arXiv research

Enhanced rotation prediction improves SSL models by capturing both shape and texture information.

The paper learns pose variations within shape populations using constrained mixtures of factor analyzers.

Explains minimal surfaces and their properties.

A new algorithm computes elastic shape distances between curves efficiently.

Deep model predicts shapes of curves with multiple covariates.

A new method for 3D surface registration using dynamic programming.

New polynomials detect non-rotatable knotoid shapes.

A new method for analyzing shapes and forms using additive models on manifolds.

Overview of methods for rotating 2D and 3D data.

A new method for analyzing shapes using FDA techniques.

We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation mat…

The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.

A new FFT-based method for fast rigid alignment of 2D closed curves.

This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of $k$ planar landmarks ($k>2$)-modulo translation, scaling a…

Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…

Modeling functional data, this study uncovers the size-and-shape of functions under noisy observations.

New shape representation for airfoils improves design and manufacturing.

In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to s…

Characterizes geodesic completeness for landmark spaces.

Proves inequality for special 3D shapes, generalizing to non-symmetric ones.

Paper introduces a method to generate stable shapes using Grassmann manifolds.

Geometric reduction of the Newtonian planar three-body problem is investigated in the framework of equivariant Riemannian geometry, which reduces the study of trajectories of three-body motions to the study of their moduli curves, that is, curves which record the change of size and shape, in the moduli space of oriente…

A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants. These surfaces are solutions of a variational problem that describes the shape of a …

A new rotation invariant method for 3D medical imaging classification.

This work characterizes how data augmentation shapes neural representations.

New methods prove existence of rotating shapes moving in space.

We present and study a family of metrics on the space of compact subsets of $R^N$ (that we call ``shapes''). These metrics are ``geometric'', that is, they are independent of rotation and translation; and these metrics enjoy many interesting properties, as, for example, the existence of minimal geodesics. We view our s…

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being associated to specific qualifications of the space of curves (closed-open, modulo…

Optimal thresholds ensure curves remain embedded in flows.

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the last layer of a network. Instead, an idealized model would preserve a meaningful r…

Proposes a new layer for efficient 3D shape discrimination.

ES-VAE models skeletal pose trajectories by removing nuisance factors.

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only…

Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles …

The introduction of automated flight control and management systems have made possible aircraft designs that sacrifice arodynamic stability in order to incorporate stealth technology intro their shape, operate more efficiently, and are highly maneuverable. Therefore, modern flight management systems are reliant on mult…

We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of the area and the height in terms of the boundary. In case that the boundary is a …

See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the vertical axis. We restrict ourselves here to surfaces which are cylinders over …

Improved performance in shape identification tasks using elastic metrics in t-SNE and UMAP.

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in S^n x R or H^n x R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isomet…

We introduce SARR for symmetric object pose estimation, improving CNN performance.

Planar neural networks learn image transformations from sequences.

A new method for computing shape barycenters from point clouds using Procrustes-Wasserstein distance.

Given a discrete subgroup of the isometries of n-dimensional hyperbolic space there is always a region kept precisely invariant under the stabilizer of a parabolic fixed point, called the Margulis region. While in dimensions 2 and 3 this region is a horoball, it has in general a more complicated shape due to the existe…

In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ are given by means of their extrinsic geometry. Under suitable conditions on the shape operator, we classify conformally flat hypersurfaces in terms of …

Study on Brownian motion on discrete curve spaces, proving stochastic completeness.

Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.

In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full…

Quantum model outperforms classical in training but underperforms in real-world metrics.