Projects:ProstateSegmentation
Back to Georgia Tech Algorithms
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 Random Walks for prostate segmentation. While the second is using a shape based method. 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.
Shape based segmentation
The shape based method could constrain the resulting segmentation within the learned variance of the shape. The algorithm consists two stages, learning the shapes and segment new case.
shape learning
segment new shape
Key Investigators
- Georgia Tech Algorithms: Yi Gao, Allen Tannenbaum
