Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China.
PLoS One. 2019 Apr 19;14(4):e0214851. doi: 10.1371/journal.pone.0214851. eCollection 2019.
This paper presents a fast two-stage image segmentation method for intensity inhomogeneous image using an energy function based on a local region-based active contour model with exponential family. In the first stage, we preliminary segment the down-sampled images by the local correntropy-based K-means clustering model with exponential family, which can fast obtain a coarse result with low computational complexity. Subsequently, by taking the up-sampled contour of the first stage as initialization, we precisely segment the original images by the improved local correntropy-based K-means clustering model with exponential family in the second stage. This stage can achieve accurate result rapidly as the result of the proper initialization. Meanwhile, we converge the energy function of two-stage by the Riemannian steepest descent method. Comparing with other statistical numerically methods, which are used to solve the partial differential equations(PDEs), this method can obtain the global minima with less iterations. Moreover, to promote regularity of energy function, we use a popular regular method which is an inner product and applies spatial smoothing to the gradient flow. Extensive experiments on synthetic and real images demonstrate that the proposed method is more efficient than the other state-of-art methods on intensity inhomogeneous images.
本文提出了一种基于局部区域主动轮廓模型的能量函数的快速两阶段强度不均匀图像分割方法，该模型基于指数族。在第一阶段，我们通过基于局部相关熵的指数族 K-均值聚类模型对下采样图像进行初步分割，该模型可以快速获得低计算复杂度的粗分割结果。随后，通过取第一阶段的上采样轮廓作为初始化，我们在第二阶段通过改进的基于局部相关熵的指数族 K-均值聚类模型对原始图像进行精确分割。由于适当的初始化，该阶段可以快速获得准确的结果。同时，我们通过黎曼最速下降法来收敛两阶段的能量函数。与其他用于求解偏微分方程（PDEs）的统计数值方法相比，该方法可以通过较少的迭代次数获得全局最小值。此外，为了提高能量函数的正则化程度，我们使用一种常用的正则化方法，即内积，并将空间平滑应用于梯度流。在合成和真实图像上的广泛实验表明，与其他强度不均匀图像的最新方法相比，该方法在效率上更具优势。
