Initial Classification Using Probabilistic Atlases

The proposed classification algorithm seeks local optima of mutual information from an initial assignment of class labels, $\{ \mathcal{T}_k^0 \}_{k=1}^K$. These labels must be sufficiently close to the solution to provide distinct density estimates for the different classes. For this, we use co-registered probabilistic atlases for the white matter, gray matter, and cerebrospinal fluid. We obtain these atlases from the ICBM repository [139], which also provides an average-T1 image registered with these atlases. These atlases give the a priori probability for a voxel belonging to one of these tissue types. The probabilities are obtained using an empirical procedure whose goal is to obtain an average-anatomy of the human brain. The procedure for constructing these atlases involved averaging 452 brain tissue-class images, after aligning all of them to a common coordinate system [139].

We define the initialization as the maximum-a-priori estimate. We first register the average-T1 image to the data using an affine transformation and then use the transformation to resample the three probability images. The initialization is therefore:

1. 
   Perform affine registration between the average-T1 image, associated with the atlas, and the data.
   
2. 
   Resample the white matter, gray matter, and cerebrospinal fluid atlases based on the transformation obtained in the previous step.
   Let $P^a_k (t), k=1,2,3$ be the a priori probability, given by the atlas, for the $t$-th voxel belonging to the $k$-th tissue type.
   
3. 
   Compute the probabilities for the class (say class $k = 4$) comprising all the nonbrain tissue types:
   

   $$\forall t \in \mathcal{T}: P^a_4 (t) = 1 - \sum_{k=1}^3 P^a_k (t).$$ (146)

   
   
   
   
4. 
   Assign the initial class labels:
   

   $$\forall t \in \mathcal{T}: L^0(t) = \mathop{\mbox{argmax }}_{k} P^a_k (t).$$ (147)