TY - GEN
T1 - Brain surface conformal parameterization with algebraic functions
AU - Wang, Yalin
AU - Gu, Xianfeng
AU - Chan, Tony F.
AU - Thompson, Paul M.
AU - Yau, Shing Tung
PY - 2006
Y1 - 2006
N2 - In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
AB - In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.
UR - http://www.scopus.com/inward/record.url?scp=79551688463&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79551688463&partnerID=8YFLogxK
U2 - 10.1007/11866763_116
DO - 10.1007/11866763_116
M3 - Conference contribution
C2 - 17354864
AN - SCOPUS:79551688463
SN - 354044727X
SN - 9783540447276
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 946
EP - 954
BT - Medical Image Computing and Computer-Assisted Intervention, MICCAI 2006 - 9th International Conference, Proceedings
PB - Springer Verlag
T2 - 9th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2006
Y2 - 1 October 2006 through 6 October 2006
ER -