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The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al., it…
Deep learning revolutionized data science, and recently its popularity has grown exponentially, as did the amount of papers employing deep networks. Vision tasks, such as human pose estimation, did not escape from this trend. There is a…
We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a…
One of the earliest results in enumerative combinatorial geometry is the following theorem of de Bruijn and Erd\H{o}s: Every set of points $E$ in a projective plane determines at least $|E|$ lines, unless all the points are contained in a…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
This paper introduces an extension of the backpropagation algorithm that enables us to have layers with constrained weights in a deep network. In particular, we make use of the Riemannian geometry and optimization techniques on matrix…
The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth…
Self-supervised multi-frame depth estimation achieves high accuracy by computing matching costs of pixel correspondences between adjacent frames, injecting geometric information into the network. These pixel-correspondence candidates are…
In this paper, we propose a new global geometry constraint for depth completion. By assuming depth maps often lay on low dimensional subspaces, a dense depth map can be approximated by a weighted sum of full-resolution principal depth…
We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…
We present a new approach to modeling sequential data: the deep equilibrium model (DEQ). Motivated by an observation that the hidden layers of many existing deep sequence models converge towards some fixed point, we propose the DEQ approach…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X…
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…
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,…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Self-supervised surround-view depth estimation enables dense, low-cost 3D perception with a 360{\deg} field of view from multiple minimally overlapping images. Yet, most existing methods suffer from depth estimates that are inconsistent…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…