Nowadays imaging techniques such as MRI and CT are commonly used for medical procedures and research. The huge amount of medical images of different modalities demand the development of automatic or semi-automatic, accurate and efficient processing techniques. The digitalization of information and the easy access of fast computers make the task of image processing widely possible. Among many image processing procedures, image denoising, image deblurring and image segmentation are fundamental tasks. The goal of image denoising is to get rid of certain noises, image debluring is to restored sharpness of image boundaries, and image segmentation is to decompose an image into regions of special interest.

In this talk the basic mathematics used for image processing tasks will be discussed. In particular, modern level set methods using partial differential equations for medical image processing will be introduced. These methods have been successfully applied to synthetic and real images of different modalities, including optical, MR, and ultrasound images.