A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determin…
The paper explores three methods to assign a metric to shape spaces.
New shape representation for airfoils improves design and manufacturing.
A new method for analyzing shapes using FDA techniques.
Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.
Analyze and predict complex 3D shape deformations using LSTM autoencoders and oriented bounding boxes.
The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.
Cardiac motion modeling using LDDMM and shape splines.
Study compares geometric approaches for shape and deformation statistics.
Researchers use shape analysis to recover protein structures from Cryo-EM data.
The class of surfaces in 3-space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We review some of the known examples and results, demonstrate the integrability of the c…
A horospherical torus about a cusp of a hyperbolic manifold inherits a Euclidean similarity structure, called a cusp shape. We bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp. The bounds are in terms of the change in structure in a neighb…
Flow turns star-shaped curves into circles.
The manifold of star-shaped curves in is considered via the theory of connections on vector bundles, and cyclic -modules. The appropriate notion of an "integral curve" (i.e. certain admissible deformations) on is defined, and the resulting space of admissible defo…
New method for partial matching of shapes with Varifolds.
In trying to generalize Bianchi's Bäcklund transformation of quadrics to Bäcklund transformations of isometric deformations of other (classes of) surfaces, we investigate basic features of the isometric deformation of surfaces via the Bäcklund transformation with isometric correspondence of leaves of a general nature (…
Generative modeling of 3D shapes has become an important problem due to its relevance to many applications across Computer Vision, Graphics, and VR. In this paper we build upon recently introduced 3D mesh-convolutional Variational AutoEncoders which have shown great promise for learning rich representations of deformab…
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…
Study characterizes bladder motion using dynamic MRI and statistical analysis.
Paper develops a new method to analyze 3D tree-like objects.
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…
In two former papers, the authors independently proved that the space of hyperbolic cone-3-manifolds with cone angles less than 2π and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the local shape of the deformation space when the singular locus is no longer fixed, i.e.…
The paper explores metrics and models for analyzing biological shapes.
We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which preserve both principal directions and principal curvatures (or, equivalently, the s…
New method allows sheets to morph into multiple shapes via spatially varying stimuli.
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
Bistable structures associated with non-linear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects …
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…
Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposi…
New method for surface analysis using restricted deformation bases.
The importance of training robust neural network grows as 3D data is increasingly utilized in deep learning for vision tasks in robotics, drone control, and autonomous driving. One commonly used 3D data type is 3D point clouds, which describe shape information. We examine the problem of creating robust models from the …
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and decomposition in generalized surface space) hold interest from a theoretical pe…
The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that measure shape changes using deformations of the ambient space and they find appli…
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
Extended orbit model theory for shape analysis using graded group action framework.
The paper studies a curve flow preserving anisotropic length for convex curves, leading to a homothetic limit.
Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is a…
User interfaces provide an interactive window between physical and virtual environments. A new concept in the field of human-computer interaction is a soft user interface; a compliant surface that facilitates touch interaction through deformation. Despite the potential of these interfaces, they currently lack a signal …
New Hopf algebras help classify 4D shapes.
New metrics for surface shapes incorporating curve properties.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
New proof shows 3D shapes can be continuously deformed.
A registration-free framework monitors shape and color in 4D point clouds.
Method flattens complex surfaces with consistent density and shape.
We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration allows one-dimensional deformations which form a circle in the configuration spa…
Efficient method for shape modeling invariant to rigid motion.
LIMP learns latent shapes with metric preservation, improving generative models.
We consider the results of combining two approaches developed for the design of Riemannian metrics on curves and surfaces, namely parametrization-invariant metrics of the Sobolev type on spaces of immersions, and metrics derived through Riemannian submersions from right-invariant Sobolev metrics on groups of diffeomorp…