Medical morphometry is an important topic in medical imaging. Its goal is to systematically analyze anatomical structures of different subjects, and to generate diagnostic images to help doctors to visualise abnormalities for disease analysis. Quasiconformal(QC) Teichmuller theory, which studies the deformation patterns between shapes, is a useful tool for this purpose. In this talk, I will talk about how computational QC geometry can be practically applied to medical imaging for disease analysis. In particular, I will talk about how QC geometry can be used for surface registration and shape analysis.