We will discuss the mathematical, statistical and engineering challenges in stereotaxic brain mapping, including data acquisition, pre-processing, denoising, statistical analysis and result interpretation. Of particular importance will be the problem of efficient signal representation and quantitative evaluation of different 3D image registration methods. MRI (magnetic resonance imaging) and PET (positron emission tomography) data from elderly normal controls and dementia patients will be used to illustrate the functionality and disadvantages of a variety of mathematical techniques.