Related papers: A distance on curves modulo rigid transformations
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
We provide a definition of the quantum distances of correlated many fermion wave functions in terms of the expectation values of certain operators that we call exchange operators. We prove that the distances satisfy the triangle…
We study a variational framework to compare shapes, modeled as Radon measures on R^N, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
This paper contains a comparative study of two families of simple curves drawn in the plane. On the one hand, we have the fractal curves on the unit interval, with self-similar structure, which have associated a Hausdorff dimension. On the…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
We define a new type of Hardy-Orlicz spaces of conformal mappings on the unit disk where in place of the value |f(x)| we consider the intrinsic path distance between f(x) and f(0) in the image domain. We show that if the Orlicz function is…
In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not…
One-parameter persistence modules are applied to various subjects as tools in data analysis. On the other hand, since the theoretical study of multi-parameter persistence modules is not enough and in progress, they have few applications.…
We compute the minimum distance of the parameterized code of order 1 over an even cycle.
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Due to its many applications, \emph{curve simplification} is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve $P$ with $n$ vertices,…
We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…
A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between…
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…
The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…