers remain close under slight perturbations of the data distributions, enabling efficient transfer across related tasks.
  arXiv  Detail & Related papers  (2025-11-24T21:59:12Z)
• Unified Linear Parametric Map Modeling and Perception-aware Trajectory Planning for Mobile Robotics [1.7495208770207367]
  We introduce a lightweight linear parametric map by first mapping data to a high-dimensional space, followed by a sparse random projection for dimensionality reduction.<n>For UAVs, our method grid and Euclidean Signed Distance Field (ESDF) maps.<n>For UGVs, the model characterizes terrain and provides closed-form gradients, enabling online planning to circumvent large holes.
  arXiv  Detail & Related papers  (2025-07-12T16:39:19Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• InfoOT: Information Maximizing Optimal Transport [58.72713603244467]
  InfoOT is an information-theoretic extension of optimal transport. It maximizes the mutual information between domains while minimizing geometric distances. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples.
  arXiv  Detail & Related papers  (2022-10-06T18:55:41Z)
• GAN Estimation of Lipschitz Optimal Transport Maps [0.0]
  This paper introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. We demonstrate that, under regularity assumptions, the obtained generator converges uniformly to the optimal transport map as the sample size increases to infinity. In contrast to previous work tackling either statistical guarantees or practicality, we provide an expressive and feasible estimator which paves way for optimal transport applications.
  arXiv  Detail & Related papers  (2022-02-16T10:15:56Z)
• An Optimal Transport Perspective on Unpaired Image Super-Resolution [97.24140709634203]
  Real-world image super-resolution (SR) tasks often do not have paired datasets, which limits the application of supervised techniques.<n>We investigate optimization problems which arise in such models and find two surprising observations.<n>We prove and empirically show that the learned map is biased, i.e., it does not actually transform the distribution of low-resolution images to high-resolution ones.
  arXiv  Detail & Related papers  (2022-02-02T16:21:20Z)
• Neural Optimal Transport [82.2689844201373]
  We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. We prove that neural networks are universal approximators of transport plans between probability distributions.
  arXiv  Detail & Related papers  (2022-01-28T16:24:13Z)
• Near-optimal estimation of smooth transport maps with kernel sums-of-squares [81.02564078640275]
  Under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. The object of interest for applications such as generative modeling is the underlying optimal transport map. We propose the first tractable algorithm for which the statistical $L2$ error on the maps nearly matches the existing minimax lower-bounds for smooth map estimation.
  arXiv  Detail & Related papers  (2021-12-03T13:45:36Z)
• Approximating Optimal Transport via Low-rank and Sparse Factorization [19.808887459724893]
  Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. A novel approximation for OT is proposed, in which the transport plan can be decomposed into the sum of a low-rank matrix and a sparse one.
  arXiv  Detail & Related papers  (2021-11-12T03:10:45Z)
• Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark [133.46066694893318]
  We evaluate the performance of neural network-based solvers for optimal transport. We find that existing solvers do not recover optimal transport maps even though they perform well in downstream tasks.
  arXiv  Detail & Related papers  (2021-06-03T15:59:28Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)
• Statistical Optimal Transport posed as Learning Kernel Embedding [0.0]
  This work takes the novel approach of posing statistical Optimal Transport (OT) as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings. A key result is that, under very mild conditions, $epsilon$-optimal recovery of the transport plan as well as the Barycentric-projection based transport map is possible with a sample complexity that is completely dimension-free.
  arXiv  Detail & Related papers  (2020-02-08T14:58:53Z)

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.