
Bayesian Active Contours with Affine-Invariant Elastic Shape Prior 145
which is equal to the length of the curve and is na turally invariant to any
re-parameterization. It is shown in [10] that the gradient of E
smooth
is given
by the Euclidean heat flow equation
∇E
smooth
(β)(t) = κ
β
(t)n(t), (7.6)
where κ
β
(t) is the curvature of β(t). It has been shown that this penalty on
a curve’s length automa tically leads to smoothing of a curve by forcing the
curve to become convex over time. Eventually, the curve evolves to a circle
and shrinks to a point as the evo lution time goe s to infinity.
7.3.4 Computing E
prior
and its gradient
Given a prio r shape class ({[q