Level Sets Method2011

# Level Sets Method2011 - We will focus on 11/15/2011 5...

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11/15/2011 1 Level Sets Method Introduction Images Curves as isolevels of an image, image as a surface

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11/15/2011 2 Parametrized Curves p N T Arc Length, Unit Tengent, and Curvature Arc length: Unit tangent vector (verify: ) Curvature tensor: So °± °² and ³ ? are parallel and (for some ´(?) , the curvature) ? = 0 ? = ?
11/15/2011 3 Two Important Formulas Verify and Curves as Iso-Level of a Function u Differentiate (*) again: Consider (*) (**)

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11/15/2011 4 Formulas for Curvature of Level Curves From |T’(s)|=1, we have Thus We can re-write the formula as Boundary Detection Functional We will apply calculus of variation to some image analysis problems. First let us consider the problem of detecting the boundary of an object in an image. Recall that boundary points are where the intensity changed most. This means, the magnitude of the gradient of the intensity is very large on the boundary points.