title: Skeletal shape correspondence via entropy minimization.
abstract: OBJECTIVE
  Improving the shape statistics of medical image objects by generating correspondence of interior skeletal points.
  
  
  METHODS
  Synthetic objects and real world lateral ventricles segmented from MR images.
  
  
  METHODS
  Each object's interior is modeled by a skeletal representation called the s-rep, which is a quadrilaterally sampled, folded 2-sided skeletal sheet with spoke vectors proceeding from the sheet to the boundary. The skeleton is divided into three parts: up-side, down-side and fold-curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along their skeletal parts in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and sampling regularity. The spokes' geometric properties are skeletal position, spoke length and spoke direction. The properties used to measure the regularity are the volumetric subregions bounded by the spokes, their quadrilateral sub-area and edge lengths on the skeletal surface and on the boundary.
  
  
  RESULTS
  Evaluation on synthetic and real world lateral ventricles demonstrated improvement in the performance of statistics using the resulting probability distributions, as compared to methods based on boundary models. The evaluation measures used were generalization, specificity, and compactness.
  
  
  CONCLUSIONS
  S-rep models with the proposed improved correspondence provide significantly enhanced statistics as compared to standard boundary models.
authors.affiliation: Chongqing University, Shapingba, Chongqing, China ; University of North Carolina at Chapel Hill, Chapel Hill NC, USA.
authors.forename: Liyun
authors.initials: L
authors.lastname: Tu
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill NC, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Styner
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill NC, USA.
authors.forename: Jared
authors.initials: J
authors.lastname: Vicory
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill NC, USA.
authors.forename: Beatriz
authors.initials: B
authors.lastname: Paniagua
authors.affiliation: Brigham and Women's hospital, Center of Neurological Imaging, Boston MA, USA.
authors.forename: Juan Carlos
authors.initials: JC
authors.lastname: Prieto
authors.affiliation: Chongqing University, Shapingba, Chongqing, China.
authors.forename: Dan
authors.initials: D
authors.lastname: Yang
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill NC, USA.
authors.forename: Stephen M
authors.initials: SM
authors.lastname: Pizer
keywords: Shape; correspondence; lateral ventricles; modeling; shape analysis; skeletal representation