Segmentation criteria can be arbitrarily complex, and take into account global as well as local criteria. A common requirement is that each region must be [[connected]] in some sense.
An example of a global segmentation criterion is the famous [[Mumford-Shah]] [[functional]]. This functional measures the degree of match between an image and its segmentation. A segmentation consists of a set of non-overlapping connected regions (the union of which is the image), each of which is smooth and each of which has a piecewise smooth boundary. The functional penalizes deviations from the original image, deviations from smoothness within in each region and the total length of the boundaries of all the regions. Mathematically,
<math>
E \left( f,\Gamma \right) ={\mu}^{2}\int \!\!\!\int_{R} \! \left( f-g
