A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
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Analyzing the data and performing computation effectively on surfaces with complicated geometry is an important research topic, especially in Human Brain Mapping. In this work, we are interested in computing the conformal structure of the Riemann surface and applying it to Human Brain Mapping. In order to analyze the brain data efficiently, the complicated brain cortical surface is usually parameterized to a simple parameter domain such as the sphere or 2D rectangles. This allows us to transform the 3D problems into 2D problems. In order to compare data more effectively, the parameterization has to preserve the geometry of the brain structure while aligning the important anatomical features consistently. Conformal parameterization, that preserves the local geometry, is often used. In our work, we propose algorithms to compute the optimized conformal parameterization of the brain surface which aligns the anatomical features consistently while preserving the conformality of the parameterization as much as possible. With the conformal parameterization, we can solve variational problems and partial differential equations on the surface easily by solving the corresponding equations on the 2D parameter domain. The computation is simple because of the simple Riemannian metric of the conformal map. Finally, we develop an automatic landmark tracking algorithm to detect the sulcal landmarks on the brain cortical surface, which involves solving variational problems on the brain surface.