相关论文: On Nonrigid Shape Similarity and Correspondence

We present a new generalizable NeRF method that is able to directly generalize to new unseen scenarios and perform novel view synthesis with as few as two source views. The key to our approach lies in the explicitly modeled correspondence…

Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced similarity measure for quantifying the closeness of two graphs.…

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use…

Positive semidefinite (PSD) matrices are indispensable in many fields of science. A similarity measurement for such matrices is usually an essential ingredient in the mathematical modelling of a scientific problem. This paper proposes a…

The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into a pseudo-Riemannian manifold whose Ricci tensor vanishes up…

Marc Rieffel had introduced the notion of the quantum Gromov-Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on $2$-sphere in this distance. One…

One of the fundamental elements of both traditional and certain deep learning medical image registration algorithms is measuring the similarity/dissimilarity between two images. In this work, we propose an analytical solution for measuring…

For representing articulated shapes, as an alternative to the structured models based on graphs representing part hierarchy, we propose a pixel-based distinctness measure. Its spatial distribution yields a partitioning of the shape into a…

It is known that epipolar geometry can be computed from three epipolar line correspondences but this computation is rarely used in practice since there are no simple methods to find corresponding lines. Instead, methods for finding…

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two…

Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…

Nonparametric curve estimation by kernel methods has attracted widespread interest in theoretical and applied statistics. One area of conflict between theory and application relates to the evaluation of the performance of the estimators.…

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…

In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…

Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…

Establishing consistent and dense correspondences across multiple images is crucial for Structure from Motion (SfM) systems. Significant view changes, such as air-to-ground with very sparse view overlap, pose an even greater challenge to…

In the past decades, feature-learning-based 3D shape retrieval approaches have been received widespread attention in the computer graphic community. These approaches usually explored the hand-crafted distance metric or conventional distance…

Given metric quotients $S$ and $S_n$, $n \in \mathbb{N}$, of a metric space $X$, sufficient conditions are provided on the data defining them guaranteeing that $S$ is the Gromov-Hausdorff limit of $S_n$. These conditions are recognized…

Let $G$ be a finite, connected metric graph and let $X\subseteq G$ be a subset. If $X$ is sufficiently dense in $G$, we show that the Gromov--Hausdorff distance matches the Hausdorff distance, namely $d_\gh(G,X)=d_\h(G,X)$. When the metric…