ABSTRACT
E E Eext img con( )V ( )s ( )V ( )s + ( )V ( )s (2) In the formula, Eimg (V(s)) is the image energy,
Econ (V(s)) is the external binding energy. Given a gray level image I (x,y) which viewed as
a function of continuous position variables (x,y), typical external energies designed to lead an active contour toward step edges are
E x yimg | (I , ) |( )V ( )s = ∇ 2 (3) E y x yimg | [ ( ) (I , )] |( )V ( )s ∇ ∗G ,xσ 2 (4) where Gσ(x, y) is a two-dimensional Gaussian function with standard deviation σ and ∇ is the gradient operator. A snake that minimizes E must satisfy the Euler equation:
′′′′ − ∇ =α Xβ Eext( )s 0 (5)
This equation can be used as an energy balance equation, i.e.
