Related papers: Why are images smooth?
Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that…
Previously, Barlow and Attneave hypothesised a link between biological vision and information maximisation. Following Shannon, information was defined using the probability of natural images. Several physiological and psychophysical…
Understanding the 3D world from 2D images involves more than detection and segmentation of the objects within the scene. It also includes the interpretation of the structure and arrangement of the scene elements. Such understanding is often…
Within the set of the many complex factors driving gaze placement, the properities of an image that are associated with fixations under free viewing conditions have been studied extensively. There is a general impression that the field is…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We study samples of natural images for which a set of statistical characteristics is computed and scale-invariant properties of samples are demonstrated computationally. Computations of the power spectrum are carried out and a power-law…
In this paper we address the problem of matching two images with two different resolutions: a high-resolution image and a low-resolution one. The difference in resolution between the two images is not known and without loss of generality…
Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably…
How much does a single image reveal about the environment it was taken in? In this paper, we investigate how much of that information can be retrieved from a foreground object, combined with the background (i.e. the visible part of the…
Why are simple, regular, and symmetric shapes common in nature? Many natural shapes arise as solutions to energy minimisation or other optimisation problems, but is there a general relation between optima and simple, regular shapes and…
The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a…
We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry…
Size uniformity is one of the main criteria of superpixel methods. But size uniformity rarely conforms to the varying content of an image. The chosen size of the superpixels therefore represents a compromise - how to obtain the fewest…
We consider the bounds imposed by naturalness on the masses of superpartners for arbitrary points in nonminimal supersymmetric extensions of the standard model and for arbitrary messenger scales. This constitutes a significant…
We use an agnostic information-theoretic approach to investigate the statistical properties of natural images. We introduce the Multiscale Relevance (MSR) measure to assess the robustness of images to compression at all scales. Starting in…
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the…
Scaling and architectural advances have produced strikingly photorealistic image generative models, yet their mechanisms still remain opaque. Rather than advancing scaling, our goal is to strip away complicated engineering tricks and…