Zou Guangyu, Hu Jiaxi, Gu Xianfeng, Hua Jing
Innovisgroup, Inc., China.
Med Image Comput Comput Assist Interv. 2011;14(Pt 2):335-42. doi: 10.1007/978-3-642-23629-7_41.
In this paper, we propose a novel area-preserving surface flattening method, which is rigorous in theory, efficient in computation, yet general in application domains. Leveraged on the state-of-the-art flattening techniques, an infinitesimal area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms on the manifold, which yields strict equality of area elements between the flattened and the original surfaces at its final state. With a surface represented by a triangular mesh, we present how an deterministic algorithm can be faithfully implemented to its continuous counterpart. To demonstrate the utility of this method, we have applied our method to both the cortical hemisphere and the entire cortex. Highly complied results are obtained in a matter of seconds.
在本文中，我们提出了一种新颖的保面积曲面扁平化方法，该方法理论严谨、计算高效且应用领域广泛。利用最先进的扁平化技术，构建了一种无穷小面积恢复微分同胚流，作为流形上微分2-形式的李平流，在其最终状态下，扁平化曲面与原始曲面之间的面积元素严格相等。对于由三角形网格表示的曲面，我们展示了如何将确定性算法忠实地实现为其连续对应算法。为了证明该方法的实用性，我们已将我们的方法应用于皮质半球和整个皮质。在几秒钟内就获得了高度一致的结果。
