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We introduce an inference-time scene optimization algorithm utilizing triangle soup, a collection of disconnected translucent triangle primitives, as the representation for the geometry and appearance of a scene. Unlike full-rank Gaussian…
In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the…
We propose a method for 3D shape reconstruction from unoriented point clouds. Our method consists of a novel SE(3)-equivariant coordinate-based network (TF-ONet), that parametrizes the occupancy field of the shape and respects the inherent…
We present Symphony, an $E(3)$-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
In classical analysis, the convergence behavior of power series solutions to differential or recurrence equations is generally assumed to be invariant under internal rearrangement. This paper challenges that belief by proving that, for…
We propose a variation on wavefield reconstruction inversion for seismic inversion, which takes advantage of randomized linear algebra as a way to overcome the typical limitations of conventional inversion techniques. Consequently, we can…
We study time and space equivariant wave maps from $M\times\RR\rightarrow S^2,$ where $M$ is diffeomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metric on $M$ can be written as…
Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
Watermarking is a commonly used strategy to protect creators' rights to digital images, videos and audio. Recently, watermarking methods have been extended to deep learning models -- in principle, the watermark should be preserved when an…
Recent progress in self-supervised representation learning has resulted in models that are capable of extracting image features that are not only effective at encoding image level, but also pixel-level, semantics. These features have been…
In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…
Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…
Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains.However, it remains a challenging task due to the inherent spherical distortion and geometry characteristics, resulting in…
Finding matching keypoints between images is a core problem in 3D computer vision. However, modern matchers struggle with large in-plane rotations. A straightforward mitigation is to learn rotation invariance via data augmentation. However,…
Underwater scene reconstruction is essential for immersive exploration of aquatic environments, yet remains challenging due to complex participating-media effects such as absorption and scattering, as well as the limited field of view (FoV)…
Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…
We argue that in the quantum motion of a scalar particle of mass "m" on S^3_R perturbed by the trigonometric Scarf potential (Scarf I) with one internal quantized dimensionless parameter, \ell, the 3D orbital angular momentum, and another,…
Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision…