相关论文: Cinematica Topologica
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
A pedestrian model's computation speed impacts the model applicability. However, little attention has been given to this model property in the field of pedestrian dynamics modelling. As such, no framework exists to guide the systematic…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
An effective maximum likelihood method is suggested to characterize the absorption/amplification properties of active optical media through homodyne detection.
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
We consider the problem of taking a video that is comprised of multiple periods of repetitive motion, and reordering the frames of the video into a single period, producing a detailed, single cycle video of motion. This problem is…
We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will…
Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…
We propose a new multi-frame method for efficiently computing scene flow (dense depth and optical flow) and camera ego-motion for a dynamic scene observed from a moving stereo camera rig. Our technique also segments out moving objects from…
We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has $\mathbb{R}^2$ as its ambient space, and is…
Consider the problem of finding a point in an ultrametric space with the minimum average distance to all points. We give this problem a Monte Carlo $O((\log^2(1/\epsilon))/\epsilon^3)$-time $(1+\epsilon)$-approximation algorithm for all…
We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in…
A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
We introduce the first audio-visual dataset for traffic anomaly detection taken from real-world scenes, called MAVAD, with a diverse range of weather and illumination conditions. In addition, we propose a novel method named AVACA that…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…