Patch-based Representation and Learning for Efficient Deformation Modeling

In this paper, we present a patch-based representation of surfaces, PolyFit, which is obtained by fitting jet functions locally on surface patches. Such a representation can be learned efficiently in a supervised fashion from both analytic functions and real data. Once learned, it can be generalized to various types of surfaces. Using PolyFit, the surfaces can be efficiently deformed by updating a compact set of jet coefficients rather than optimizing per-vertex degrees of freedom for many downstream tasks in computer vision and graphics. We demonstrate the capabilities of our proposed methodologies with two applications: 1) Shape-from-template (SfT): where the goal is to deform the input 3D template of an object as seen in image/video. Using PolyFit, we adopt test-time optimization that delivers competitive accuracy while being markedly faster than offline physics-based solvers, and outperforms recent physics-guided neural simulators in accuracy at modest additional runtime. 2) Garment draping. We train a self-supervised, mesh- and garment-agnostic model that generalizes across resolutions and garment types, delivering up to an order-of-magnitude faster inference than strong baselines.

Image-Guided Shape-from-Template Using Mesh Inextensibility Constraints

Shape-from-Template (SfT) refers to the class of methods that reconstruct the 3D shape of a deforming object from images/videos using a 3D template. Traditional SfT methods require point correspondences between images and the texture of the 3D template in order to reconstruct 3D shapes from images/videos in real time. Their performance severely degrades when encountered with severe occlusions in the images because of the unavailability of correspondences. In contrast, modern SfT methods use a correspondence-free approach by incorporating deep neural networks to reconstruct 3D objects, thus requiring huge amounts of data for supervision. Recent advances use a fully unsupervised or self-supervised approach by combining differentiable physics and graphics to deform 3D template to match input images. In this paper, we propose an unsupervised SfT which uses only image observations: color features, gradients and silhouettes along with a mesh inextensibility constraint to reconstruct at a $400\times$ faster pace than (best-performing) unsupervised SfT. Moreover, when it comes to generating finer details and severe occlusions, our method outperforms the existing methodologies by a large margin. Code is available at https://github.com/dvttran/nsft.

SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models

A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is obtained by solving differential equations (DE) defined by the learnt model, a process which has shown to be prohibitively slow. Numerous efforts on speeding-up this process have consisted on crafting powerful ODE solvers. Despite being quick, such solvers do not usually reach the optimal quality achieved by available slow SDE solvers. Our goal is to propose SDE solvers that reach optimal quality without requiring several hundreds or thousands of NFEs to achieve that goal. In this work, we propose Stochastic Exponential Derivative-free Solvers (SEEDS), improving and generalizing Exponential Integrator approaches to the stochastic case on several frameworks. After carefully analyzing the formulation of exact solutions of diffusion SDEs, we craft SEEDS to analytically compute the linear part of such solutions. Inspired by the Exponential Time-Differencing method, SEEDS uses a novel treatment of the stochastic components of solutions, enabling the analytical computation of their variance, and contains high-order terms allowing to reach optimal quality sampling $\sim3$-$5\times$ faster than previous SDE methods. We validate our approach on several image generation benchmarks, showing that SEEDS outperforms or is competitive with previous SDE solvers. Contrary to the latter, SEEDS are derivative and training free, and we fully prove strong convergence guarantees for them.