Related papers: Estimating Tukey Depth Using Incremental Quantile …

This paper proposes to use keypoints as a self-supervision clue for learning depth map estimation from a collection of input images. As ground truth depth from real images is difficult to obtain, there are many unsupervised and…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade…

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…

Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics,…

Depth of the Tukey median is investigated for empirical distributions. A sharper upper bound is provided for this value for data sets in general position. This bound is lower than the existing one in the literature, and more importantly…

Modern cameras are equipped with a wide array of sensors that enable recording the geospatial context of an image. Taking advantage of this, we explore depth estimation under the assumption that the camera is geocalibrated, a problem we…

Depth information plays a crucial role in autonomous systems for environmental perception and robot state estimation. With the rapid development of deep neural network technology, depth estimation has been extensively studied and shown…

The estimation of depth in two-dimensional images has long been a challenging and extensively studied subject in computer vision. Recently, significant progress has been made with the emergence of Deep Learning-based approaches, which have…

In monocular depth estimation, disturbances in the image context, like moving objects or reflecting materials, can easily lead to erroneous predictions. For that reason, uncertainty estimates for each pixel are necessary, in particular for…

We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we are interested in the probabilities of observing specific…

Depth estimation is an important task, applied in various methods and applications of computer vision. While the traditional methods of estimating depth are based on depth cues and require specific equipment such as stereo cameras and…

It is difficult to collect data on a large scale in a monocular depth estimation because the task requires the simultaneous acquisition of RGB images and depths. Data augmentation is thus important to this task. However, there has been…

In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…

Halfspace (or Tukey) depth is a fundamental and robust measure of centrality of data points in multivariate datasets. Computing the depth of a point with respect to the uniform distribution on an open convex body in $\mathbb{R}^d$ is a…

Depth information is useful for many applications. Active depth sensors are appealing because they obtain dense and accurate depth maps. However, due to issues that range from power constraints to multi-sensor interference, these sensors…

In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This…

Existing depth estimation methods are fundamentally limited to predicting depth on discrete image grids. Such representations restrict their scalability to arbitrary output resolutions and hinder the geometric detail recovery. This paper…

We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…

Accurate monocular depth estimation is crucial for 3D scene understanding, but existing methods often blur depth at object boundaries, introducing spurious intermediate 3D points. While achieving sharp edges usually requires very…