South China University of Technology, Guangzhou, China.
IEEE Trans Image Process. 2012 Mar;21(3):946-57. doi: 10.1109/TIP.2011.2168408. Epub 2011 Sep 15.
Active contour models (ACMs) integrated with various kinds of external force fields to pull the contours to the exact boundaries have shown their powerful abilities in object segmentation. However, local minimum problems still exist within these models, particularly the vector field's "equilibrium issues." Different from traditional ACMs, within this paper, the task of object segmentation is achieved in a novel manner by the Poincaré map method in a defined vector field in view of dynamical systems. An interpolated swirling and attracting flow (ISAF) vector field is first generated for the observed image. Then, the states on the limit cycles of the ISAF are located by the convergence of Newton-Raphson sequences on the given Poincaré sections. Meanwhile, the periods of limit cycles are determined. Consequently, the objects' boundaries are represented by integral equations with the corresponding converged states and periods. Experiments and comparisons with some traditional external force field methods are done to exhibit the superiority of the proposed method in cases of complex concave boundary segmentation, multiple-object segmentation, and initialization flexibility. In addition, it is more computationally efficient than traditional ACMs by solving the problem in some lower dimensional subspace without using level-set methods.
主动轮廓模型（ACMs）与各种外部力场相结合，以将轮廓拉到准确的边界，在目标分割中显示出强大的能力。然而，这些模型仍然存在局部最小值问题，特别是向量场的“平衡问题”。与传统的 ACM 不同，在本文中，通过动力系统中定义的向量场的 Poincaré 映射方法，以新颖的方式实现了目标分割任务。首先为观察到的图像生成插值螺旋吸引流（ISAF）向量场。然后，通过在给定的 Poincaré 截面的牛顿-拉普森序列的收敛，找到 ISAF 的极限环上的状态。同时，确定极限环的周期。因此，对象的边界由具有相应收敛状态和周期的积分方程表示。通过与一些传统的外部力场方法进行实验和比较，展示了该方法在复杂凹边界分割、多目标分割和初始化灵活性方面的优越性。此外，通过在没有使用水平集方法的情况下在较低维子空间中解决问题，该方法比传统的 ACM 更具计算效率。
