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Active Appearance Models (AAMs) are one of the most popular and well-established techniques for modeling deformable objects in computer vision. In this paper, we study the problem of fitting AAMs using Compositional Gradient Descent (CGD)…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
Origami inspired architectures offer a powerful route toward lightweight, reconfigurable, and programmable robotic systems. Yet, a unified mechanics framework capable of seamlessly bridging rigid folding, elastic deformation, and stability…
End-to-end autonomous driving has evolved from the conventional paradigm based on sparse perception into vision-language-action (VLA) models, which focus on learning language descriptions as an auxiliary task to facilitate planning. In this…
Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies.…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
We present a learning-based approach for virtual try-on applications based on a fully convolutional graph neural network. In contrast to existing data-driven models, which are trained for a specific garment or mesh topology, our fully…
We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric…
The creation of high-fidelity, digital versions of human heads is an important stepping stone in the process of further integrating virtual components into our everyday lives. Constructing such avatars is a challenging research problem, due…
With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic…
The problem of deforming an artist-drawn caricature according to a given normal face expression is of interest in applications such as social media, animation and entertainment. This paper presents a solution to the problem, with an…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
Multi-view 3D reconstruction has achieved remarkable progress with the advent of feed-forward 3D reconstruction models. However, these models are typically trained and evaluated under ideal, degradation-free imaging conditions, whereas…
Joint rendering and deformation of mesh and 3D Gaussian Splatting (3DGS) have significant value as both representa tions offer complementary advantages for graphics applica tions. However, due to differences in representation and ren dering…
Coronary computed tomography angiography (CCTA) provides 3D information on obstructive coronary artery disease, but cannot fully visualize high-resolution features within the vessel wall. Intravascular imaging, in contrast, can spatially…
Despite the impressive progress on understanding and generating images shown by the recent unified architectures, the integration of 3D tasks remains challenging and largely unexplored. In this paper, we introduce UniUGG, the first unified…