Line segment similarity criterion for vector images

Abstract

Vector representation of the images, maps, schematics and other information is widely used, and in computer processing of these data, comparison and similarity evaluation of two sets of line segments is often necessary. Various techniques are already in use, but these mostly rely on the algorithmic functions such as minimum/maximum of two or more variables, which limits their applicability for many optimization algorithms. In this paper we propose a novel area based criterion function for line segment similarity evaluation, which is easily differentiable and the derivatives are continuous in the whole domain of definition. The second important feature is the possibility of preprocessing of the input data. Once finished, it takes constant time to evaluate the criterion for different transformations of one of the input sets of line segments. This has potential to greatly speed up iterative matching algorithms. In such case, the computational complexity is reduced from O(pt) to O(p+t), where p is the number of line segment pairs being examined and t is the number of transformations performed.