Conformal Mapping via Metric Optimization with Application for Cortical Label Fusion

• Published in: Information Processing in Medical Imaging Vol. 23; pp. 244 - 255
• Main Authors: Shi, Yonggang, Lai, Rongjie, Toga, Arthur W.
• Format: Book Chapter Journal Article
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2013
• Series: Lecture Notes in Computer Science
• Subjects: Algorithms; Alzheimer Disease - pathology; Anatomical Surface; Brain - pathology; Cortical Surface; Gyral Region; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Label Surface; Magnetic Resonance Imaging - methods; Pattern Recognition, Automated - methods; Reproducibility of Results; Right Hemisphere; Sensitivity and Specificity; Staining and Labeling; Subtraction Technique
• ISBN: 3642388671; 9783642388675
• ISSN: 0302-9743; 1011-2499; 1611-3349
• DOI: 10.1007/978-3-642-38868-2_21

In this paper we develop a novel approach for computing conformal maps between anatomical surfaces with the ability of aligning anatomical features and achieving greatly reduced metric distortion. In contrast to conventional approaches that focused on conformal maps to the sphere or plane, our method computes the conformal map between surfaces in the embedding space formed the intrinsically defined Laplace-Beltrami (LB) eigenfunctions. Utilizing the power of LB eigenfunctions as informative descriptors of global geometry, the conformal maps computed by our method can effectively align anatomical features on cortical surfaces. By computing such feature-aware conformal maps to a group-wisely optimal atlas surface, which is also computed with metric optimization in the LB embedding space, we develop a fully automated system for cortical labeling with the fusion of labels on a large number of atlas surfaces. In our experiments, we build our system with 40 labeled surfaces and demonstrate its excellent performance with leave-one-out cross validation. We also applied the automated labeling system to cortical surfaces reconstructed from MR scans of 50 patients with Alzheimer’s disease (AD) and 50 normal controls (NC) to illustrate its robustness and effectiveness in clinical data analysis.