Related papers: Exactly computing bivariate projection depth conto…

Estimating depth from a single RGB image is an ill-posed and inherently ambiguous problem. State-of-the-art deep learning methods can now estimate accurate 2D depth maps, but when the maps are projected into 3D, they lack local detail and…

Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…

We design an efficient data structure for computing a suitably defined approximate depth of any query point in the arrangement $\mathcal{A}(S)$ of a collection $S$ of $n$ halfplanes or triangles in the plane or of halfspaces or simplices in…

The depth rule is a level truncation of tensor product coefficients expected to be sufficient for the evaluation of fusion coefficients. We reformulate the depth rule in a precise way, and show how, in principle, it can be used to calculate…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

Monocular and binocular self-supervised depth estimations are two important and related tasks in computer vision, which aim to predict scene depths from single images and stereo image pairs respectively. In literature, the two tasks are…

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,…

Notions of depth in regression have been introduced and studied in the literature. Regression depth (RD) of Rousseeuw and Hubert (1999), the most famous one, is a direct extension of Tukey location depth (Tukey (1975)) to regression. Like…

In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn…

This paper as technology report is focusing on evaluation and performance about depth estimations based on lidar data and stereo images(front left and front right). The lidar 3d cloud data and stereo images are provided by ford. In…

Prompts play a critical role in unleashing the power of language and vision foundation models for specific tasks. For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation…

We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…

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…

Let $P$ be a set of $n$ points in $d$-dimensions. The simplicial depth, $\sigma_P(q)$ of a point $q$ is the number of $d$-simplices with vertices in $P$ that contain $q$ in their convex hulls. The simplicial depth is a notion of data depth…

3D point clouds are rich in geometric structure information, while 2D images contain important and continuous texture information. Combining 2D information to achieve better 3D semantic segmentation has become mainstream in 3D scene…

Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…

Accurate depth estimation is at the core of many applications in computer graphics, vision, and robotics. Current state-of-the-art monocular depth estimators, trained on extensive datasets, generalize well but lack 3D consistency needed for…

Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly…

Current methods for depth map prediction from monocular images tend to predict smooth, poorly localized contours for the occlusion boundaries in the input image. This is unfortunate as occlusion boundaries are important cues to recognize…