Related papers: Euclidean and Affine Curve Reconstruction
Recent results on curve reconstruction are described.
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
We develop an anabelian framework for general Deligne-Mumford curves, showing that their stack and orbifold structures are encoded in the group-theoretic properties of their \'etale fundamental groups. After establishing the required…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear…
We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…
The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…
In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.
In this note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein. As an application, we give a simple construction of the outer automorphism of S_6.
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution…
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…
We propose a family of curvature-based regularization terms for deep generative model learning. Explicit coordinate-invariant formulas for both intrinsic and extrinsic curvature measures are derived for the case of arbitrary data manifolds…
Curvilinear structures, which include line-like continuous objects, are fundamental geometrical elements in image-based applications. Reconstructing these structures from images constitutes a pivotal research area in computer vision.…
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its…
We study equivariant affine embeddings of homogeneous spaces and their equivariant automorphisms. An example of a quasiaffine, but not affine, homogeneous space with finitely many equivariant automorphisms is presented. We prove the…
We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.