Uncertainty Estimation

The segmentation program built so far uses an elliptical shape model to delineate the interface between the skull and brain. This location is found by using information along lines normal to the ellipse location using the intensity information through intensity profiles. Optimization is completed using gradient descent. To get the initial starting coordinates a center of mass is calculated for the lighter voxels that represent the brain matter. Now to calculate the uncertainty of the segmentation a function was added to itk::IntensityProfileMetric that implements Markov Chain Monte Carlo (MCMC) using the Metropolis-Hastings algorithm.

The MCMC method quantifies the uncertainty by being able to calculate a variance for the distribution. In this case the distribution concerns two parameters, the two-dimensional coordinates that represent the location of the ellipse in respect to the MRI image.

The following is the output of the MCMC run and shows all the sampled coordinate locations in yellow that represent the locations of the center of the ellipses shape model. The red squares in the background represent the probability associated in the region encompassing the square, with darker red meaning more probable and lighter meaning less. The background in the slice that is being segmented with the yellow center points coinciding to their relative position on the MRI image.The following image represents the MCMC coordinates that were sampled by showing the different ellipses in their appropriate location. When the ellipse is darker that means the location is more probable and when the ellipse is less probable the color is a lighter red.