title: Intensity inhomogeneity correction for the breast sonogram: constrained fuzzy cell-based bipartitioning and polynomial surface modeling.
abstract: OBJECTIVE
  To develop an intensity inhomogeneity algorithm for breast sonograms in order to assist visual identification and automatic delineation of lesion boundaries.
  
  
  METHODS
  The proposed algorithm was composed of two essential ideas. One was decomposing the region of interest (ROI) into foreground and background regions by a cell-based segmentation algorithm, called constrained fuzzy cell-based bipartition-EM (CFCB-EM) algorithm. The CFCB-EM algorithm deformed the contour in a fuzzy cell-based deformation fashion with the cell structures derived by the fuzzy cell competition (FCC) algorithm as the deformation unit and the boundary estimated by the normalized cut (NC) algorithm as the reference contour. The other was modeling the intensity inhomogeneity in an ROI as a spatially variant normal distribution with a constant variance and spatially variant means, which formed a polynomial surface of order n. The proposed algorithm was formulated as a nested EM algorithm comprising the outer-layer EM algorithm, i.e., the intensity inhomogeneity correction-EM (IIC-EM) algorithm, and the inner-layer EM algorithm, i.e., the CFCB-EM algorithm. The E step of the IIC-EM algorithm was to provide a reasonably good bipartition separating the ROI into foreground and background regions, which included three major component algorithms, namely, the FCC, the NC, and the CFCB-EM. The M step of the IIC-EM algorithm was to estimate and correct the intensity inhomogeneity field by least-squared fitting the intensity inhomogeneity to an nth order polynomial surface. Forty-nine breast sonograms with intensity inhomogeneity, each from a different subject, were randomly selected for performance analysis. Three assessments were carried out to evaluate the effectiveness of the proposed algorithm.
  
  
  RESULTS
  Based on the visual evaluation of two experienced radiologists, in the first assessment, 46 out of 49 breast lesions were considered to have better contrasts on the inhomogeneity-corrected images by both radiologists. The interrater reliability for the radiologists was found to be kappa = 0.479 (p = 0.001). In the second assessment, the mean gradients of the low-gradient boundary points before and after correction of the intensity inhomogeneity were compared by the paired t-test, yielding a p-value of 0.000, which suggested the proposed intensity inhomogeneity algorithm may enhance the mean gradient of the low-gradient boundary points. By using the paired t-test, the third assessment further showed that the Chan and Vese level set method could derive a much better lesion boundary on the inhomogeneity-corrected image than on the original image (p = 0.000).
  
  
  CONCLUSIONS
  The proposed intensity inhomogeneity correction algorithm could not only augment the visibility of lesion boundary but also improve the segmentation result on a breast sonogram.
authors.affiliation: Institute of Biomedical Engineering, College of Medicine and College of Engineering, National Taiwan University, Number 1, Section 1, Jen-Ai Road, Taipei 100, Taiwan.
authors.forename: Chia-Yen
authors.initials: CY
authors.lastname: Lee
authors.forename: Yi-Hong
authors.initials: YH
authors.lastname: Chou
authors.forename: Chiun-Sheng
authors.initials: CS
authors.lastname: Huang
authors.forename: Yeun-Chung
authors.initials: YC
authors.lastname: Chang
authors.forename: Chui-Mei
authors.initials: CM
authors.lastname: Tiu
authors.forename: Chung-Ming
authors.initials: CM
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001331:Automation; D001943:Breast Neoplasms / Q000175:diagnosis* / Q000473:pathology*; D005260:Female; D017143:Fuzzy Logic; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical; D008962:Models, Theoretical; D015588:Observer Variation; D012984:Software; D014463:Ultrasonography / Q000379:methods*