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Level Set Methods Nilanjan Ray Department of Computing Science University of Alberta.

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1 Level Set Methods Nilanjan Ray Department of Computing Science University of Alberta

2 What is Level Set Methods? A numerical technique for front propagation Level set methods represent a contour / front geometrically Consider a function  (x, y) over the rectangular image domain; intersection of the x-y plane and  represents a contour

3 Representation of Fronts Picture source: wikipedia A plane and a function  (x, y) can together represent a front: Eulerian or implicit representation

4 A Bit of Math Let (x(t), y(t)) represent coordinates of a front at time t, then Using chain rule of differentiation: Note that front velocity is speed (F) times the direction of flow (normal to curve): Substituting we have front propagation equation:

5 Matlab Demo Matlab demo (lev_demo.m)

6 An Example Segmentation video

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