This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Automatic Alignment of Genus-Zero Surfaces
March 2014 (vol. 36 no. 3)
pp. 466-478
Patrice Koehl, University of California, Davis, Davis
Joel Hass, University of California, Davis, Davis
A new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation, as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero. The algorithm takes as input a pair of surfaces that are topological 2-spheres, each surface given by a distinct triangulation. The algorithm then constructs a map $(f)$ between the two surfaces. First, each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm. The two mappings are then composed with a Möbius transformation to generate the function $(f)$. The Möbius transformation is chosen by minimizing an energy that measures the distance of $(f)$ from an isometry. We illustrate our approach using several "real life" data sets. We show first that the algorithm allows for accurate, automatic, and landmark-free nonrigid registration of brain surfaces. We then validate our approach by comparing shapes of proteins. We provide numerical experiments to demonstrate that the distances computed with our algorithm between low-resolution, surface-based representations of proteins are highly correlated with the corresponding distances computed between high-resolution, atomistic models for the same proteins.
Index Terms:
Shape,Conformal mapping,Proteins,Shape measurement,Geometry,Equations,nonrigid registration,Conformal mapping,mesh warping,Möbius transformation
Citation:
Patrice Koehl, Joel Hass, "Automatic Alignment of Genus-Zero Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 3, pp. 466-478, March 2014, doi:10.1109/TPAMI.2013.139
Usage of this product signifies your acceptance of the Terms of Use.