Related papers: Sampling Visible GGX Normals with Spherical Caps
The growing use of wide angle image capture devices and the need for fast and accurate image analysis in computer visions have enforced the need for dedicated under-representation approaches. Most recent decomposition methods segment an…
Novel view synthesis from images, for example, with 3D Gaussian splatting, has made great progress. Rendering fidelity and speed are now ready even for demanding virtual reality applications. However, the problem of assisting humans in…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing…
Accurately estimating scene lighting is critical for applications such as mixed reality. Existing works estimate illumination by generating illumination maps or regressing illumination parameters. However, the method of generating…
Sky imaging systems use lenses to acquire images concentrating light beams in a sensor. The light beams received by the sky imager have an elevation angle with respect to the device normal. Thus, the pixels in the image contain information…
We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
In computed tomography, data consist of measurements of the attenuation of X-rays passing through an object. The goal is to reconstruct the linear attenuation coefficient of the object's interior. For each position of the X-ray source,…
In this contribution, we present a short account of gravitational lenses and how to calculate different properties of its images in the case of having a transparent distribution of matter such as the uniform transparent sphere, isothermal…
Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
A centred system forms the coherent image of the optical field on a spherical cap, taken as an object, on another spherical cap, whose vertex and curvature center are the respective paraxial images of the vertex and center of the object…
This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…
This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the…
We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, hence the lens cross section, for realistic…
The probability distribution of lens image separations is calculated for the ``standard'' gravitational lensing statistics model in an arbitrary, flat Robertson-Walker universe, where lensing galaxies are singular isothermal spheres that…
This paper explores the X-ray properties of `normal' galaxies using a shallow XMM-Newton survey covering an area of ~1.5deg2. The X-ray survey overlaps with the 2dF Galaxy Redshift Survey. Compared with previous studies this has the…
The fraction of high-redshift sources which are multiply-imaged by intervening galaxies is strongly dependent on the cosmological constant, and so can be a useful probe of the cosmological model. However its power is limited by various…