Related papers: Reflection in a Translation Invariant Surface

We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images,…

Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…

We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

In this paper, we present a novel method to draw a circle tangent to three given circles lying on a plane. Using the analytic geometry and inversion (reflection) theorems, the center and radius of the inversion circle are obtained. Inside…

We tackle the problem of generating highly realistic and plausible mirror reflections using diffusion-based generative models. We formulate this problem as an image inpainting task, allowing for more user control over the placement of…

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…

We consider the problem of mirror invisibility for plane sets. Given a circle and a finite number of unit vectors (defining the directions of invisibility) such that the angles between them are commensurable with $\pi$, for any $\varepsilon…

This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…

We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

This paper continues the study of a class of compact convex hypersurfaces in Euclidean space $R^{n+1}, ~n \geq 1$, which are boundaries of compact convex bodies obtained by taking the intersection of (solid) confocal paraboloids of…

Generative image models can produce convincingly real images, with plausible shapes, textures, layouts and lighting. However, one domain in which they perform notably poorly is in the synthesis of transparent objects, which exhibit…

A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function…

Diffusion models have become central to various image editing tasks, yet they often fail to fully adhere to physical laws, particularly with effects like shadows, reflections, and occlusions. In this work, we address the challenge of…

Reflectometry is a technique that uses the light reflected by a sample to determine properties of the sample. Interferometric reflectometry uses interference between two beams, one of which is incident on ---and reflected back by--- a…

In this paper, we address the problem of reflection removal and deblurring from a single image captured by a plenoptic camera. We develop a two-stage approach to recover the scene depth and high resolution textures of the reflected and…