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Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human…
Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…
This paper is about enabling robots to improve their perceptual performance through repeated use in their operating environment, creating local expert detectors fitted to the places through which a robot moves. We leverage the concept of…
In the rapidly evolving field of computer vision, the task of accurately estimating the poses of multiple individuals from various viewpoints presents a formidable challenge, especially if the estimations should be reliable as well. This…
The illumination conjecture is a classical open problem in convex and discrete geometry, asserting that every compact convex body~$K$ in $\mathbb R^n$ can be illuminated by a set of no more than $2^n$ points. If $K$ has smooth boundary, it…
A basic task in the design of a robotic production cell is the relative placement of robot and workpiece. The fundamental requirement is that the robot can reach all process positions; only then one can think of further optimization.…
Localization is an essential capability for mobile robots. A rapidly growing field of research in this area is Visual Place Recognition (VPR), which is the ability to recognize previously seen places in the world based solely on images.…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
We consider detecting objects in an image by iteratively selecting from a set of arbitrarily shaped candidate regions. Our generic approach, which we term visual chunking, reasons about the locations of multiple object instances in an image…
We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…
Prediction capability is considered an important issue in response surface methodology. Following the line of argument that a design should have several desirable properties we have extended an existing compound design criterion to include…
Given the complexities inherent in visual scenes, such as object occlusion, a comprehensive understanding often requires observation from multiple viewpoints. Existing multi-viewpoint object-centric learning methods typically employ random…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The Next Best View problem is a computer vision problem widely studied in robotics. To solve it, several methodologies have been proposed over the years. Some, more recently, propose the use of deep learning models. Predictions obtained…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…