Related papers: Illumination depth
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
Low-light image enhancement is challenging in that it needs to consider not only brightness recovery but also complex issues like color distortion and noise, which usually hide in the dark. Simply adjusting the brightness of a low-light…
We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.
Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have…
Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable tridimensional imaging in a single shot. We demonstrate that it is possible to implement…
Underwater image restoration has been a challenging problem for decades since the advent of underwater photography. Most solutions focus on shallow water scenarios, where the scene is uniformly illuminated by the sunlight. However, the vast…
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
Illuminant estimation aims to infer scene illumination from image measurements despite intrinsic ambiguities between surface reflectance and lighting. Most existing methods operate on trichromatic RGB images and are therefore fundamentally…
Two transformation-optics inspired flat lenses are used to build up an optical system capable to transpose an area surrounding the object focal point in a magnified area surrounding the image focal point. The object and image focal points…
The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best…
Low light conditions not only degrade human visual experience, but also reduce the performance of downstream machine analytics. Although many works have been designed for low-light enhancement or domain adaptive machine analytics, the…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
We introduce the arithmetic width of a convex body, defined as the number of distinct values a linear functional attains on the lattice points within the body. Arithmetic width refines lattice width by detecting gaps in the lattice point…
This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…
Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…