Related papers: Complete and Sufficient Spatial Domination of Mult…
The quality of life of many people could be improved by autonomous humanoid robots in the home. To function in the human world, a humanoid household robot must be able to locate itself and perceive the environment like a human; scene…
Understanding the spatial relations between objects in images is a surprisingly challenging task. A chair may be "behind" a person even if it appears to the left of the person in the image (depending on which way the person is facing). Two…
The paper focuses on a classical tracking model, subspace learning, grounded on the fact that the targets in successive frames are considered to reside in a low-dimensional subspace or manifold due to the similarity in their appearances. In…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles,…
Accurately recognizing a revisited place is crucial for embodied agents to localize and navigate. This requires visual representations to be distinct, despite strong variations in camera viewpoint and scene appearance. Existing visual place…
We propose a new method to count objects of specific categories that are significantly smaller than the ground sampling distance of a satellite image. This task is hard due to the cluttered nature of scenes where different object categories…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
Clustering, a fundamental task in data science and machine learning, groups a set of objects in such a way that objects in the same cluster are closer to each other than to those in other clusters. In this paper, we consider a well-known…
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations,…
Let $n>m$, and let $A$ be an $(m\times n)$-matrix of full rank. Then obviously the estimate $\|Ax\|\leq\|A\|\|x\|$ holds for the euclidean norm of $x$ and $Ax$ and the spectral norm as the assigned matrix norm. We study the sets of all $x$…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
In this paper we study three domination-like problems, namely identifying codes, locating-dominating codes, and locating-total-dominating codes. We are interested in finding the minimum cardinality of such codes in circular and infinite…
Recent progress in robotic manipulation has dealt with the case of previously unknown objects in the context of relatively simple tasks, such as bin-picking. Existing methods for more constrained problems, however, such as deliberate…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…