Fast and scalable algorithms for the Euclidean distance transform on a linear array with a reconfigurable pipelined bus system

Abstract

The Euclidean distance transform ( EDT) is an operation to convert a binary image consisting of black and white pixels to a representation where each pixel has the Euclidean distance of the nearest black pixel. The EDT has many applications in computer vision and image processing. We present two algorithms for computing the EDT on the linear array with a reconfigurable pipelined bus system (LARPBS), a recently proposed architecture based on optical buses. Our first algorithm runs in O( log log N) time for a binary N× N image on an LARPBS with N 2+ ε processors, for any fixed ε, 0< ε<1. Our second algorithm is highly scalable and runs in O( N 2 p 2 log log p) time if the LARPBS has only p 2+ ε processors for p< N. The previous best deterministic algorithm for computing the EDT on the LARPBS is by Pan et al. Proceedings of IPDPS 2000 Workshop on Parallel and Distributed Computing in Image Processing, Video Processing and Multimedia (PDIVM 2000), Lecture Notes in Computer Science, Vol. 1800, Springer, Berlin, 178). Their algorithm runs either in O( log N log log N) time on an LARPBS with N 2 processors or in O( log log N) time on an LARPBS with O( N 3) processors.