title: Medical image segmentation via atlases and fuzzy object models: Improving efficacy through optimum object search and fewer models.
abstract: OBJECTIVE
  Statistical object shape models (SOSMs), known as probabilistic atlases, are popular in medical image segmentation. They register an image into the atlas coordinate system, such that a desired object can be delineated from the constraints of its shape model. While this strategy facilitates segmenting objects with even weak-boundary contrast, it tends to require more models per object to cope with possible registration errors. Fuzzy object shape models (FOSMs) gain substantial speed by avoiding image registration and placing more relaxed model constraints with optimum object search. However, they tend to require stronger object boundary contrast for effective delineation. In this work, the authors show that optimum object search, the essential underpinning of FOSMs, can improve segmentation efficacy of SOSMs with fewer models per object.
  
  
  METHODS
  For the sake of efficiency, the authors use three atlases per object (SOSM-3) as baseline for segmentation based on the best match with posterior probability maps. A novel strategy for SOSM with a single atlas and optimum object search (SOSM-S) is presented. When registering an image to the atlas system, one should expect that the object's boundary falls within the uncertainty region of the model-region wherein voxels show probabilities greater than 0 and less than 1 to be in the object. Since registration may fail, SOSM-S translates the atlas locally and, at each location, delineates and scores a candidate object in the uncertainty region. Segmentation is defined by the candidate with the highest score. The presented FOSM also uses a single model per object, but model construction uses only shape translations, building a fuzzy object model with larger uncertainty region. Optimum object search requires estimation of the object's location and/or optimization algorithms to speed-up segmentation.
  
  
  RESULTS
  The authors evaluate SOSM-3, SOSM-S, and FOSM on 75 CT-images of the thorax and 35 MR T1-weighted images of the brain, with nine objects of interest. The results show that SOSM-S and FOSM can segment seven out of the nine objects with higher accuracy than SOSM-3, according to the average symmetric surface distance and statistical test. SOSM-S was consistently more accurate than FOSM, FOSM being 2-3 orders of magnitude faster than SOSM-S and SOSM-3 for model construction and hundreds of times faster than them for segmentation.
  
  
  CONCLUSIONS
  Although multiple models per object can usually improve segmentation efficacy, the optimum object search has shown to reduce the number of required models. The efficiency gain of FOSM over SOSM-S motivates its use for interactive applications and studies with large image data sets. FOSM and SOSM impose different degrees of shape constraints from the model, making one approach more suitable than the other, depending on contrast. This suggests the use of hybrid models that can take advantage from the strengths of fuzzy and statistical models.
authors.affiliation: LIV, Institute of Computing, University of Campinas, Av. Albert Einstein, 1251, Cidade Universitária "Zeferino Vaz," Campinas, SP 13083-852, Brazil.
authors.forename: Renzo
authors.initials: R
authors.lastname: Phellan
authors.affiliation: LIV, Institute of Computing, University of Campinas, Av. Albert Einstein, 1251, Cidade Universitária "Zeferino Vaz," Campinas, SP 13083-852, Brazil.
authors.forename: Alexandre X
authors.initials: AX
authors.lastname: Falcão
authors.affiliation: Medical Image Processing Group Department of Radiology, University of Pennsylvania, 423 Guardian Drive, Philadelphia, Pennsylvania 19104-6021.
authors.forename: Jayaram K
authors.initials: JK
authors.lastname: Udupa
mesh_terms: D000465:Algorithms; D002531:Cerebellum; D017143:Fuzzy Logic; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D013902:Radiography, Thoracic; D013909:Thorax; D014057:Tomography, X-Ray Computed