Project I-2011 - Project I Calculus of Variation and Active...

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Unformatted text preview: Project I Calculus of Variation and Active Contours Model In this project, you are asked to first extend our discussion on the calculus of variation from a single function to two functions and then you are asked to apply your results to derive the partial differential equations that minimizes the energy functional for curve evolution. 1. Consider the following functional ( ) ∫ ( () () () ( )) for functions ( ) and ( ) from F the collection of continuously differentiable functions ( ) satisfying the boundary conditions ( ) ( ). Find the Euler’s equations for and that minimize ( ) among all F. (Show all your steps.) 2. Apply your equations to find the equations for the curve ( ) ( ( ) ( )), (with ( ) ( )) that minimizes the energy functional () ∫ (| ( ( ) ( ))|)| ( )| among all possible smooth curves contained in a rectangle [ [ ], differentiable, nonnegative function defined on [ ( ) (( ) ( )), | | √ , () [ ( () continuously differentiable, decreasing function defined on [ () () and , where is a ( )) and is a ) with the property ...
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This note was uploaded on 11/27/2011 for the course MAP 4371 taught by Professor Xli during the Fall '11 term at University of Central Florida.

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