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Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
The minimum feedback arc set problem asks to delete a minimum number of arcs (directed edges) from a digraph (directed graph) to make it free of any directed cycles. In this work we approach this fundamental cycle-constrained optimization…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
Image segmentation is usually addressed by training a model for a fixed set of object classes. Incorporating additional classes or more complex queries later is expensive as it requires re-training the model on a dataset that encompasses…
An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two…
Region-based artificial attention constitutes a framework for bio-inspired attentional processes on an intermediate abstraction level for the use in computer vision and mobile robotics. Segmentation algorithms produce regions of coherently…
Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…
Shortcut sets are a vital instrument for reducing the diameter of a static graph and, consequently, its shortest path complexity, which is relevant in numerous subfields of graph theory. We explore the notion of shortcut sets in temporal…
Previous studies on sequence-based extraction of human movement trajectories have an issue of inadequate trajectory representation. Specifically, a pair of locations may not be lined up in a sequence especially when one location includes…
$\renewcommand{\Re}{\mathbb{R}}\newcommand{\eps}{{\varepsilon}}\newcommand{\poly}{\mathrm{poly}} $In this paper, we study the problem of $L_1$-fitting a shape to a set of $n$ points in $\Re^d$ (where $d$ is a fixed constant), where the…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
Consider a set $P \subseteq \Re^d$ of $n$ points, and a convex body $C$ provided via a separation oracle. The task at hand is to decide for each point of $P$ if it is in $C$ using the fewest number of oracle queries. We show that one can…
For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
Detecting local features, such as corners, segments or blobs, is the first step in the pipeline of many Computer Vision applications. Its speed is crucial for real-time applications. In this paper we present ELSED, the fastest line segment…
The nearest prototype classification is a less computationally intensive replacement for the $k$-NN method, especially when large datasets are considered. In metric spaces, centroids are often used as prototypes to represent whole clusters.…
Let $B$ be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let $P$ be a convex polygon with $n$ vertices. Given a starting configuration (a location and a direction of travel)…
Rotoscoping, the detailed delineation of scene elements through a video shot, is a painstaking task of tremendous importance in professional post-production pipelines. While pixel-wise segmentation techniques can help for this task,…
While robotic manipulation of rigid objects is quite straightforward, coping with deformable objects is an open issue. More specifically, tasks like tying a knot, wiring a connector or even surgical suturing deal with the domain of…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
Rich geometric understanding of the world is an important component of many robotic applications such as planning and manipulation. In this paper, we present a modular pipeline for pose and shape estimation of objects from RGB-D images…