Related papers: Wormhole Loss for Partial Shape Matching
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…