Adaptable Precomputation for Random Walker Image Segmentation and Registration

TL;DR

This paper introduces methods for dynamically updating precomputed eigenvectors in the random walker algorithm, enhancing its flexibility and efficiency in image segmentation and registration tasks, especially in interactive medical imaging applications.

Contribution

The authors develop online update techniques for eigenvectors in precomputed random walker algorithms, allowing parameter changes without full recomputation, improving robustness and efficiency.

Findings

Online eigenvector updates maintain accuracy with minimal error.

Precomputation becomes more flexible and adaptable to parameter changes.

Significant speed-ups in interactive segmentation and registration tasks.

Abstract

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