Algorithm 2.

fiber orientation mixture estimation

Input:
p0: the input spatial position for estimation
M0: the input reference model
${\{(p_i,M_i)\}}_{i=1}^C$: the local neighborhood of C position/model pairs
Ni: the number of fibers in the i-th local model
fij: the volume fraction of the j-th fiber of the i-th local model
vij: the fiber orientation of the j-th fiber of the i-th local model
hpos: the spatial positional bandwidth
hdir : the bilateral data-adaptive bandwidth
λ: the model complexity regularization parameter
Kmax: the maximum number of fiber compartments
Output:
K̂: estimated number of fiber compartments
$\hat{M}={\{({\hat{f}}_k,{\hat{\mathbf{v}}}_k)\}}_{k=1}^{\hat{K}}$: estimated model
/* Compute sum-normalized model weights			*/
Ksum ← 0
for i=1 to C do
	$k_i\leftarrow K(-{\Vert p_0-p_i\Vert }^2/h_{\mathit{\text{pos}}}^2)$
	$k_i\leftarrow k_i*K(-d_m^2(M_0,M_i)/h_{\mathit{\text{dir}}}^2)$
	Ksum ← Ksum + ki
for i=1 to C do
	ki ← ki/Ksum
/* Compute fiber weights			*/
L ← 0, Fsum ← 0
for i=1 to C do
	for j=1 to Ni do
		wL ← ki * fij, vL ← vij
		L ← L + 1, Fsum ← Fsum + fij
/* Optimize by clustering with Algo. 1			*/
$\hat{K},{\{({ŵ}_k,{\hat{\mathbf{v}}}_k)\}}_{k=1}^{\hat{K}}\leftarrow \mathit{\text{cluster}}({\{(w_i,{\mathbf{v}}_i)\}}_{i=1}^L,\lambda ,K_{\mathit{\text{max}}})$
for k=1 to K̂ do
	f̂k ← ŵk * Fsum
return