IEEE Trans Image Process. 2018 Oct;27(10):5016-5031. doi: 10.1109/TIP.2018.2848471.
Intensity inhomogeneity is common in real-world images and inevitably leads to many difficulties for accurate image segmentation. Numerous level-set methods have been proposed to segment images with intensity inhomogeneity. However, most of these methods are based on linear approximation, such as locally weighted mean, which may cause problems when handling images with severe intensity inhomogeneities. In this paper, we view segmentation of such images as a nonconvex optimization problem, since the intensity variation in such an image follows a nonlinear distribution. Then, we propose a novel level-set method named local approximation of Taylor expansion (LATE), which is a nonlinear approximation method to solve the nonconvex optimization problem. In LATE, we use the statistical information of the local region as a fidelity term and the differentials of intensity inhomogeneity as an adjusting term to model the approximation function. In particular, since the first-order differential is represented by the variation degree of intensity inhomogeneity, LATE can improve the approximation quality and enhance the local intensity contrast of images with severe intensity inhomogeneity. Moreover, LATE solves the optimization of function fitting by relaxing the constraint condition. In addition, LATE can be viewed as a constraint relaxation of classical methods, such as the region-scalable fitting model and the local intensity clustering model. Finally, the level-set energy functional is constructed based on the Taylor expansion approximation. To validate the effectiveness of our method, we conduct thorough experiments on synthetic and real images. Experimental results show that the proposed method clearly outperforms other solutions in comparison.
强度不均匀性在真实世界的图像中很常见，不可避免地给准确的图像分割带来了许多困难。已经提出了许多水平集方法来分割具有强度不均匀性的图像。然而，这些方法中的大多数都基于线性逼近，例如局部加权均值，这在处理具有严重强度不均匀性的图像时可能会引起问题。在本文中，我们将此类图像的分割视为一个非凸优化问题，因为图像中的强度变化遵循非线性分布。然后，我们提出了一种新的水平集方法，称为泰勒展开的局部逼近（LATE），它是一种解决非凸优化问题的非线性逼近方法。在 LATE 中，我们使用局部区域的统计信息作为保真度项，以及强度不均匀性的微分作为调整项来建模逼近函数。特别是，由于一阶微分由强度不均匀性的变化程度表示，因此 LATE 可以提高逼近质量，并增强具有严重强度不均匀性的图像的局部强度对比度。此外，LATE 通过放宽约束条件来解决函数拟合的优化问题。此外，LATE 可以被视为对经典方法的约束松弛，例如区域可扩展拟合模型和局部强度聚类模型。最后，基于泰勒展开逼近构建了水平集能量泛函。为了验证我们方法的有效性，我们在合成和真实图像上进行了彻底的实验。实验结果表明，与其他方法相比，所提出的方法明显更优。
