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The random walker (RW) algorithm is used for both image segmentation andregistration, and possesses several useful properties that make it popular inmedical imaging, such as being globally optimizable, allowing user interaction,and providing uncertainty information. The RW algorithm defines a weightedgraph over an image and uses the graph's Laplacian matrix to regularize itssolutions. This regularization reduces to solving a large system of equations,which may be excessively time consuming in some applications, such as wheninteracting with a human user. Techniques have been developed that precomputeeigenvectors of a Laplacian offline, after image acquisition but before anyanalysis, in order speed up the RW algorithm online, when segmentation orregistration is being performed. However, precomputation requires certainalgorithm parameters be fixed offline, limiting their flexibility. In thispaper, we develop techniques to update the precomputed data online when RWparameters are altered. Specifically, we dynamically determine the number ofeigenvectors needed for a desired accuracy based on user input, and deriveupdate equations for the eigenvectors when the edge weights or topology of theimage graph are changed. We present results demonstrating that our techniquesmake RW with precomputation much more robust to offline settings while onlysacrificing minimal accuracy.

Adaptable Precomputation for Random Walker Image Segmentation and Registration