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The normalized segmentation method described by Shi and Malik (2000) is designed to look for clusters of pixels with similar intensity. To do this, a weight matrix is created that relates each pixel to every other pixel within a local neighborhood. The strongest weights are given to pixels of similar intensity and close proximity. The method then seeks to partition the image into two groups, *A* and *B*, by minimizing the normalized cut:
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(1) |

where *cut* is the sum of the weights cut by the partition. *total*_{A} is the sum of all weights in Group *A*, and *total*_{B} is the sum of all weights in Group *B*. Normalizing the cut by the sum of all the weights in each group prevents the partition from selecting overly small groups of nodes.
The minimum of *N*_{cut} can be found by solving the generalized eigensystem:

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(2) |

created from weight matrix () and a diagonal matrix (), with each value on the diagonal being the sum of each column of . The eigenvector () with the second smallest eigenvalue ) is used to partition the image by taking all values greater than zero to be in one group, and its complement to be in the other.

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Stanford Exploration Project

5/23/2004