Boundary-Based Segmentation

In order to overcome some of the limitations of region-based methods for classification and segmentation, boundary-based methods are often used to look for explicit or implicit boundaries between regions corresponding to different tissue types. The two most commonly used boundary based methods are known as ridge detection and edge-detection:

• Ridge detection follows the peaks (local maxima) in the original image. For example, one way to outline the shape of a crater in a two-dimensional surface plot is to ``walk along'' the crest of the crater's rim. The circular path that would be traced out would be a much more compact representation of the crater than say, the set of all points inside the crater.
• When objects don't have large enough ridges at the region boundaries for ridge detection, the gradient operator can be used to enhance the boundaries (i.e., edges) between distinct regions. Edge detection is identical to ridge detection except that peaks are tracked in the gradient space of the image instead of the original image space. The gradient space can be computed by simply applying the gradient operator to the entire image. The two-dimensional gradient-operator is defined as,

  

  When it is necessary to distinguish the inside versus the outside of the edge, the Laplacian operator can be used. In two dimensions, the Laplacian operator is defined as,

  

The drawbacks of ridge-and edge-detection methods are that they can produce spurious, missing, or discontinuous edges. Hence, they can suffer from inadequate sensitivity and specificity because the image in the gradient space must be thresholded or otherwise classified according to edge or non-edge membership. Also, the problem of tracking an edge that bifurcates into two or more edges is one that cannot be adequated resolved using these low-level image operators alone. Furthermore, the derivative operator is inherently noisy and will exacerbate any noise already present in the image. Hence, the images must be smoothed before applying the gradient or Laplacian operators. Unfortunately, smoothing an image can hide or blur fine structures and other subtle features.