# euler lagrange and gradient descent in level set

the problem began when i read the paper "Active Contours Without Edges" http://www.math.ucla.edu/~lvese/PAPERS/IEEEIP2001.pdf

my trouble in equation(9) on page5 derived from page4.

At that time,i can't understand how author derive this equation. afterward i know author use euler-lagrange and gradient descent methods, but there are something still upset me...

(1)why we can use the result of euler-lagrange to be the gradient?

(2)why there is a parameter "t" appear in the equation(9),it doesn't appear in Page4 eqution.

i have found many papers in internet,but i still can't understand the reasons. i'm sorry for my poor english,and i hope that i have showed my question completely. thank you!

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