Distance Transform Algorithms And Their Implementation And Evaluation

Consider an n-dimensional binary image consisting of one or more objects. A value of 1 indicates a point within some object and a value of 0 indicates that that point is part of the background (i.e., is not part of any object). For every point in some object, a distance transform assigns a value indicating the distance from that point within the object to the nearest background point. Similarly for every point in the background, a distance transform assigns a value indicating the minimum distance from that background point to the nearest point in any object. By convention, positive values indicate points within some object and negative values indicate background points. A number of elegant and efficient distance transform algorithms have been proposed, with Danielsson being one of the earliest in 1980 and Borgefors in 1986 being a notable yet simple improvement. In 2004 Grevera proposed a further improvement of this family of distance transform algorithms that maintains their elegance but increases accuracy and extends them to n-dimensional space as well. In this paper, we describe this family of algorithms and compare and contrast them with other distance transform algorithms. We also present a novel framework for evaluating distance transform algorithms and discuss applications of distance transforms to other areas of image processing and analysis such as interpolation and skeletonization.