title: Flattening maps for the visualization of multibranched vessels.
abstract: In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels. The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals. From a triangulated representation of vessel surfaces, we show how the algorithm can be implemented using a finite element technique. The second method is an algorithm which adjusts the conformal mapping to produce a flattened representation of the original surface while preserving areas. This approach employs the theory of optimal mass transport. Furthermore, a new way of extracting center lines for vessel fly-throughs is provided.
authors.affiliation: Schools of Biomedical and Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. gte538w@prism.gatech.edu
authors.forename: Lei
authors.initials: L
authors.lastname: Zhu
authors.forename: Steven
authors.initials: S
authors.lastname: Haker
authors.forename: Allen
authors.initials: A
authors.lastname: Tannenbaum
mesh_terms: D000465:Algorithms; D001158:Arteries / Q000033:anatomy & histology*; D001185:Artificial Intelligence; D003196:Computer Graphics; D003198:Computer Simulation; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D018810:Magnetic Resonance Angiography / Q000379:methods*; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014584:User-Computer Interface