(a) Input image (b) Scaling (c) Visibility map for (d) (d) Seam carving (e) Visibility map for (f) (f) Seam carving energy terms (distortion energy: absolute magnitude distance, nD = 1) (g) Visibility map for (h) (h) Distortion energy: absolute magnitude distance, nD = 1; unary with nU = 1 (i) Visibility map for (j) (j) Distortion energy: absolute magnitude distance, nD = 1; seam term: repeat c...

We investigate the problem of determining visible regions given a set of (moving) obstacles and a (moving) vantage point. Our approach to this problem is through an implicit framework, where the obstacles are represented by a level set function. The visibility problem is formally formulated as a boundary value problem (BVP) of a first order partial differential equation. It is based on the cont...

The visibility graph V(P ) of a point set P ⊆ R has vertex set P , such that two points v, w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P ). We characterise the 2and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main r...

The visibility graph V(X) of a discrete point set X ⊂ R2 has vertex set X and an edge xy for every two points x, y ∈ X whenever there is no other point in X on the line segment between x and y. We show that for every graph G, there is a point set X ∈ R2, such that the subgraph of V(X∪Z2) induced by X is isomorphic to G. As a consequence, we show that there are visibility graphs of arbitrary hig...

We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counter-clockwise order but have no means of visibly identifying them. We show that such robots can always solve the weak rendezvous problem and re...

This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq (or WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P and creates a data structure from which WVP(pq) is efficiently reported in an output sensitive manner. Our algorithm needs O(n log n) time and O(n) space in the preprocessing phase to report WVP(pq)...

We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon whose visibility graph is isomorphic to the given graph.

The subject of this thesis is the problem of computing the visibility graph of m points P within a polygon Q. The vertices of the visibility graph are the points of P and the edges of the graph are the pairs of points in P×P , where the line between them is fully contained inside Q. Known algorithms by Ben-Moshe et al. are presented for computing the visibility graph of a simple polygon, the vi...

Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines of sight which can traverse up to k bars. These graphs were introduced by Dean et al. [3] who conjectured that bar 1-visibility graphs have thickness at most 2. We construct a bar 1-visibility graph having thickness 3...

Graph-based operationalizations of space are used in architecture as well as in cognitive science. In such models, environments are usually described by means of nodes and edges, roughly corresponding to places and their spatial relations. In the field of cognitive science, view and place graphs are models of mental representations of environments and used for the explanation of wayfinding beha...