International Journal of Biomedical Imaging

Research Article

Cortical Surface Reconstruction from High-Resolution MR Brain Images

Algorithm 1

The level set function update algorithm.
{Compute time step for each point in the narrow band}
for all βƒ— π‘Ÿ 𝑖 ∈ 𝑁 π‘Ž π‘Ÿ π‘Ÿ π‘œ 𝑀 𝐡 π‘Ž 𝑛 𝑑   do
  {1. Compute the updated value}
   πœ™ n e w ← πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ ) + Ξ” 𝑑 Ξ” πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ )
  {2. Check if there is a sign change}
  if s g n ( πœ™ n e w ) = = s g n ( πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ ) )    then
   {3.1 No sign change}
    πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ + 1 ) ← πœ™ n e w {apply the update}
  else if βƒ— π‘Ÿ 𝑖 ∈ 𝑆 then {Check if is in the barrier}
   {3.2 Is in the barrier, do not allow sign change}
    πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ + 1 ) ← πœ€ {set to a small positive value}
  else {3.3 Is clear; check for topology change}
   if IsSimple ( πœ™ ( βƒ— π‘Ÿ , 𝑑 π‘˜ ) , πœ™ n e w , βƒ— π‘Ÿ 𝑖 )   then
    {3.3.1 No change in topology}
     πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ + 1 ) ← πœ™ n e w { apply the update}
   else {3.3.2 Do not allow topology change}
     πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ + 1 ) ← πœ€ β‹… s g n ( πœ™ ( βƒ— π‘Ÿ 𝑖 , 𝑑 π‘˜ ) ) {set to a small value of the same sign}
   end if
  end if
end for