Dual Active Contour Models for Segmentation: Survey on Level Set and Variational Formulations

Abstract

Dual snake models are powerful techniques for boundary extraction
and segmentation of medical and biological images. In these methods the key idea is:
one contour contracts from outside the target and another one expands
from inside as a balanced technique with the ability to reject local
minima. Such approach was originally proposed in the context of parametric
snakes. More recently, it was re-worked through implicit formulation where
the deformable contours are zero level sets of embedding functions.
In this paper we review implicit dual active contours for medical image segmentation. We start with variational formulations of
dual models, aiming to set the background to derive the evolution
scheme through the Euler-Lagrange equations, and to clarify the global
optimization capabilities of dual techniques. Then, we summarize numerical
aspects regarding finite difference approaches, initial and boundary
conditions for dual techniques. Following, we review variational implicit
models which are very influenced by the Chan-Vese Active contour model.
Next, non-variational approaches are described, where the governing
equations are not explicit derived from Euler-Lagrange
expressions. We survey applications for shape recovery in transmission
electron microscopy, computed tomographic (CT), and magnetic resonance
imaging (MRI) modalities. We offer a discussion about important
points that have emerged from this review and point out drawbacks of dual approaches.
Besides, we present promising perspectives of dual active contour
models and related topics for image segmentation.