Conformal Brain Mapping using Variational Methods and PDEs.
Tony Chan
UCLA
Mathematics
We developed a general method for global surface conformal parameterization. For genus-zero surfaces, our algorithm can find a conformal mapping between any two genus-zero manifolds by minimizing the harmonic energy. We apply this algorithm to the cortical surface matching problem. A mesh structure is used to represent the brain surface, and additional constraints are imposed to ensure that the conformal map is unique.
Empirical tests on MRI data show that the mappings preserve angular relationships, are stable for MRIs acquired at different times, and are robust to differences in data triangulation and resolution. Compared with other brain surface conformal mapping algorithms, our approach is more stable and has good extensibility.
In our recent work, we further extended the algorithm to compute a three-dimensional volumetric harmonic map from a 3D brain volumetric model to a solid sphere. Experimental results and future directions will be discussed.
