Related papers: The Scenery Flow for Self-Affine Measures

Estimating the 3D motion of points in a scene, known as scene flow, is a core problem in computer vision. Traditional learning-based methods designed to learn end-to-end 3D flow often suffer from poor generalization. Here we present a…

Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…

We prove real analyticity of all the streamlines, including the free surface, of a steady stratified flow of water over a flat bed in the absence of stagnation points, with a H\"older continuous Bernoulli function and a H\"older…

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then…

We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…

Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but…

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid…

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…

We introduce a way to learn to estimate a scene representation from a single image by predicting a low-dimensional subspace of optical flow for each training example, which encompasses the variety of possible camera and object movement.…

Particle suspensions, present in many natural and industrial settings, typically contain aggregates or other microstructures that can complicate macroscopic flow behaviors and damage processing equipment. Recent work found that applying…

Scene flow describes 3D motion in a 3D scene. It can either be modeled as a single task, or it can be reconstructed from the auxiliary tasks of stereo depth and optical flow estimation. While the second method can achieve real-time…

Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli…

We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic…

Scene flow enables an understanding of the motion characteristics of the environment in the 3D world. It gains particular significance in the long-range, where object-based perception methods might fail due to sparse observations far away.…

In this paper we investigate effects of boundary conditions on one dimensional pedestrian flow which involves purely longitudinal interactions. Qualitatively, stop-and-go waves are observed under closed boundary condition and dissolve when…

The importance and demands of visual scene understanding have been steadily increasing along with the active development of autonomous systems. Consequently, there has been a large amount of research dedicated to semantic segmentation and…

Quantitative measurements of fluid flow properties can be achieved by background oriented schlieren. In this paper it is shown that this depends on several factors. Image quality index is used to investigate the influence of the image…

For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…

In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than…

For the problem describing steady, gravity waves with vorticity on a two-dimensional, unidirectional flow of finite depth the following results are obtained. (i) Bounds for the free-surface profile and for Bernoulli's constant. (ii) If only…