Eurographics Digital Library
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Recent Submissions
Toward General-Purpose Monte Carlo PDE Solvers for Graphics Applications
(University of Waterloo, 2025-09-22) Sugimoto, Ryusuke
This thesis develops novel Monte Carlo methods for solving a wide range of partial differential equations (PDEs) relevant to computer graphics. While traditional discretization-based approaches efficiently compute global solutions, they often require expensive global solves even when only local evaluations are needed, and can struggle with complex or fine-scale geometries. Monte Carlo methods based on the classical Walk on Spheres (WoS) approach [Muller 1956] offer pointwise evaluation with strong geometric robustness, but in practice, their application has been largely limited to interior Dirichlet problems in volumetric domains. We significantly broaden this scope by designing versatile Monte Carlo solvers that handle a diverse set of PDEs and boundary conditions, validated through comprehensive experimental results.
First, we introduce the Walk on Boundary (WoB) method [Sabelfeld 1982, 1991] to graphics. While retaining WoS’s advantages, WoB applies to a broader range of second-order linear elliptic and parabolic PDE problems: various boundary conditions (Dirichlet, Neumann, Robin, and mixed) in both interior and exterior domains. Because WoB is based on boundary integral formulations, its structure more closely parallels Monte Carlo rendering than WoS, enabling the application of advanced variance reduction techniques. We present WoB formulations for elliptic Laplace and Poisson equations, time-dependent diffusion problems, and develop a WoB solver for vector-valued Stokes equations. Throughout, we discuss how sampling and variance reduction methods from rendering can be adapted to WoB.
Next, we address the nonlinear Navier-Stokes equations for fluid simulation, whose complexity challenges Monte Carlo techniques. Employing operator splitting, we separate nonlinear terms and solve the remaining linear terms with pointwise Monte Carlo solvers. Recursively applying these solvers with timestepping yields a spatial-discretization-free method. To deal with the resulting exponential computational cost, we also propose cache-based alternatives. Both vorticity- and velocity-based formulations are explored, retaining the advantages of Monte Carlo methods, including geometric robustness and variance reduction, while integrating traditional fluid simulation techniques.
We then propose Projected Walk on Spheres (PWoS), a novel solver for surface PDEs, inspired by the Closest Point Method. PWoS modifies WoS by projecting random walks onto the surface manifold at each step, preserving geometric flexibility and discretization-free, pointwise evaluation. We also adapt a noise filtering technique for WoS to improve PWoS.
Finally, we outline promising future research directions for Monte Carlo PDE solvers in graphics, including concrete proposals to enhance WoB.
Correction to 'Antarstick: Extracting Snow Height From Time-Lapse Photography'
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Lang, M.; Mráz, R.; Trtík, M.; Stoppel, S.; Byška, J.; Kozlíková, B.; Wimmer, Michael; Alliez, Pierre; Westermann, Rüdiger
Correction note to the article "Antarstick: Extracting Snow Height From Time-Lapse Photography".
Self-Supervised Image Harmonization via Region-Aware Harmony Classification
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Tian, Chenyang; Wang, Xinbo; Zhang, Qing; Wimmer, Michael; Alliez, Pierre; Westermann, Rüdiger
Image harmonization is a widely used technique in image composition, which aims to adjust the appearance of the composited foreground object according to the style of the background image so that the resulting composited image is visually natural and appears to be photographed. Previous methods are mostly trained in a fully supervised manner, while demonstrating promising results, they do not generalize well to complex unseen cases involving significant style and semantic difference between the composited foreground object and the background image. In this paper, we present a self-supervised image harmonization framework that enables superior performance on complex cases. To do so, we first synthesize a large amount of data with wide diversity for training. We then develop an attentive harmonization module to adaptively adjust the foreground appearance by querying relevant background features. To allow more effective image harmonization, we develop a region-aware harmony classifier to explicitly judge whether an image is harmonious or not. Experiments on several datasets show that our method performs favourably against previous methods. Our code will be made publicly available.
GeoDEN: A Visual Exploration Tool for Analyzing the Geographic Spread of Dengue Serotypes
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Marler, Aidan; Roell, Yannik; Knoblauch, Steffen; Messina Jane, P.; Jaenisch, Thomas; Karimzadeh, Mohammad; Wimmer, Michael; Alliez, Pierre; Westermann, Rüdiger
Static maps and animations remain popular in spatial epidemiology of dengue, limiting the analytical depth and scope of visualizations. Over half of the global population live in dengue endemic regions. Understanding the spatiotemporal dynamics of the four closely related dengue serotypes, and their immunological interactions, remains a challenge at a global scale. To facilitate this understanding, we worked with dengue epidemiologists in a user-centred design framework to create GeoDEN, an exploratory visualization tool that empowers experts to investigate spatiotemporal patterns in dengue serotype reports. The tool has several linked visualizations and filtering mechanisms, enabling analysis at a range of spatial and temporal scales. To identify successes and failures, we present both insight-based and value-driven evaluations. Our domain experts found GeoDEN valuable, verifying existing hypotheses and uncovering novel insights that warrant further investigation by the epidemiology community. The developed visual exploration approach can be adapted for exploring other epidemiology and disease incident datasets.
Herds From Video: Learning a Microscopic Herd Model From Macroscopic Motion Data
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Gong, Xianjin; Gain, James; Rohmer, Damien; Lyonnet, Sixtine; Pettré, Julien; Cani, Marie-Paule; Wimmer, Michael; Alliez, Pierre; Westermann, Rüdiger
We present a method for animating herds that automatically tunes a microscopic herd model based on a short video clip of real animals. Our method handles videos with dense herds, where individual animal motion cannot be separated out. Our contribution is a novel framework for extracting macroscopic herd behaviour from such video clips, and then deriving the microscopic agent parameters that best match this behaviour. To support this learning process, we extend standard agent models to provide a separation between leaders and followers, better match the occlusion and field-of-view limitations of real animals, support differentiable parameter optimization and improve authoring control. We validate the method by showing that once optimized, the social force and perception parameters of the resulting herd model are accurate enough to predict subsequent frames in the video, even for macroscopic properties not directly incorporated in the optimization process. Furthermore, the extracted herding characteristics can be applied to any terrain with a palette and region-painting approach that generalizes to different herd sizes and leader trajectories. This enables the authoring of herd animations in new environments while preserving learned behaviour.