Related papers: Average degree of the essential variety
6D Object pose estimation is a fundamental component in robotics enabling efficient interaction with the environment. It is particularly challenging in bin-picking applications, where many objects are low-feature and reflective, and…
Estimating the relative camera pose from $n \geq 5$ correspondences between two calibrated views is a fundamental task in computer vision. This process typically involves two stages: 1) estimating the essential matrix between the views, and…
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results…
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…
We introduce a class of convex equivolume partitions. Expected $L_2-$discrepancy are discussed under these partitions. There are two main results. First, under this kind of partitions, we generate random point sets with smaller expected…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
In this paper we address the uncertainty issues involved in the low-level vision task of image segmentation. Researchers in computer vision have worked extensively on this problem, in which the goal is to partition (or segment) an image…
Affordances are a fundamental concept in robotics since they relate available actions for an agent depending on its sensory-motor capabilities and the environment. We present a novel Bayesian deep network to detect affordances in images, at…
The purpose of this note is to show that the subvarieties of small degree inside a general hypersurface of large degree come from intersecting with linear spaces or other varieties.
Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have…
Modern computer vision algorithms often rely on very large training datasets. However, it is conceivable that a carefully selected subsample of the dataset is sufficient for training. In this paper, we propose a gradient-based importance…
In this work, we present a new algorithm to approximate the percolation centrality of every node in a graph. Such a centrality measure quantifies the importance of the vertices in a network during a contagious process. In this paper, we…
We consider the typical distance between vertices of the giant component of a random intersection graph having a power law (asymptotic) vertex degree distribution with infinite second moment. Given two vertices from the giant component we…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
In this article we introduce a family of valuative invariants defined in terms of the $p$-th moment of the expected vanishing order. These invariants lie between $\alpha$ and $\delta$-invariants. They vary continuously in the big cone and…
Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
The essential matrix incorporates relative rotation and translation parameters of two calibrated cameras. The well-known algebraic characterization of essential matrices, i.e. necessary and sufficient conditions under which an arbitrary…