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Recent Submissions
Intrinsic approaches to learning and computing on curved surfaces
(2024-10-15) Wiersma, Ruben Timotheüs
This dissertation develops intrinsic approaches to learning and computing on curved surfaces. Specifically, we work on three tasks: analyzing 3D shapes using convolutional neural networks (CNNs), solving linear systems on curved surfaces, and recovering appearance properties from curved surfaces using multi-view capture. We argue that we can find more efficient and better performing algorithms for these tasks by using intrinsic geometry.
Chapter two and three consider CNNs on curved surfaces. We would like to find patterns with meaningful directional information, such as edges or corners.
On images, it is straightforward to define a convolution operator that encodes directional information, as the pixel grid provides a global reference for directions. Such a global coordinate system is not available for curved surfaces. Chapter two presents Harmonic Surface Networks. We apply a 2D kernel to the surface by using local coordinate systems. These local coordinate systems could be rotated in any direction around the normal, which is a problem for consistent pattern recognition. We overcome this ambiguity by computing complex-valued, rotation-equivariant features and transporting these features between coordinate systems with parallel transport along shortest geodesics.
Chapter three presents DeltaConv. DeltaConv is a convolution operator based on geometric operators from vector calculus, such as the Laplacian. A benefit of the Laplacian is that it is invariant to local coordinate systems. This solves the problem of a missing global coordinate system. However, the Laplacian operator is also isotropic. That means it cannot pick up on directional information. DeltaConv constructs anisotropic operators by splitting the Laplacian into gradient and divergence and applying a non-linearity in between. The resulting convolution operators are demonstrated on learning tasks for point clouds and achieve state-of-the-art results with a relatively simple architecture.
Chapter four considers solving linear systems on curved surfaces. This is relevant for many applications in geometry processing: smoothing data, simulating or animating 3D shapes, or machine learning on surfaces. A common way to solve large systems on grid-based data is a multigrid method. Multigrid methods require a hierarchy of grids and the operators that map between the levels in the hierarchy. We show that these components can be defined for curved surfaces with irregularly spaced samples using a hierarchy of graph Voronoi diagrams. The resulting approach, Gravo Multigrid, achieves solving times comparable to the state-of-the-art, while taking an order of magnitude less time for pre-processing: from minutes to seconds for meshes with over a million vertices.
Chapter five demonstrates the use of intrinsic geometry in the setting of appearance modeling, specifically capturing spatially-varying bidirectional reflectance distribution functions (SVBRDF). A low-cost setup to recover SVBRDFs is to capture photographs from multiple viewpoints. A challenge here, is that some reflectance behavior only shows up under certain viewing positions and lighting conditions, which means that we might not be able to tell one material type from another. We frame this as a question of (un)certainty: how certain are we, based on the input data? We build on previous work that shows that the reflection function can be modeled as a convolution of the BRDF with the incoming light. We propose improvements to the convolution model and develop algorithms for uncertainty analysis fully contained in the frequency domain. The result is a fast and uncertainty-aware SVBRDF recovery on curved surfaces.
Photorealistic Simulation and Optimization of Lighting Conditions
(2024-05) Vitsas, Nick
Lighting plays a very important role in our everyday life, affecting our safety, comfort, well-being and performance. Today, computational methods and tools can be applied to provide recommendations for improving light conditions and finding energy-efficient ways to exploit natural lighting. This thesis addresses the problem of computational optimization of light transport to improve lighting effectiveness, by improving on various aspects of the process, such as goal-driven parametric geometry configuration for building openings and interior design, efficient natural lighting sampling and interactive photorealistic simulation of light transport. Physically-based light transport is at the core of each task and we show how lighting evaluation has a broader application scope than image synthesis. In the domain of light-driven geometry optimization, the thesis makes two contributions, one concerning the opening design problem and one regarding the optimal arrangement of movable objects for interior design. Opening design comes at the early stages of architectural design. and concerns decisions about the geometric characteristics of windows, skylights, hatches, etc. It greatly impacts the overall energy efficiency, thermal profile, air flow and appearance of a building, both internally and externally. It also directly controls daylighting availability, which is very difficult to predict and assess without automatic tools. We developed a computational methodology and a system to automate the process of opening recommendations in a fully interactive virtual environment, fully supporting parametric constraints and illumination intentions. We optimize openings with respect to their shape, position, size and cardinality, based on Bayesian optimization to propose physically correct openings on the geometry of the building. For the light-driven interior design problem, we proposed and evaluated an automatic interior layout process to produce valid object arrangements guided by geometric and illumination constraints, optimizing for glare, correct illuminance levels and lighting uniformity. Geometric and lighting goals are combined into a cost function that allows for a hierarchical, stochastic exploration of the available space of valid configurations. Optimizing for the contribution of natural lighting is an integral part of any outdoor and indoor environment design process. Analytic formulas for clear skies are a computationally and memory efficient method to create physically accurate sky maps of clear sunny days. However, to simulate light transport, sky models must be efficiently sampled. This is typically done via standard importance sampling approaches for image-based lighting, which tend to be slow and wasteful for the predictable nature of the radiance distribution of analytic sky models. We propose and evaluate a method for fitting a truncated Gaussian mixture model on the radiance distribution of the sky map that is both compact and fast to evaluate. Light-driven geometry optimization requires both accurate and fast light transport evaluation, since a very large number of light-carrying paths needs to be evaluated at each new proposal state. Advances in graphics hardware have enabled interactive ray tracing, which relies on highly optimized data structures for the acceleration of ray queries. Bounding volume hierarchies based on axis-aligned bounding boxes have been the go-to data structure for fast ray-primitive intersections. Similar hierarchies of oriented bounding boxes (OBBs) provide much higher early hierarchy traversal termination rates, however their construction requires complex algorithms for the extraction of tight-fitting OBBs. To further accelerate ray tracing for our tasks, we properly adapt a high quality OBB extraction algorithm from unordered point sets to operate directly on existing hierarchies, to effectively construct an OBB tree on the GPU. By combining our method with existing fast algorithms from the literature that construct hierarchies in real-time, we are able to produce OBB trees that are extremely fast to build and traverse on the GPU. Furthermore, to allow for accurate light transport evaluators accessible as industry-grade tools, we developed and presented WebRays, the first generic ray intersection framework for the Web that offers a programming interface similar to modern ray tracing pipelines for desktop platforms and allows the implementation of light-driven design tools accessible from any platform
Robust Diffusion-based Motion In-betweening
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Qin, Jia; Yan, Peng; An, Bo; Chen, Renjie; Ritschel, Tobias; Whiting, Emily
The emergence of learning-based motion in-betweening techniques offers animators a more efficient way to animate characters. However, existing non-generative methods either struggle to support long transition generation or produce results that lack diversity. Meanwhile, diffusion models have shown promising results in synthesizing diverse and high-quality motions driven by text and keyframes. However, in these methods, keyframes often serve as a guide rather than a strict constraint and can sometimes be ignored when keyframes are sparse. To address these issues, we propose a lightweight yet effective diffusionbased motion in-betweening framework that generates animations conforming to keyframe constraints.We incorporate keyframe constraints into the training phase to enhance robustness in handling various constraint densities. Moreover, we employ relative positional encoding to improve the model's generalization on long range in-betweening tasks. This approach enables the model to learn from short animations while generating realistic in-betweening motions spanning thousands of frames. We conduct extensive experiments to validate our framework using the newly proposed metrics K-FID, K-Diversity, and K-Error, designed to evaluate generative in-betweening methods. Results demonstrate that our method outperforms existing diffusion-based methods across various lengths and keyframe densities. We also show that our method can be applied to text-driven motion synthesis, offering fine-grained control over the generated results.
G-Style: Stylized Gaussian Splatting
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Kovács, Áron Samuel; Hermosilla, Pedro; Raidou, Renata Georgia; Chen, Renjie; Ritschel, Tobias; Whiting, Emily
We introduce G -Style, a novel algorithm designed to transfer the style of an image onto a 3D scene represented using Gaussian Splatting. Gaussian Splatting is a powerful 3D representation for novel view synthesis, as-compared to other approaches based on Neural Radiance Fields-it provides fast scene renderings and user control over the scene. Recent pre-prints have demonstrated that the style of Gaussian Splatting scenes can be modified using an image exemplar. However, since the scene geometry remains fixed during the stylization process, current solutions fall short of producing satisfactory results. Our algorithm aims to address these limitations by following a three-step process: In a pre-processing step, we remove undesirable Gaussians with large projection areas or highly elongated shapes. Subsequently, we combine several losses carefully designed to preserve different scales of the style in the image, while maintaining as much as possible the integrity of the original scene content. During the stylization process and following the original design of Gaussian Splatting, we split Gaussians where additional detail is necessary within our scene by tracking the gradient of the stylized color. Our experiments demonstrate that G -Style generates high-quality stylizations within just a few minutes, outperforming existing methods both qualitatively and quantitatively
Palette-Based Recolouring of Gradient Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Houssaije, Willard A. Verschoore de la; Echevarria, Jose; Kosinka, Jirí; Chen, Renjie; Ritschel, Tobias; Whiting, Emily
Gradient meshes are a vector graphics primitive formed by a regular grid of bicubic quad patches. They allow for the creation of complex geometries and colour gradients, with recent extensions supporting features such as local refinement and sharp colour transitions. While many methods exist for recolouring raster images, often achieved by modifying an automatically detected palette of the image, gradient meshes have not received the same amount of attention when it comes to global colour editing. We present a novel method that allows for real-time palette-based recolouring of gradient meshes, including gradient meshes constructed using local refinement and containing sharp colour transitions. We demonstrate the utility of our method on synthetic illustrative examples as well as on complex gradient meshes.