Another comment on “a note on ‘distance transformations in digital images’”

Abstract

In Comput. Vision Graphics Image Process. 43, 1988 , 88–97, Vossepoel introduced rescaling of integer valued digital distance transforms. He showed that rescaling can improve the approximation to the Euclidean distance transform significantly. However, he computed the rescaling factors only for selected distance transforms, and only approximately, using numerical iteration. Here the optimal rescaling factors are expressed as functions of the integer local distances for both 3 × 3 and 5 × 5 neighborhood distance functions. Thus the rescaling factor can be easily computed for any integer distance transform. We also give the optimal, real-valued, local distances for the 5 × 5 neighborhood distance transform in the general case. Previously only the solution in a special case have been published, ( Borgefors, Comput. Vision Graphics image Process. 34, 1986 , 344–371).