Signed Anti-Aliased Euclidean Distance Transform : Going from unsigned to signed with the assistance of a vector based method

Abstract: Knowing the shapes, sizes and positional relations between features in an image can be useful for different types of image processing.Using a Distance Transform can give us these properties as a Distance Map.There are many different variations of distance transforms that can increase accuracy or add functionality, two such transforms are the Anti-Aliased Euclidean Distance Transform and the Signed Euclidean Distance Transform.To get the benefits of both of these it is of interest to see if they can be combined and if so, how does it perform?Investigating the possibility of such a transform is the main object of this thesis. To create this combined transform a copy of the image was created and then inverted, both images are transformed and the resulting distance maps are combined into one.Signed distance maps are created for three transforms using this method. The transforms in question are, EDT, AAEDT and VAAEDT.All transforms are then evaluated using a series of images containing two randomly placed circles, the circles are created using simple Signed Distance Functions. The signed transforms work and the AAEDT performs well compared to the Signed Euclidean Distance Transform.These results were expected as a similar gap in results can be seen between the regular EDT and AAEDT.But, this transform is not perfect and there is room for improvements in the accuracy, a good start for future work.