Related papers: Measuring Depth of Matroids
A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called "balanced", such that no theta subgraph contains exactly two balanced circles. A biased graph has two natural matroids, the frame matroid and the lift…
Radar-Camera depth estimation aims to predict dense and accurate metric depth by fusing input images and Radar data. Model efficiency is crucial for this task in pursuit of real-time processing on autonomous vehicles and robotic platforms.…
We initiate the study of matroid problems in a new oracle model called dynamic oracle. Our algorithms in this model lead to new bounds for some classic problems, and a "unified" algorithm whose performance matches previous results developed…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
Monocular Depth Estimation (MDE) enables spatial understanding, 3D reconstruction, and autonomous navigation, yet deep learning approaches often predict only relative depth without a consistent metric scale. This limitation reduces…
Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise as the natural extension of graphic…
We propose a novel two-stage framework for sensor depth enhancement, called Perfecting Depth. This framework leverages the stochastic nature of diffusion models to automatically detect unreliable depth regions while preserving geometric…
This paper investigates the theory of sum-rank metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory…
We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$. To the best of our knowledge, this is the…
The theory of matroids or combinatorial geometries originated in linear algebra and graph theory, and has deep connections with many other areas, including field theory, matching theory, submodular optimization, Lie combinatorics, and total…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersecting codes with the Hamming metric and illustrate how these…
We study the parallel (adaptive) complexity of the classic problem of finding a basis in an $n$-element matroid, given access via an \emph{independence oracle}. In this model, the algorithm may submit polynomially many independence queries…
Deep metric learning aims to learn features relying on the consistency or divergence of class labels. However, in monocular depth estimation, the absence of a natural definition of class poses challenges in the leveraging of deep metric…
The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…
In this thesis, we study nearly finitary matroids by introducing new definitions and prove various properties of nearly finitary matroids. In 2010, an axiom system for infinite matroids was proposed by Bruhn et al. We use this axiom system…
We present a novel approach for metric dense depth estimation based on the fusion of a single-view image and a sparse, noisy Radar point cloud. The direct fusion of heterogeneous Radar and image data, or their encodings, tends to yield…
There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…
Digital Transformation (DT) initiatives frequently face high failure rates, and while Digital Maturity Models (DMMs) offer potential solutions, they have notable shortcomings. Specifically, there is significant disparity in the dimensions…
Scaling has powered recent advances in vision foundation models, yet extending this paradigm to metric depth estimation remains challenging due to heterogeneous sensor noise, camera-dependent biases, and metric ambiguity in noisy…