Related papers: Shape analysis on homogeneous spaces: a generalise…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…
We apply an orthogonalization procedure on the effective field theory of large scale structure (EFT of LSS) shapes, relevant for the angle-averaged bispectrum and non-Gaussian covariance of the matter power spectrum at one loop. Assuming…
We present a Riemannian framework for linear and quadratic discriminant classification on the tangent plane of the shape space of curves. The shape space is infinite dimensional and is constructed out of square root velocity functions of…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when…
Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…
The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
The aim of Shape From Shading (SFS) problem is to reconstruct the relief of an object from a single gray level image. In this paper we present a new method to solve the problem of SFS using Machine learning method. Our approach belongs to…
The square root velocity function (SRVF), introduced by Srivastava et al, has proved to be an effective way to compare absolutely continuous curves in $R^N$ modulo reparametrization. Several computational papers have been published based on…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in…
With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…
We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main…
Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…