Size-invariant four-scan Euclidean distance transformation

Distance transform (DT)⁽¹⁾ is used to convert a binary image that consists of object (foreground) and nonobject (background) pixels into another image in which each object pixel has a value corresponding to the minimum distance from the background by a predefined distance function. The Euclidean distance is more accurate than the others, such as city-block, chessboard and chamfer, but it takes more computational time due to its nonlinearity. By using the relative X and Y coordinates computed from the object pixel to the source mapping pixel of its neighbors as well as correction of particular cases, the Euclidean distance transformation (EDT) can be correctly obtained in just four scans of an image. In other words, the new algorithm achieves the computational complexity of EDT to be linear to the size of an image.