Anti-aliased Euclidean distance transform

Abstract

a b s t r a c tWe present a modified distance measure for use with distance transforms of anti-aliased, area sampled grayscale images of arbitrary binary contours. The modified measure can be used in any vector-propagation Euclidean distance transform. Our test implementation in the traditional SSED8 algorithm shows a considerable improvement in accuracy and homogeneity of the distance field compared to a traditional binary image transform. At the expense of a 10Â slowdown for a particular image resolution, we achieve an accuracy comparable to a binary transform on a supersampled image with 16 Â 16 higher resolution, which would require 256 times more computations and memory.

A Graph-Based Implementation of the Anti-aliased Euclidean Distance Transform

“…The implementation of AAEDT in [5] is based on raster scanning. This method is normally used for scalar distance transforms on binary images, in which case it completes the transform by traversing the image twice, and has a complexity of O(N ), where N is the number of pixels in the image.…”

“…The anti-aliased Euclidean distance transform (AAEDT) is presented in [5]. Assuming smooth objects, it uses the fuzzy edge data in an area sampled image to obtain the Euclidean distance from an object with sub-pixel precision.…”

“…The authors of [5] propose that AAEDT can be used for improving the accuracy of level sets, and of morphological operations on sub-pixel level, on synthetic as well as real world data. This could, of course, also be done by supersampling a crisp image, but increasing the number of sample points also increases memory requirements and processing time.…”

“…In [5], AAEDT is implemented for 2D images using iterative raster scanning. Our aim is an AAEDT implementation that is easily generalized to arbitrary dimensions and sampling lattices, smoothly incorporated into software able to apply several different distance transforms, and, preferably, computationally efficient.…”

“…As we shall se in Section II, raster scanning does not fulfill all of these criteria. We also present and evaluate a major improvement in comparison to the algorithm in [5], handling what we choose to call omitted edge pixels. We hope that this paper will lead to deeper understanding, as well as better accuracy, of AAEDT.…”