Related papers: RT-HDIST: Ray-Tracing Core-based Hausdorff Distanc…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
We show that the Hausdorff distance for two sets of non-intersecting line segments can be computed in parallel in $O(\log^2 n)$ time using O(n) processors in a CREW-PRAM computation model. We discuss how some parts of the sequential…
Illumination estimation remains a pivotal challenge in image processing, particularly for robotics, where robust environmental perception is essential under varying lighting conditions. Traditional approaches, such as RGB histograms and…
Neighbor search is of fundamental important to many engineering and science fields such as physics simulation and computer graphics. This paper proposes to formulate neighbor search as a ray tracing problem and leverage the dedicated ray…
Vector filters based on order-statistics have proved successful in removing impulsive noise from color images while preserving edges and fine image details. Among these filters, the ones that involve the cosine distance function…
The advent of hardware ray tracing (RT) units has brought unprecedented realism to real-time rendered computer graphics. However, the potential of these units extends beyond graphics, offering acceleration for various computational tasks…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
Without a shape-aware response, it is hard to characterize the 3D geometry of a point cloud efficiently with a compact set of kernels. In this paper, we advocate the use of Hausdorff distance as a shape-aware distance measure for…
Distribution comparison plays a central role in many machine learning tasks like data classification and generative modeling. In this study, we propose a novel metric, called Hilbert curve projection (HCP) distance, to measure the distance…
Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
In [Computer Aided Geometric Design 27 (2010), 212-231] the authors present an algorithm to parametrize approximately $\epsilon$-rational curves, and they show in 2 examples that the Hausdorff distance, w.r.t. to the Euclidean distance,…
In this paper, we study the problem of continuous 3D shape representations. The majority of existing successful methods are coordinate-based implicit neural representations. However, they are inefficient to render novel views or recover…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
Modern GPUs are equipped with tensor cores (TCs) that are commonly used for matrix multiplication in artificial intelligence workloads. However, because they have high computational throughput, they can lead to significant performance gains…
Detection Transformers (DETR) have recently set new benchmarks in object detection. However, their performance in detecting rotated objects lags behind established oriented object detectors. Our analysis identifies a key observation: the…
Transportation distances have been used for more than a decade now in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
We investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the Hausdorff distance of two semi-algebraic sets is bounded by a given threshold is complete for…