Lawrence Berkeley National Laboratory

Nonlinear edge preserving smoothing often is performed prior to medical image segmentation. The goal of the nonlinear smoothing is to improve the accuracy of the segmentation by preserving changes in image intensity at the boundaries of structures of interest, while smoothing random fluctuations due to noise in the interiors of the structures. Methods include median filtering and morphology operations such as gray scale erosion and dilation, as well as spatially varying smoothing driven by local contrast measures. Rather than irreversibly altering the image data prior to segmentation, the approach described here has the potential to unify nonlinear edge preserving smoothing with segmentation based on differential edge detection at multiple scales. The analysis of n-D image data is decomposed into independent 1-D problems that can be solved relatively quickly. Smoothing in various directions along 1-D profiles through n-D data is driven by a measure of local structure separation, rather than by a local contrast measure. Isolated edges are preserved independent of their contrast, given an adequate contrast to noise ratio. In addition, analytic expressions are obtained for the derivatives of the edge preserved 1-D profiles. Using these expressions, multidimensional edge detection operators such as the Laplacian or the second derivative in the direction of the image intensity gradient can be composed and used to segment n-D data. The smoothing and segmentation algorithms are applied to simulated 4-D medical image data.