相关论文: Global Illumination of non-Euclidean spaces

We report on the status of the string-inspired world line path integral formalism, a recently developed powerful tool for the reorganisation of standard perturbative amplitudes in quantum field theory. The method is outlined and the present…

We introduce a Geometry Informed Model for financial forecasting by embedding high dimensional market data onto constant curvature 2manifolds. Guided by the uniformization theorem, we model market dynamics as Brownian motion on spherical…

We propose a novel iterative method for optimally placing and orienting multiple cameras in a 3D scene. Sample applications include improving the accuracy of 3D reconstruction, maximizing the covered area for surveillance, or improving the…

Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…

The observation of objects located in inaccessible regions is a recurring challenge in a wide variety of important applications. Recent work has shown that indirect diffuse light reflections can be used to reconstruct objects and…

Illumination estimation from a single image is critical in 3D rendering and it has been investigated extensively in the computer vision and computer graphic research community. On the other hand, existing works estimate illumination by…

We solve the classic albedo and Milne problems of plane-parallel illumination of an isotropically-scattering half-space when generalized to a Euclidean domain $\mathbb{R}^d$ for arbitrary $d \ge 1$. A continuous family of pseudo-problems…

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra.…

We proposed Precomputed RadianceTransfer of GaussianSplats (PRTGS), a real-time high-quality relighting method for Gaussian splats in low-frequency lighting environments that captures soft shadows and interreflections by precomputing 3D…

We present a method for estimating lighting from a single perspective image of an indoor scene. Previous methods for predicting indoor illumination usually focus on either simple, parametric lighting that lack realism, or on richer…

We propose a computational model for shape, illumination and albedo inference in a pulsed time-of-flight (TOF) camera. In contrast to TOF cameras based on phase modulation, our camera enables general exposure profiles. This results in added…

We contribute several practical extensions to the probe based irradiance-field-with-visibility representation to improve image quality, constant and asymptotic performance, memory efficiency, and artist control. We developed these…

We propose a method for demonstrating equivalences beyond the saddlepoint approximation between quantities in quantum gravity that are defined by the Euclidean path integral, without assumptions about holographic duality. The method…

As a candidate for dark matter in galaxies, we study an SU(3) triplet of complex scalar fields which are non-minimally coupled to gravity. In the spherically symmetric static spacetime where the flat rotational velocity curves of stars in…

LiDAR (Light Detection and Ranging) is an advanced active remote sensing technique working on the principle of time of travel (ToT) for capturing highly accurate 3D information of the surroundings. LiDAR has gained wide attention in…

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave…

We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of…

This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the…

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…