Related papers: Qualitative shape representation based on the qual…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on one's purpose,…
An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…
Polymer representations of the Weyl algebra of linear systems provide the simplest analogues of the representation used in loop quantum gravity. The construction of these representations is algebraic, based on the Gelfand-Naimark-Segal…
Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges…
We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…
A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our…
Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrodinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
The paths on the {\bf R$^3$} real Euclidean manifold are defined as 2-dimensional simplicial strips; points are replaced by 2-simplexes and the orbits of the action of a one discrete-parameter group on the base manifold becomes a convex…