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We present 3D Surface Splatting (3DSS), the first differentiable surface splatting renderer for physically-based inverse rendering from multi-view images. Our central insight is that the surface separation problem at the heart of surface…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
An exact analogy between wave mechanics in quantum theory and the scalar wave treatment of optics emerges from the marriage of Newtonian formulation of geometrical optics [1] and the ``formal quantum theory of light rays'' [2]. Here the…
Gamma-Ray Bursts (GRBs) offer a potential way to extend the Hubble diagram to very high redshifts and to constrain the nature of dark energy in a way complementary to distant type Ia supernovae. However, gravitational lensing systematically…
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering…
The distributions of toroidal data, often viewed as an extension of circular distributions, do not consider the intrinsic geometry of a curved torus. For the first time, Diaconis et al. (2013)[Diaconis, P., Holmes, S., & Shahshahani, M.…
The Artmann formula provides an accurate determination of the Goos-Haenchen lateral displacement in terms of the light wavelength, refractive index and incidence angle. In the total reflection region, this formula is widely used in the…
3D Gaussian Splatting (3DGS) has demonstrated impressive capabilities in novel view synthesis. However, rendering reflective objects remains a significant challenge, particularly in inverse rendering and relighting. We introduce RTR-GS, a…
Many modern imaging and remote sensing applications require reconstructing a function from spherical averages (mean values). Examples include photoacoustic tomography, ultrasound imaging or SONAR. Several formulas of the back-projection…
The altitude distribution of optical turbulence is derived from the MASS instrument data by solving an inverse problem. In this paper, some modifications of the profile restoration are described. The principal change is the introduction of…
Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…
Aims: We explore the lensing properties of asymmetric matter density distributions in Bekenstein's Tensor-Vector-Scalar theory (TeVeS). Methods: Using an iterative Fourier-based solver for the resulting non-linear scalar field equation, we…
To the best of our knowledge, there are no specific calculations of gravity-darkening exponents for white dwarfs in the literature. On the other hand, the number of known eclipsing binaries whose components are tidally and/or rotationally…
We present here a compactly formulated application of the previously posted general formalism of the reflection of Gaussian beams at a dielectric interface ({arXiv:0710.1643v2 [physics.optics]}). Specifically, we calculate the…
In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…
This study concentrates on advancing mathematical and computational methodology for radar tomography imaging in which the unknown volumetric velocity distribution of a wave within a bounded domain is to be reconstructed. Our goal is to…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible…
Angular deviations and lateral displacements are optical effects widely investigated in literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic expression for the beam reflected by and…