Once the distributions of the indicator variables \(z_i\) are
calculated we can separate the components of the mixture.
Individual components are selected according to the most probable
\(z_i\) value in a given region of the distributional space,
leading to a partition of this space into regions.
Intensity threshold values are associated with the partition of the
distributional space to drive the image segmentation.
In brief, the partition of the distributional space induced by the
\(z\) values is used to segment the data space.
From a computational point of view, the use of these two separate
spaces enables us to optimize the MCMC implementation.