相关论文: Fast and exact implementation of 3-dimensional Tuk…

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…

Tracking dense 3D motion from monocular videos remains challenging, particularly when aiming for pixel-level precision over long sequences. We introduce DELTA, a novel method that efficiently tracks every pixel in 3D space, enabling…

We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…

We present a novel 3D shape completion method that operates directly on unstructured point clouds, thus avoiding resource-intensive data structures like voxel grids. To this end, we introduce KAPLAN, a 3D point descriptor that aggregates…

Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data.…

Zuo (2019) (Z19) addressed the computation of the projection regression depth (PRD) and its induced median (the maximum depth estimator). Z19 achieved the exact computation of PRD via a modified version of regular univariate sample median,…

Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing…

Predicting depth is an essential component in understanding the 3D geometry of a scene. While for stereo images local correspondence suffices for estimation, finding depth relations from a single image is less straightforward, requiring…

In this paper, we introduce a novel unsupervised domain adaptation technique for the task of 3D keypoint prediction from a single depth scan or image. Our key idea is to utilize the fact that predictions from different views of the same or…

We review the problem of finding an apparent horizon in Cauchy data (Sigma, g_ab, K_ab) in three space dimensions without symmetries. We describe a family of algorithms which includes the pseudo-spectral apparent horizon finder of Nakamura…

As an inherently ill-posed problem, depth estimation from single images is the most challenging part of monocular 3D object detection (M3OD). Many existing methods rely on preconceived assumptions to bridge the missing spatial information…

Accurate depth estimation is crucial for 3D scene comprehension in robotics and autonomous vehicles. Fisheye cameras, known for their wide field of view, have inherent geometric benefits. However, their use in depth estimation is restricted…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…

The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…

In this paper, we present a fast monocular depth estimation method for enabling 3D perception capabilities of low-cost underwater robots. We formulate a novel end-to-end deep visual learning pipeline named UDepth, which incorporates domain…

Over the past few years, monocular depth estimation and completion have been paid more and more attention from the computer vision community because of their widespread applications. In this paper, we introduce novel physics…