Related papers: Surface Comparison with Mass Transportation
A surface moving mesh method is presented for general surfaces with or without explicit parameterization. The method can be viewed as a nontrivial extension of the moving mesh partial differential equation method that has been developed for…
We present a model to measure the similarity in appearance between different materials, which correlates with human similarity judgments. We first create a database of 9,000 rendered images depicting objects with varying materials, shape…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our…
We present methods for approximating the mapping that defines the invariant manifold for two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If…
Transportation systems can be conceptualized as an instrument of spreading people and resources over the territory, playing an important role in developing sustainable cities. The current rationale of transport provision is based on…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and…
In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…
We are in the midst of a technology-driven transformation of the urban mobility landscape. However, unfortunately these new innovations are still dominated by car-centric personal mobility, which leads to concerns such as environmental…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…
Modelling and simulation of mixed-traffic zones is an important tool for transportation planners to assess safety, efficiency, and human-friendliness of future urban areas. This paper addresses problems of calibration and transferability of…
The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by partial…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
This paper presents a novel computational approach for evaluating urban metrics through density gradient analysis using multi-modal satellite imagery, with applications including public transport and other urban systems. By combining…
Spatio-temporal trajectory analytics is at the core of smart mobility solutions, which offers unprecedented information for diversified applications such as urban planning, infrastructure development, and vehicular networks. Trajectory…
We review the research literature investigating systems in which mobile entities can carry data while they move. These entities can be either mobile by nature (e.g., human beings and animals) or mobile by design (e.g., trains, airplanes,…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…