Algorithm 1.

Prediction of cortical surface shape evolution from a baseline shape

1: INPUTS:

The learnt mean atlases

The learnt cloud C

The baseline ground truth shape S0

2: Initialize Svirtual ←0.

3: Initialize S̃i ←i for i ∈ {1, . . . , N}

4: Initialize ε as the mean distance between S0 and 0 plus its standard deviation

5: for every vertex x in the virtual shape Svirtual that is located outside the ε–neighborhood from S0 do

Update its position using the closeness metric (1 or 2)

Retrieve (or update if using Metric 2) its dynamic feature (evolution trajectory) c(x, t)t∈[0,T]

$${\stackrel{\sim }{S}}_i(x)=c(x,t_i)$$

6: end for

7: Estimate the geodesic current-based baseline shape evolution using {S0, {S̃i}} by minimizing: $$\stackrel{\sim }{E}={\int }_0^1{\Vert v_t\Vert }_V^{2}dt+\frac{1}{\gamma }{\sum }_i{\Vert {\stackrel{\sim }{S}}_i-{\varphi }_{t_i}^v·S_0\Vert }_{W^{\ast }}$$

8: OUTPUT:

Set of predicted surfaces { S̃i} at timepoints ti with i ∈ {0, . . . , N}

Set of smooth temporal evolution trajectories for vertices in S0 for t ∈ [0, tN]