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Unformatted text preview: We will focus on 11/15/2011 5 Deriving the Equations • Let ° = ° (?, ?) denote the curve (in ? ) that evolve with time (an artificial parameter ? ). To minimize ± 2 , we set To minimize ± 1 , we set Similarly, Example OF Mean Curvature Motion 11/15/2011 6 From Curve to Level Sets Method Curve evolution equation °±(?, ?) °? = ²³´ ± 0, ? = ± µ (?) In level set notation: So Plug in the curve evolution equation ´ = the unit normal of ±, Curve Evolution in Level Set Method • Inward (always on your leftside) normal of u=0 : • So, we can write ´ = − ∇? ∇? 11/15/2011 7 Boundary and Initial Conditions HamiltonJacobi Equation 11/15/2011 8 11/15/2011 9 11/15/2011 10 11/15/2011 11 11/15/2011 12 11/15/2011 13 11/15/2011 14 Homework • Verify all the cirlcled formulas....
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 Fall '11
 Xli
 Manifold, Gradient, Level set, Level set method

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