title: Sensitivity analysis of a geometric calibration method using projection matrices for digital tomosynthesis systems.
abstract: OBJECTIVE
  To study the sensitivity of a geometric calibration method using projection matrices for digital tomosynthesis systems.
  
  
  METHODS
  A generic geometric calibration method for tomographic imaging systems has been presented in our previous work. The method involves a scan of a calibration phantom with multiple markers. Their locations in projection images are detected and are associated with their 3D coordinates to compute 3 x 4 projection matrices, which can be used in subsequent image reconstruction. The accuracy of geometric calibration may be affected by errors in the input data of marker positions. The effects of errors may depend on the number of markers and the volume surrounded by them in 3D space. This work analyzed the sensitivity of the calibration method to the above factors. A 6 cm CIRS breast research phantom and a prototype breast tomosynthesis system were used for our tests. A high contrast ring and two small speck groups were reconstructed in various testing cases for comparison. To achieve quantitative assessment, a 15 x 15 point detection mask was adopted for detecting signals and for computing changes between testing cases and the regular geometric calibration.
  
  
  RESULTS
  When 3D coordinates and 2D projections of markers were accurate, all tested numbers of markers, 6-44, provided similar high quality reconstructions of the ring and the two speck groups. Errors in marker positions resulted in image degradations and signal changes, which increased with fewer markers and smaller volume surrounded by markers in the 3D object space. Signal changes of small specks were more significant than those of the ring. Errors in marker projections produced drastic image degradations. Coplanar marker placement caused a failure in projection matrix computation.
  
  
  CONCLUSIONS
  For practical geometric calibration phantom design, ample markers are desired. They need to have a large volumetric coverage in the 3D space and be far from being coplanar. Precise determination of marker projections on detector planes is crucial for accurate geometric calibration and for small object detection using the reconstructed images.
authors.affiliation: Department of Radiology, Division of Diagnostic Imaging Physics, Massachusetts General Hospital, Boston, Massachusetts 02114, USA.
authors.forename: Xinhua
authors.initials: X
authors.lastname: Li
authors.forename: Zhang
authors.initials: Z
authors.lastname: Da
authors.forename: Bob
authors.initials: B
authors.lastname: Liu
mesh_terms: D001940:Breast; D002138:Calibration; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted; D016011:Normal Distribution; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods* / Q000592:standards*