A straight-line drawing of a planar graph G is a planar drawing of G, where each vertex is mapped to a point on the Euclidean plane and each edge is drawn as a straight line segment. A segment in a straight-line drawing is a maximal set of edges that form a straight line segment. A minimum-segment drawing of G is a straightline drawing of G, where the number of segments is the minimum among all...

Line recognition is an important aspect in image processing. Many line detection algorithms were introduced. Hough Transform for line detection is difficult to accelerate using the GPU because it essentially requires rasterization of sinusoids into a highresolution raster of accumulators, which is not a suitable task for GPU. In this paper, a GPU implementation of the PClines a new parameteriza...

We give an algorithm that reduces the straight skeleton to the motorcycle graph in O(n log n) time for (weakly) simple polygons and O(n(log n) logm) time for a planar straight line graph with m connected components. The current fastest algorithms for computing motorcycle graphs are an O(n ) time algorithm for non-degenerate cases and O(n ) for degenerate cases. Together with our algorithm this ...

Among mathematical models of visual confusion of letters and similar material, those that posit a feature detect ion process have been especially popular. The present s tudy provides direct tests of several of the central assumptions of such models with feature-stimuli composed of the blank, one of two straight line features, or both line. features posit ioned at a right angle. In one condition...

We give a new probabilistic algorithm for interpolating a “sparse” polynomial f given by a straight-line program. Our algorithm constructs an approximation f of f , such that f − f probably has at most half the number of terms of f , then recurses on the difference f−f. Our approach builds on previous work by Garg and Schost (2009), and Giesbrecht and Roche (2011), and is asymptotically more ef...

A linear axis is a straight line skeleton for a polygonal shape. The concept of a linear axis ε-equivalent to the medial axis has been introduced and studied for simple polygons and for those with holes. In this paper, we generalize the notions of a linear axis and of ε-equivalence to the case of planar straight line graphs. We show that for some graphs, a linear axis ε-equivalent to the medial...

This paper addresses the features of Hough Transform (HT) butterflies suitable for image-based segment detection and measurement. The full segment parameters such as the position, slope, width, length, continuity, and uniformity are related to the features of the HT butterflies. Mathematical analysis and experimental data are presented in order to demonstrate and build the relationship between ...