Related papers: Directions and projective shapes
Dual to Koldobsky's notion of j-intersection bodies, the class of j-projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j-projection bodies…
In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The…
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
A generalized connection, including Christoffel coefficients, torsion, non-metricity tensor and metric-asymmetricity object, is analyzed according to the Schouten classification. The inverse structure matrix is found in the linearized…
We study families of linear spaces in projective space whose union is a proper subvariety X of the expected dimension. We establish relations between configurations of focal points and existence or non-existence of a fixed tangent space to…
A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously…
Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…
In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces, and we find exact expressions for Frechet derivatives. Since Frechet differentiability implies Gateaux…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented $m$-partite graphs. These formulas are functions of the weight and…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…