Adaptive finite-element meshes for progressive contour models

This paper presents a progressive contour model based on the idea of deforming a contour from an initial shape as a source of prior knowledge by minimizing a defined contour energy to extract a desired contour from an image. The internal component of the contour energy imposes smoothness constraints on the displacements of deformations and the external component establishes the correspondence between the contour and image edges. A sequence of deformations is determined by repeatedly deforming and updating the initial contour. We show that the contour deformed by this sequence will smoothly and progressively approach a uniquely defined contour. We implement this model using a finite-element method, a multigrid algorithm, and an unconstrained optimization method. This approach offers several attractive advantages including a satisfactory convergence rate and the adaptation of the smoothness constraints.