Related papers: Why are images smooth?
For some images, descriptions written by multiple people are consistent with each other. But for other images, descriptions across people vary considerably. In other words, some images are specific $-$ they elicit consistent descriptions…
The Assouad and lower dimensions and dimension spectra quantify the regularity of a measure by considering the relative measure of concentric balls. On the other hand, one can quantify the smoothness of an absolutely continuous measure by…
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
Images tell stories, trigger emotions, and let us recall memories -- they make us think. Thus, they have the ability to attract and hold one's attention, which is the definition of being "interesting". Yet, the appeal of an image is highly…
Measuring visual similarity is critical for image understanding. But what makes two images similar? Most existing work on visual similarity assumes that images are similar because they contain the same object instance or category. However,…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
The texture is defined as spatial structure of the intensities of the pixels in an image that is repeated periodically in the whole image or regions, and makes the concept of the image. Texture, color and shape are three main components…
We propose a novel method of efficient upsampling of a single natural image. Current methods for image upsampling tend to produce high-resolution images with either blurry salient edges, or loss of fine textural detail, or spurious noise…
Moving our hands smoothly is essential to execute ordinary tasks, such as carrying a glass of water without spilling. Past studies have revealed a natural tendency to generate smooth trajectories when moving the hand from one point to…
It is hard for us humans to recognize things in nature until we have invented them ourselves. For image-forming optics, nature has made virtually every kind of lens humans have devised. But what about lensless "imaging"? Recently, we showed…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on…
The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates…
A fundamental problem in computer vision is that of inferring the intrinsic, 3D structure of the world from flat, 2D images of that world. Traditional methods for recovering scene properties such as shape, reflectance, or illumination rely…
Natural image matting separates the foreground from background in fractional occupancy which can be caused by highly transparent objects, complex foreground (e.g., net or tree), and/or objects containing very fine details (e.g., hairs).…
Humans are sensitive to complexity and regularity in patterns. The subjective perception of pattern complexity is correlated to algorithmic (Kolmogorov-Chaitin) complexity as defined in computer science, but also to the frequency of…
Objective measures of image quality generally operate by comparing pixels of a "degraded" image to those of the original. Relative to human observers, these measures are overly sensitive to resampling of texture regions (e.g., replacing one…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…
Image smoothing is a fundamental task in computer vision, that aims to retain salient structures and remove insignificant textures. In this paper, we aim to address the fundamental shortcomings of existing image smoothing methods, which…