In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.