A study of Wavelets for edge detection of anatomical structure on medical images

Abstract

Osteoporosis is a bone disease that makes your bone crumble away. To find out how thick your bone structure is, medical personnel uses x-ray images and measure the thickness of your bones. Today this is done manually by the use of a ruler. In this thesis we have examined the use of Wavelets for edge detection in order to find a better and smarter way of measuring the bone thickness digitally. Wavelets are a relatively new mathematical method that allows you to split up and examine a signal. Three different Mother Wavelets; Haar, Mexican Hat and Morlet were examined to find the one that was best suited for finding edges. Tests have been performed involving the different Mother Wavelets. They all have their own qualities, and are to some extent able to detect edges, but Mexican Hat proved to be the best. We came up with our own theory for how to use Mexican Hat to detect the edges of objects in images. The theory was named “Champagne glass” theory, and it tells you something about which scaling you need to use in order to best find the edges. The task was to find the edges of bone structure on x-ray images. With our methods we were able to find the outer edges of the bone structure and to some extent the inner edges. The problem with the inner edges is that they are very diffuse, and it is hard to state where the edge actually is.