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We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…
3D Gaussian Splatting (3DGS) has demonstrated remarkable real-time performance in novel view synthesis, yet its effectiveness relies heavily on dense multi-view inputs with precisely known camera poses, which are rarely available in…
Variable projection methods prove highly efficient in solving separable nonlinear least squares problems by transforming them into a reduced nonlinear least squares problem, typically solvable via the Gauss-Newton method. When solving…
In this paper, we present a new mathematical foundation for image-based lighting. Using a simple manipulation of the local coordinate system, we derive a closed-form solution to the light integral equation under distant environment…
We present a method for reconstructing 3D shape of arbitrary Lambertian objects based on measurements by miniature, energy-efficient, low-cost single-photon cameras. These cameras, operating as time resolved image sensors, illuminate the…
We present an inverse method to compute freeform optical surfaces that transform a light distribution, parameterized by two source planes, into two separate target distributions. The surfaces can be reflectors or lenses, and control both…
We develop a non--perturbative method that yields analytical expressions for the deflection angle of light in a general static and spherically symmetric metric. It is an improvement on a method previously devised by the authors, and…
We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards…
This paper makes a first attempt to bring the Shape from Polarization (SfP) problem to the realm of deep learning. The previous state-of-the-art methods for SfP have been purely physics-based. We see value in these principled models, and…
Almost universally in computer vision, when surface derivatives are required, they are computed using only first order accurate finite difference approximations. We propose a new method for computing numerical derivatives based on 2D…
The paper introduces an accurate solution to dense orthographic Non-Rigid Structure from Motion (NRSfM) in scenarios with severe occlusions or, likewise, inaccurate correspondences. We integrate a shape prior term into variational…
Two-view structure-from-motion (SfM) is the cornerstone of 3D reconstruction and visual SLAM. Existing deep learning-based approaches formulate the problem by either recovering absolute pose scales from two consecutive frames or predicting…
Third order equations, which describe spherical surfaces (ss) or pseudospherical surfaces (pss), of the form \[ \nu\,z_{t}-\lambda\,z_{xxt}=A(z,z_{x},z_{xx})\,z_{xxx}+B(z,z_{x},z_{xx}) \] with $\nu$, $\lambda$ $\in$ $\mathbb{R}$,…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…
We present a physics-based inverse rendering method that learns the illumination, geometry, and materials of a scene from posed multi-view RGB images. To model the illumination of a scene, existing inverse rendering works either completely…
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock,…
We propose a novel model for decomposing grayscale images into three distinct components: the structural part, representing sharp boundaries and regions with strong light-to-dark transitions; the smooth part, capturing soft shadows and…
Imaging objects obscured by occluders is a significant challenge for many applications. A camera that could "see around corners" could help improve navigation and mapping capabilities of autonomous vehicles or make search and rescue…
Conventional imaging requires a line of sight to create accurate visual representations of a scene. In certain circumstances, however, obtaining a suitable line of sight may be impractical, dangerous, or even impossible. Non-line-of-sight…