Fast Conformal Mapping for Prone / Supine Registration in CT Colonography
Seminar Room 1, Newton Institute
AbstractIn this talk I will present a challenging mathematical problem in biomedical imaging: that of registering (bringing into spatial alignment) two highly deformable surfaces of the colon. Solving this problem has clinical application in CT Colonography, also known as "virtual colonoscopy", used to screen patients for colorectal lesions. Our registration approach relies on conformally flattening each colon surface using Ricci flow, which is a partial differential equation that deforms the metric of a Riemannian manifold.
We then map 3D differential geometric shape descriptors to the flattened surfaces, and perform a cylindrical registration to derive the final registration. With the registration in place, we can determine corresponding points between the different surfaces, which is accurate to within approximately 6 millimeters.