Related papers: The moving frame method for iterated-integrals: or…

In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…

LiDAR point clouds provide rich geometric information, which is particularly useful for the analysis of complex scenes of urban regions. Finding structural and semantic differences between two different three-dimensional point clouds, say,…

Geometric shape classification of vector polygons remains a challenging task in spatial analysis. Previous studies have primarily focused on deep learning approaches for rasterized vector polygons, while the study of discrete polygon…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

Signature tensors of paths are a versatile tool for data analysis and machine learning. Recently, they have been applied to persistent homology, by embedding barcodes into spaces of paths. Among the different path embeddings, the…

The log Euclidean polyrigid registration framework provides a way to smoothly estimate and interpolate poly-rigid/affine transformations for which the invertibility is guaranteed. This powerful and flexible mathematical framework is…

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…

Anatomical structures such as the hippocampus, liver, and bones can be analyzed as orientable, closed surfaces. This permits the computation of volume, surface area, mean curvature, Gaussian curvature, and the Euler-Poincar\'e…

This paper analyzes the robustness of recent 3D shape descriptors to SO(3) rotations, something that is fundamental to shape modeling. Specifically, we formulate the task of rotated 3D object instance detection. To do so, we consider a…

This paper introduces GeoMorph, a novel geometric deep-learning framework designed for image registration of cortical surfaces. The registration process consists of two main steps. First, independent feature extraction is performed on each…

In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…

In this paper, we systematically investigate the short periodic orbits of the Lorenz system by the aid of the similarity signature curve, and a novel method to find the short-period orbits of the Lorenz system is proposed. The similarity…

Transformation-robustness is an important feature for machine learning models that perform image classification. Many methods aim to bestow this property to models by the use of data augmentation strategies, while more formal guarantees are…

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…

In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation…

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…

The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…

A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…