gaussian heatmap generation

Real-world data often reside on low-dimensional, nontrivial manifolds embedded in high-dimensional spaces or within constrained domains with unknown boundaries—structures that conventional Gaussian processes (GPs) fail to capture due to their implicit Euclidean and global-coordinate assumptions. Existing manifold-aware GP approaches either presuppose a single flat latent embedding or degrade significantly under sparse and non-uniform sampling. To address this, we propose Riemannian-Corrected Atlas Gaussian Processes (RC-AGPs), which estimate the manifold’s heat kernel via an Atlas Brownian motion framework, integrate global heat-kernel priors with local RBF kernels, and perform Riemannian metric correction through manifold learning—without requiring global coordinates. RC-AGPs substantially improve heat-kernel estimation accuracy and regression performance on sparse and irregular point clouds. Extensive experiments on synthetic and real-world benchmarks demonstrate consistent superiority over state-of-the-art manifold GP methods, establishing a robust, geometry-aware paradigm for high-dimensional statistical inference on complex topological domains.

This paper addresses Gaussian process regression (GPR) under privacy constraints where only aggregated spatial data—such as representative features, summary statistics, and sample counts—are available, precluding access to raw point-level observations. To bridge this gap, we propose a novel GPR framework tailored to aggregated inputs. Its core innovation is the introduction of “sample pseudo-likelihood,” a theoretically grounded approximation that characterizes the error induced by aggregation and establishes a mapping between the variance function and non-Gaussian likelihoods—thereby relaxing GPR’s classical dependence on exact point data. Theoretical analysis reveals that model accuracy hinges on the ratio between aggregation granularity and the covariance length scale. Extensive experiments on real-world spatial datasets demonstrate that our method significantly improves modeling utility and inference reliability in privacy-preserving settings, while maintaining rigorous statistical foundations.

To address the ambiguity between free and unknown space in continuous occupancy mapping for mobile robots, this paper proposes a geometry-aware occupancy mapping method based on Gaussian process (GP) latent function fields. Unlike conventional three-class (free/occupied/unknown) grid classification, we reformulate occupancy as a zero-measure boundary between free and unknown states—effectively reducing the problem to a binary free-vs-unknown decision. Crucially, we introduce sensor field-of-view geometric priors directly into the GP latent domain, enabling end-to-end modeling via logistic regression coupled with implicit function optimization. This formulation avoids discretization errors and redundant observation modeling inherent in grid-based approaches. Evaluated in simulation, our method achieves state-of-the-art reconstruction accuracy while significantly improving computational efficiency.

This study addresses the technical gap between domain experts and non-experts in geostatistics by proposing and implementing the first open-source, integrated spatial interpolation library. To bridge this gap, we develop a unified framework that synergistically combines classical geostatistical methods (e.g., ordinary and universal kriging) with modern machine learning techniques. Our approach employs ensemble learning to automatically select and optimize interpolation strategies, and integrates stochastic simulation for posterior distribution inference—enabling both point estimation and rigorous uncertainty quantification. Built on a hybrid Python/C++ architecture, the library balances usability, computational efficiency, and extensibility. Empirical evaluation across diverse real-world spatial datasets demonstrates accuracy competitive with or superior to conventional methods. Moreover, the library provides standardized APIs, comprehensive uncertainty assessment, and built-in visualization tools—collectively lowering the barrier to entry for spatial modeling.

Existing 3D Gaussian splatting methods rely on manual cloning/segmentation and sensitive initialization, resulting in unstable rendering quality and poor controllability over Gaussian count. This work reformulates the 3D Gaussian point set as a Monte Carlo Markov Chain (MCMC) sampling process of the scene’s physical representation. We replace heuristic Gaussian splitting/cloning with stochastic gradient Langevin dynamics (SGLD), and recast densification and pruning as deterministic MCMC state transitions. A probabilistic density relocation mechanism supplants cloning, while an unused-Gaussian regularizer enables flexible control over Gaussian count and robust initialization. Evaluated on standard benchmarks, our method achieves significantly improved rendering quality, reduces reliance on manual hyperparameter tuning, and unifies neural rendering with principled probabilistic modeling.

This work addresses the limitations of existing online high-definition map construction methods, which rely on fixed-resolution bird’s-eye-view (BEV) grids and struggle to efficiently model sparse yet geometrically precise map elements. To overcome this, the authors propose an online mapping framework based on adaptive Gaussian representations, replacing conventional dense BEV grids with learnable Gaussian primitives that enable dynamic allocation of modeling resources and high-fidelity geometric representation in critical regions. The approach leverages Gaussian interaction modeling and multi-sensor feature fusion to generate structured BEV features through a feedforward encoder, which are subsequently decoded into vectorized maps. Evaluated on the nuScenes and Argoverse 2 datasets, the method achieves state-of-the-art performance under both pure vision and camera–LiDAR fusion settings.

This study addresses the challenge of disentangling background spatial inhomogeneity—driven by site-specific attractiveness—from inter-individual repulsive interactions in pedestrian waiting behavior, using repeated observations of spatial point patterns. To this end, the authors propose a novel semi-parametric spatial point process model that integrates a determinantal point process with a Gibbs point process. For the first time, repeated spatial point patterns are incorporated into the inference framework of such models, enabling parameter estimation and model assessment based on multiple independent and identically distributed spatial realizations. Applied to real-world pedestrian waiting scenarios, the method successfully reproduces key empirical spatial characteristics, demonstrating its effectiveness in capturing complex crowd distributions and achieving a tight integration of methodological innovation with practical application.

This paper addresses two key challenges in point-supervised density regression: (1) difficulty in modeling pixel-to-annotation correspondences, and (2) high computational cost of optimal transport (OT) computation. To this end, we propose the Gaussian Spatial Transport (GST) framework—the first to introduce Gaussian lattice discretization into point-supervised learning. GST models both the image coordinate space and the annotation map as probability measures and directly solves for the transport plan via closed-form Bayesian inference, bypassing iterative OT optimization. Furthermore, we design a differentiable loss function grounded in measure transport, enabling end-to-end network training. GST is non-iterative, computationally efficient, and fully differentiable. Experiments on crowd counting and keypoint detection demonstrate substantial acceleration in training speed while maintaining state-of-the-art accuracy, validating both its effectiveness and cross-task generalizability.

Traditional Gaussian processes suffer from computational intractability in high-dimensional spatiotemporal forecasting, while Transformers lack spatial geometric priors, limiting physical interpretability and extrapolation. Method: We propose Spatially-Aware Transformer (SAT), which embeds a learnable anisotropic covariance kernel into the self-attention mechanism, decomposing it into a physics-driven stationary prior and a data-driven non-stationary residual. We introduce “deep variogram analysis” for end-to-end inversion of spatial decay parameters and incorporate soft topological constraints to inject geostatistical inductive bias. Contribution/Results: SAT achieves state-of-the-art performance on synthetic Gaussian random fields and real-world traffic datasets—outperforming graph neural networks in both point prediction accuracy and probabilistic calibration. It yields strictly calibrated uncertainty estimates while unifying physical interpretability with data-driven expressiveness, enabling scalable, principled spatiotemporal forecasting.

This work addresses the performance degradation of existing LiDAR-inertial-visual Gaussian splatting methods in weakly textured or drastically varying illumination scenarios, where reliance on RGB photometric information proves insufficient. To overcome this limitation, we propose a novel Gaussian splatting framework that fuses LiDAR, inertial, and thermal imaging modalities. Our approach explicitly embeds planar geometry extracted from LiDAR into the optimization pipeline by enforcing point-to-plane residual constraints on pose and structure estimation. We further introduce cross-modal anchor points to establish robust correspondences between thermal images and LiDAR data. A joint optimization strategy supervised by thermal cues, combined with a plane-regularized differentiable rendering objective, effectively mitigates surface bloating and structural drift caused by low-contrast thermal imagery. Experiments demonstrate that our method significantly outperforms state-of-the-art approaches on both self-collected and public datasets, achieving superior geometric accuracy and rendering fidelity under challenging lighting conditions.