Name
Abstract | ||
|---|---|---|
In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/TMI.2007.895464 | IEEE Trans. Med. Imaging |
Keywords | Field | DocType |
conformal parameterization,riemann surface structure,neurophysiology,lateral ventricle,brain mapping,homeomorphic surface,partial differential equation,automatic sulcal landmark location algorithm,biomedical mri,two-dimensional parameter domain,surface topography,conformal mapping,jacobian matrices,surface conformal parameterization,jacobian matrix,dirichlet problem,brain,partial differential equations,3-d magnetic resonance imaging,parameterized 3-d surface model,medical imaging,anatomical modeling,curvilinear net structure,surface-based registration,medical image processing,cerebral cortex,algorithms,boundary condition,riemann surface,anatomy,boundary conditions,magnetic resonance image,biomedical imaging,magnetic resonance imaging,signal processing,visualization,conformal map | Boundary value problem,Parallelogram,Jacobian matrix and determinant,Dirichlet problem,Riemann surface,Mathematical analysis,Conformal map,Curvilinear coordinates,Manifold,Mathematics | Journal |
Volume | Issue | ISSN |
26 | 6 | 0278-0062 |
Citations | PageRank | References |
37 | 1.13 | 39 |
Authors | ||
8 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yalin Wang | 1 | 1042 | 79.53 |
| Lok Ming Lui | 2 | 332 | 30.16 |
| Xianfeng Gu | 3 | 2997 | 189.71 |
| Kiralee M. Hayashi | 4 | 308 | 18.42 |
| Tony F. Chan | 5 | 8733 | 659.77 |
| Arthur W. Toga | 6 | 3128 | 261.46 |
| Paul Thompson | 7 | 3860 | 321.32 |
| Shing-tung Yau | 8 | 925 | 92.69 |