The distance transform (DT) is a general operator forming the basis of many methods in computer vision and geometry, with great potential for practical applications. However, all the optimal algorithms for the computation of the exact Euclidean DT (EDT) were proposed only since the 1990s. In this work, state-of-theart sequential 2D EDT algorithms are reviewed and compared, in an effort to reach more solid conclusions regarding their differences in speed and their exactness. Six of the best algorithms were fully implemented and compared in practice.The work of R. Fabbri was supported by CNPq (200875/2004-3) and FAPESP (03/09834-0); O. M. Bruno acknowledges support from FAPESP (03/09834-0) and CNPq (303746/04-1); L. Da F. Costa thanks FAPESP (99/12765-2 and 05/00587-5) and CNPq (308231/03-1).

The Euclidean distance transform (EDT) is used in various methods in pattern recognition, computer vision, image analysis, physics, applied mathematics and robotics. Until now, several sequential EDT algorithms have been described in the literature, however they are time- and memory-consuming for images with large resolutions. Therefore, parallel implementations of the EDT are required specially for 3D images. This paper presents a parallel implementation based on domain decomposition of a well-known 3D Euclidean distance transform algorithm, and analyzes its performance on a cluster of workstations. The use of a data compression tool to reduce communication time is investigated and discussed. Among the obtained performance results, this work shows that data compression is an essential tool for clusters with low-bandwidth networks.

The Euclidean distance transform is the operation that converts a binary image made of object and background pixels into another image, the Euclidean distance map, where each pixel has a value corresponding to the Euclidean distance from this pixel to the background. The Euclidean distance transform has important uses in computer vision, image analysis and robotics, but it is time-consuming, mainly when processing 3-D images. In this work two types of parallel computers are used to speed up the Euclidean distance transform, (i) symmetric multiprocessors (SMPs) and (ii) clusters of workstations. Two algorithms are parallelized. The first one, an independent line-column Euclidean distance transform algorithm, is parallelized on a SMP, and on a cluster. The second one, an ordered propagation Euclidean distance transform algorithm, is paralellized on a cluster.