Digital distance transforms have been used in image processing and analysis since the 1960s. Distance transforms are excellent tools for all applications regarding shape. They are, in fact, extensively used, especially in industrial and medical applications. At the same time, from the mid 1980s until today, there has been a rich literature that investigates distance transforms theoretically, constructs new ones, and improves computation algorithms. Despite this, distance transforms have not really been incorporated into the general image analysis toolbox.
They are usually not mentioned at all -- or the oldest ones (e.g.,
City block and Chessboard) are mentioned very briefly -- in the
basic books on image analysis used in education. One reason for the under-use of distance transforms could be that the oldest distancetransforms are very rotation dependent, giving quite different results depending of the position of an object. The Euclidean distance transform is rotation independent up to digitisation effects, but often leads to complex algorithms where it is used. The compromise is the integer weighted distance transforms, that combines the simplicity of the old distance transforms with a reasonable rotation independence. Here, a large number of distance transforms will be described,with some of their properties and the simplest computation algorithms.
World Scientific, Singapore , 2005. 157-176 p.