This preview shows page 1. Sign up to view the full content.
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 ...
View
Full
Document
 Fall '11
 Xli

Click to edit the document details