A new zero-crossing edge detection method is described. Similar to Laplace of a Gaussian (LoG) algorithm, a 7x7 point spread function (PSF) is convolved with the original image to generate a smoothed image. Instead of locating edge position from the smoothed image, as in the case of LoG, we use the smoothed image as a reference to convert the original image into a three-value edge polarity map ...

This paper discusses the calculation of bend minimal shapes for non-planar graphs with given topology. Based on the Simple-Kandinsky drawing standard – a simplification of the more complex Kandinsky standard – we show the disadvantage of using standard models for this task: We show that the minimal bend count is suboptimal, when these models are applied to non-planar graphs; it is therefore ben...

A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually equivalent. We suggest merging single crossings into block crossings, that is, crossings of two neighboring groups of consecutive lines. Unfortunately, minimizing ...

It is well established by now that computer science has a number of concerns in common with natural language understanding. Common themes show up in particular with algorithmic aspects of text processing. This chapter gives an overview of border crossings from NLP to CS and back. Starting out from syntactic analysis, we trace our route via a philosophical puzzle about meaning, Hoare correctness...

We define and consider k-distant crossings and nestings for matchings and set partitions, which are a variation of crossings and nestings in which the distance between vertices is important. By modifying an involution of Kasraoui and Zeng (Electronic J. Combinatorics 2006, research paper 33), we show that the joint distribution of k-distant crossings and nestings is symmetric. We also study the...

It has been hypothesized that the rather small number of crossings in real syntactic dependency trees is a side-effect of pressure for dependency length minimization. Here we answer a related important research question: what would be the expected number of crossings if the natural order of a sentence was lost? We show that this number depends only on the number of vertices of the dependency tr...