Algorithm 1.

Point matching algorithm for initial dental alignment

t ← 0, R ← I

for β = βini to βmax do

while ${\epsilon }_0<{\epsilon }_0^{\prime }$ or the number of executions <I0 do

mij ← exp[β(α − ||pi − t − Rqj||2)]

m̃ij ← mij; (Initialization of m̃ij)

while ${\epsilon }_1<{\epsilon }_1^{\prime }$ or the number of executions <I1 do

${\stackrel{\sim }{m}}_{ij}\leftarrow ({\stackrel{\sim }{m}}_{ij})/({\sum }_{i=0}^N{\stackrel{\sim }{m}}_{ij})$, ∀j; (Row normalization)

${\stackrel{\sim }{m}}_{ij}\leftarrow ({\stackrel{\sim }{m}}_{ij})/({\sum }_{j=0}^K{\stackrel{\sim }{m}}_{ij})$, ∀i; (Column normalization)

end while

mij ← m̃ij

Calculate R and t using mij

${\mathbf{n}}_v^{\prime }\leftarrow \mathbf{R}{\mathbf{n}}_v$

if ${\mathbf{n}}_u^T{\mathbf{n}}_v^{\prime }>0$ then

− R ← R

end if

end while

β ← βincrβ

end for