Related papers: New method of averaging diffeomorphisms based on J…
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…
We establish optimal Lebesgue estimates for a class of generalized Radon transforms defined by averaging functions along polynomial-like curves. The presence of an essentially optimal weight allows us to prove uniform estimates, wherein the…
Let $X$ (resp. $Y$) be a curve of genus 1 (resp. 2) over a base field $k$ whose characteristic does not equal 2. We give criteria for the existence of a curve $Z$ over $k$ whose Jacobian is up to twist (2,2,2)-isogenous to the products of…
The paper presents an alternative way to classical stereocorrelation. First, 2D image processing of random patterns is described. Sub-pixel displacements are determined using phase analysis. Then distortion evaluation is presented. The…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
Classical deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based…
We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n \times n$ alternating…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by…
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to…
We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that…
Image classification is a well-studied task in computer vision, and yet it remains challenging under high-uncertainty conditions, such as when input images are corrupted or training data are limited. Conventional classification approaches…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
We introduce an algorithm to compute the rational torsion subgroup of the Jacobian of a hyperelliptic curve of genus 3 over the rationals. We apply a Magma implementation of our algorithm to a database of curves with low discriminant due to…
We provide criteria 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. These criteria reduce the projection problem to a certain…
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We show that, under certain circumstances, it is possible to automatically compute Jacobian-inverse-vector and Jacobian-inverse-transpose-vector products about as efficiently as Jacobian-vector and Jacobian-transpose-vector products. The…