Multifractal-based Image Analysis with applications in Medical Imaging

In this thesis we look at the use of Multifractals as a tool in image analysis. We begin by studying the mathematical theory behind the concept of multifractals and give a close description of both fractal theory and multifractal theory. Different proposed approaches for estimating the multifractal exponents for a digital image is then presented and we describe how these exponents can be used to perform image segmentation and texture classification. Based on one of the presented approaches, a method for calculating the multifractal spectrum for a grayscale image is implemented and then tested for generated images with known multifractal spectra. We see that in this case there is a large number of parameters that will affect the result, but with the right parameter setting we can obtain spectra that are close to the theoretically calculated spectra. However, finding a good parameter setting is not easy since the values depend on the type of image under consideration and the image size. To see examples of the potential use of the multifractal approach in real applications, the implemented method is also tested for two different kinds of medical images mammograms and digital microscopy images. For both these applications it seems very promising to use the multifractal spectra to distinguish between different tissue types represented in the images.