The distance transform (DT) and the medial axis transform (MAT) are two image computation tools used to extract information about the shape and position of 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, computing the shape factor, etc. There are many different DTs based on different distance metrics. Finding the DT with respect to the Euclidean distance metric is easier to use, but rather time-consuming, so many approximate Euclidean DTs (EDTs) are also widely used in the computer vision and image processing fields. The chessboard DT (CDT) is one kind of DT, which converts an image based on the chessboard distance metric. Traditionally, the MAT and the CDT have usually been 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, i.e. the two transforms are interchangeable through the proposed algorithms, so that a MAT can be found by utilizing a CDT algorithm and vice versa.