Projects:ProstateSegmentation

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Prostate Segmentation

The objective is to extract the prostate from a 3D ultrasound data set.

Description

Two ways are employed to attack the problem. The first way is a combination of Cellular Automata(CA also called Grow Cut) with Geodesic Active Contour(GAC) methods. While the second is using a ellipsoid to match the prostate in 3D image. The details are given below.

Random Walks for prostate segmentation

Overview

The algorithm starts with a few initial seeds marking object and background. Then to decide the category of each of the other(non-seed) pixels, a random walker is released and it walks on the lattice of the image. The difficulty of walking from on pixel position to another is inversely related with the difference between the intensities of the two pixels. Given those settings, the probability of the random walker first hitting each kind of seeds are calculated. And the category of the pixel is assigned to the one with the greatest first hit probability.

Ideally, through this process the category of each pixel in the image could be decided.

Algorithm detail

The philosophy of random walk segmentation being stated above, it's practically impossible to implement that way. (Say, releasing many random walkers at each pixel and get the first hit probability using Monte-Carlo method.)

An analogy between first hit probability of random walks and the electrical potential distribution on a circuit network was given in the middle of last century. The resistance(conductance) in the circuit network is analogous to the crossing difficulty in the random walking scenario. Through the analogy the problem could be converted to a Dirichlet problem: [math] \triangle u = 0[/math] with boundary conditions: [math]u = 1 for object seeds[/math] [math]u = 0 for background seeds[/math]

In the above equation the [math]\triangle [/math] is a Laplace-Beltrami operator where the spatial variant resistance is considered to be metric of the space.

Ellipsoid Matching

Prostate is usually modeled as an ellipsoid . Also, with no control of the global shape, the algorithm is highly influenced by noise and incomplete image information like weak boundary. A shape prior would be used to deal with such situations. However, firstly the prior is learned from a sufficient number of training data, which may not be available. Secondly the shapes need to be aligned in order to be learned or applied in segmentation. However for prostate which is mostly an ellipsoid in shape, there's not much prominent shape feature to drive the alignment and segmentation.

So we are trying to first model the prostate using an ellipsoid. With that global constrain of shape, extraction it from image would be more robust. Secondly, if the prostate is well captured by an ellipsoid, then starting from there more local method would be used to capture the detail feature of the organ.

This way of attacking is under developing and some result would be available before the Core 1 meeting in late May.

Key Investigators

• Georgia Tech Algorithms: Yi Gao, Allen Tannenbaum