Related papers: Density-aware Chamfer Distance as a Comprehensive …
We study the problem of computing Chamfer distance in the fully dynamic setting, where two set of points $A, B \subset \mathbb{R}^{d}$, each of size up to $n$, dynamically evolve through point insertions or deletions and the goal is to…
Advancements in sensors, algorithms, and compute hardware have made 3D perception feasible in real time. Current methods to compare and evaluate the quality of a 3D model, such as Chamfer, Hausdorff, and Earth-Mover's distance, are…
The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning…
Given two sets of points A and B, $|A| = m$, $|B| = n$, the Chamfer distance from $A$ to $B$ is defined as $\operatorname{CD}(A,B) = \sum_{a\in A} \min_{b\in B} d(a,b)$, where $d$ is a distance metric. Chamfer distance is a popular measure…
This paper presents a novel theoretical measure, $\mu^{\text{EMD}}$, based on the Earth Mover's Distance, for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized…
In order to help physicists to expand their knowledge of the climate in the Lesser Antilles, we aim to identify the spatio-temporal configurations using clustering analysis on wind speed and cumulative rainfall datasets. But we show that…
Point-cloud data collected in real-world applications are often incomplete. Data is typically missing due to objects being observed from partial viewpoints, which only capture a specific perspective or angle. Additionally, data can be…
Compressive sensing (CS) has attracted significant attention in parameter estimation tasks, where parametric dictionaries (PDs) collect signal observations for a sampling of the parameter space and yield sparse representations for signals…
The Earth Mover Distance (EMD) between two sets of points $A, B \subseteq \mathbb{R}^d$ with $|A| = |B|$ is the minimum total Euclidean distance of any perfect matching between $A$ and $B$. One of its generalizations is asymmetric EMD,…
We propose Concavity-induced Distance (CID) as a novel way to measure the dissimilarity between a pair of points in an unoriented point cloud. CID indicates the likelihood of two points or two sets of points belonging to different convex…
Quantifying the dissimilarity between two unstructured 3D point clouds is a challenging task, with existing metrics often relying on measuring the distance between corresponding points that can be either inefficient or ineffective. In this…
How can we tell complex point clouds with different small scale characteristics apart, while disregarding global features? Can we find a suitable transformation of such data in a way that allows to discriminate between differences in this…
The Earth mover's distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent.…
In this work, we develop methods for few-shot image classification from a new perspective of optimal matching between image regions. We employ the Earth Mover's Distance (EMD) as a metric to compute a structural distance between dense image…
Point cloud completion seeks to recover geometrically consistent shapes from partial or sparse 3D observations. Although recent methods have achieved reasonable global shape reconstruction, they often rely on Euclidean proximity and…
Popular clustering algorithms based on usual distance functions (e.g., Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances has adverse effects on their…
Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…