Related papers: Exactly computing bivariate projection depth conto…
We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…
In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
Recent advances have markedly improved the cross-scene generalization of relative depth estimation, yet its practical applicability remains limited by the absence of metric scale, local inconsistencies, and low computational efficiency. To…
For any given partial order in a $d$-dimensional euclidean space, under mild regularity assumptions, we show that the intersection of closed (generalized) intervals containing more than 1/2 of the probability mass, is a non-empty compact…
Based on the correspondence of projection to an eigenvalue problem via the underlying group structure, we generalize the projection algorithm proposed by Morrison et al. This algorithm is eligible for large-scale computations, because we…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of…
Depth from a monocular video can enable billions of devices and robots with a single camera to see the world in 3D. In this paper, we present an approach with a differentiable flow-to-depth layer for video depth estimation. The model…
We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data…
Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in terms of evaluation metrics such as the pixel-wise relative error, most methods neglect the…
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the…
Monocular depth estimation is an important task with rapid progress, but how to evaluate it is not fully resolved, as evidenced by a lack of standardization in existing literature and a large selection of evaluation metrics whose trade-offs…
Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…
Image analysis methods that are based on exact blur values are faced with the computational complexities due to blur measurement error. This atmosphere encourages scholars to look for handcrafted and learned features for finding depth from…
Monocular depth estimation is often described as an ill-posed and inherently ambiguous problem. Estimating depth from 2D images is a crucial step in scene reconstruction, 3Dobject recognition, segmentation, and detection. The problem can be…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function…
In this paper, we investigate the similarity property of the sample projection depth contours. It turns out that some of these contours are of \emph{the same shape} with different sizes, following a similar fashion to the Mahalanobis depth…
The paper presents a new method of depth estimation dedicated for free-viewpoint television (FTV). The estimation is performed for segments and thus their size can be used to control a trade-off between the quality of depth maps and the…