Related papers: An All-In-One Geometric Algorithm for Cutting, Tea…
Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
Geometric rectification of images of distorted documents finds wide applications in document digitization and Optical Character Recognition (OCR). Although smoothly curved deformations have been widely investigated by many works, the most…
Two-view correspondence learning is a key task in computer vision, which aims to establish reliable matching relationships for applications such as camera pose estimation and 3D reconstruction. However, existing methods have limitations in…
Geometric transformations have been widely used to augment the size of training images. Existing methods often assume a unimodal distribution of the underlying transformations between images, which limits their power when data with…
In the standard orbit model on shape analysis, a group of diffeomorphism on the ambient space equipped with a right invariant sub-riemannian metric acts on a space of shapes and induces a sub-riemannian structure on various spaces. An…
Successful point cloud registration relies on accurate correspondences established upon powerful descriptors. However, existing neural descriptors either leverage a rotation-variant backbone whose performance declines under large rotations,…
The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In…
Language-guided grasping has emerged as a promising paradigm for enabling robots to identify and manipulate target objects through natural language instructions, yet it remains highly challenging in cluttered or occluded scenes. Existing…
This paper develops a deformation-field geometry for spaces whose local frames may undergo internal stretching, compression, and shear. Ordinary Riemannian geometry takes an intrinsic metric geometry \((M,g)\) as the given datum and uses…
Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
$N$-body simulations are computationally expensive, so machine-learning (ML)-based emulation techniques have emerged as a way to increase their speed. Although fast, surrogate models have limited trustworthiness due to potentially…
Living creatures and machines interact with the world through their morphology and motions. Recent advances in creating bio-inspired morphing robots and machines have led to the study of variable geometry truss (VGT), structures that can…
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…
Decentralized learning enables a group of collaborative agents to learn models using a distributed dataset without the need for a central parameter server. Recently, decentralized learning algorithms have demonstrated state-of-the-art…
With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Real-time Light Detection And Ranging (LiDAR) simulation must find, per emitted ray, the closest intersecting triangle even in dynamic scenes containing large numbers of moving and deformable objects. Dominant acceleration-structure…
The discussion of how to apply geometric algebra to euclidean $n$-space has been clouded by a number of conceptual misunderstandings which we first identify and resolve, based on a thorough review of crucial but largely forgotten themes…