相关论文: Cinematica Topologica
As an important information for traffic condition evaluation, trip planning, transportation management, etc., average travel speed for a road means the average speed of vehicles travelling through this road in a given time duration.…
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
In the present contribution three means of measuring the geometrical and topological complexity of photons' paths in random media are proposed. This is realized by investigating the behavior of the average crossing number, the mean writhe,…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
Accurately depicting the complex traffic scene is a vital component for autonomous vehicles to execute correct judgments. However, existing benchmarks tend to oversimplify the scene by solely focusing on lane perception tasks. Observing…
A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by…
We provide a mean curvature flow method for numerical cosmology and test it on cases of inhomogenous inflation. The results show (in a proof of concept way) that the method can handle even large inhomogeneities that result from different…
Optical flow estimation is a widely known problem in computer vision introduced by Gibson, J.J(1950) to describe the visual perception of human by stimulus objects. Estimation of optical flow model can be achieved by solving for the motion…
We consider the mathematical model of photoacoustic and thermoacoustic tomography in media with a variable sound speed. When the sound speed is known, the explicit reconstruction formula by P. Stefanov and G. Uhlmann (Inverse Problems,…
We study some topological properties of attractors.
We use tools from applied topology for feature selection on time series data. We develop a method for scoring the variables in a multivariate time series that reflects their contributions to the topological features of the corresponding…
The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets $A,B$ under a mild regularity hypothesis on one of the sets. We…
We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse)…
Time--distance inversions usually provide tomographic maps of the interesting plasma properties (we will focus on flows) at various depths. These maps however do not correspond directly to the flow field, but rather to the true flow field…
This paper considers the use of compressive sensing based algorithms for velocity estimation of moving vehicles. The procedure is based on sparse reconstruction algorithms combined with time-frequency analysis applied to video data. This…