The Chessboard Distance Transform and the Medial Axis Transform are Interchangeable

Abstract

The distance transform (DT) and the medial axis transform (MAT) are two image computation tools used to extract the information about the shape and the position of the foreground pixels relative to each other. Extensively applications of these two transforms are used in the fields of computer vision and image processing, such as expanding shrinking, thinning and computing shape factor, etc. There are many different distance transforms based on different distance metrics. Finding the distance transform with respect to the Euclidean distance metric is better in using, but rather time consuming. So, many approximate Euclidean distance transform (EDT) are also widely used in the computer vision and image processing fields. The chessboard distance transform (CDT) is one kind of DT which converts an image based on the chessboard distance metrics. Traditionally, the MAT and the CDT were usually viewed as two completely different image computation problems. In this paper, we first point out that the processes to find the CDT and the MAT are almost identical. That is, two transforms are interchangeable through the proposed algorithms; a MAT can be found by utilizing an CDT algorithm and vice versa