Figure 1.

Generative model for a single patch. Data from N subjects are assumed to be patches containing categorical data. Image voxels are denoted by ${\mathit{\text{f}}}_{ni}^{(1)}$ (where n ∈ [1..N] and i ∈ [1..I⁽¹⁾]) and label voxels by ${\mathit{\text{f}}}_{ni}^{(2)}$ (i ∈ [1..I⁽²⁾]). These are encoded by their means (${\mu }_i^{(1)}$ and ${\mu }_i^{(2)}$, respectively) and a linear combination of basis functions (${\mathit{\text{W}}}_i^{(1)}$ and ${\mathit{\text{W}}}_i^{(2)}$, respectively). For each subject, the contributions of the two sets of basis functions are jointly controlled by latent variables z_n, which are assumed to be drawn from a normal distribution of mean z₀ and precision P₀.