Related papers: Metrics, quantization and registration in varifold…
Fusion and inference from multiple and massive disparate data sources - the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies - -has many and varied…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics…
In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally demanding task,…
Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the…
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…
We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural…
Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel…
A recent paper (Neural Networks, {\bf 132} (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its…
We develop and analyze a parametric registration procedure for manifolds associated with the solutions to parametric partial differential equations in two-dimensional domains. Given the domain $\Omega \subset \mathbb{R}^2$ and the manifold…