Related papers: Deformation of Framed Curves
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…
The purpose of this paper is to prove a Fourier restriction estimate for certain 2-dimensional surfaces in $\bbR^{2d}$, $d\ge 3$. These surfaces are defined by a complex curve $\gamma(z)$ of simple type, which is given by a mapping of the…
In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…
Using the Fourier-Laplace transform, we describe the isomonodromy equations for meromorphic connections on the Riemann sphere with unramified irregular singularities as those for connections with a (possibly ramified) irregular singularity…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is…
The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three…
In this paper we derive a variational formulation for a linear curved beam which is natively expressed in global Cartesian coordinates. During derivation the beam midline is assumed to be implicitly described by a vector distance function…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
A basic idea is proposed for extending the formalism of Part (II) of the series of our paper to the case of the parameter-dependent deformation. It is stressed that, through this extension, the variety of the application increases. Further,…
Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many…
In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
Deformation modeling of cardiac muscle is an important issue in the field of cardiac analysis. For this reason, many approaches have been developed to best estimate the cardiac muscle deformation, and to obtain a practical model to use in…
In this paper we consider the problem of defining transforms for signals on directed graphs, with a specific focus on defective graphs where the corresponding graph operator cannot be diagonalized. Our proposed method is based on the Schur…
Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be…
This paper presents a method for constructing flat deformations of associative algebras. We will refer to this method as method two because it is a generalisation of the method obtained in [1]. The deformations obtained using the first two…
Using the moving frame and invariants, any discrete curve in $\R^3$ could be uniquely identified by its centroaffine curvatures and torsions. In this paper, depending on the affine curvatures of the fractal curves, such as Koch curve and…