Summary

The use of partial differential equations and curvature driven flows in image analysis has become a research topic of increasing interest in the past few years. Let u_0: R² → R represent a gray-level image, where u₀(x,y) is the gray-level value and R is the set of all real numbers. Introducing an artificial time t, the image deforms via a partial differential evolution equation (PDE) according to ∂u/∂t = →[u(x, y, t)], (8.1) where u, x, y, t) : R² × [0, τ) → R is the evolving image, → : R → R is an operator that characterizes the given algorithm, and the image u₀ is the initial condition.¹ The solution u(x,y, t) of the differential equation gives the processed image at "scale" t. In the case of vector-valued images, a system of coupled PDEs of the form of Eq. (8.1) is obtained.