Recent Development of Medical Shape Analysis via Computational Quasi-conformal Geometry

Medical analysis is closely related to mathematics in many aspects. Over the past decades, mathematicians have designed numerous mathematical models and algorithms to aid medical researches. However, the space for joint-forcing mathematics with the medical industry is very limited in early years due to immature implementation and technological support. Those models are mostly limited to simple applications of the probability and statistics theory. It is until recent years when computational geometry comes into appliance, and it opens up a huge room for the incorporation of mathematics with medical analysis. For instance, medical imaging, geometric modeling for medical surfaces, and machine learning for disease classification are crucial topics nowadays having heavy reliance on image processing and geometric analysis. There are many streams in applying the study of geometry. Among those, the application of the quasi-conformal Teichmuller theory has shown to be very successful in recent years. This article serves to conclude some most updated models having solid contributions to the medical science in different aspects.