目的 通过对C-V模型能量泛函的Euler-Lagrange方程进行变形,建立其与K-means方法的等价关系,提出一种新的基于水平集函数的改进K-means活动轮廓模型。方法 该模型包含局部自适应权重矩阵函数,它根据像素点所在邻域的局部统计信息自适应地确定各个像素点的分割阈值,排除灰度非同质对分割目标的影响,进而实现对灰度非同质图像的精确分割。结果 通过分析对合成以及自然图像的分割结果,与传统及最新经典的活动轮廓模型相比,新模型不仅能较准确地分割灰度非同质图像,而且降低了对初始曲线选取的敏感度。结论 提出了包含权重矩阵函数的新活动轮廓模型,根据分割目的和分割图像性质,制定不同的权重函数,该模型具有广泛的适用性。文中给出的一种具有局部统计特性的权重函数,对灰度非同质图像的效果较好,且对初始曲线位置具有稳定性。

Objective Active contour models (ACM) are efficient frameworks for image segmentation because they can provide smooth and closed contours to recover object boundaries with sub-pixel accuracy. Region-based ACM use regional statistical information as an additional constraint to stop the contours on the boundaries of the desired objects. One of the most popular region-based ACM is the C-V model, which has been successfully used in binary phase segmentation with the assumption that each image region is statistically homogeneous. However, typical region-based models do not work well on images with intensity inhomogeneity because these models rely on the uniformity of intensities. This paper presents a new level-set-based K-means active contour model that can segment images with intensity inhomogeneity. We derived this model from a linear level-set-based K-means model constructed by researching the properties of the Euler-Lagrange equation of the C-V model. Method Our background model is the C-V model, which consists of a fitting term and a regularization term. The fitting term corresponds to classical K-means. When parameters in a threshold are fixed, all pixels in an image have identical thresholds, and the evolution function has a quadratic form, normal K-means and the associated ACM will be unable to process images with intensity inhomogeneity.By researching the reasons for the aforementioned problems of the C-V model, a novel active contour based on a modified K-means is proposed in this paper. Compared with a K-means using fixed parameters, the new K-means contains a variable-weight coefficient matrix, which can be defined with different values for different pixels. Thus, the defined K-means can overcome the drawbacks of the C-V model. Moreover, we defined a local adaptive weighting (LAW) function thatcan identify the cluster threshold of each pixel according to its neighborhood statistical information. This threshold protects the model from the influence of intensity inhomogeneity and enables a successful segmentation ofinhomogeneity images. Result The LAW-based model can successfully detect objects on a noisy synthetic image with intensity inhomogeneity. Experimental results for medical images show that compared with the local binary fitting (LBF) model, local image fitting (LIF) model, and local correntropy-based K-means model, the proposed model can yield competitive results. Furthermore, when using the provided undesirable initial contours, the proposed model can still derive a correct segmentation of inhomogeneity images, whereas the LBF and LIF models are easily trapped into local minima. This result demonstrates that the proposed model is robust to contour initialization. Conclusion Given the use of fixed-weight parameters, the typical C-V model may fail to detect meaningful objects from images with intensity inhomogeneity. This paper proposes a modified K-means-based active contour by employing a variable-weight coefficient matrix. Different choices of variable-weight coefficient matrix can be defined to process specific images. We also provide a LAW function for this framework to segment inhomogeneous images. Experiment results indicate that the proposed model can effectively process images with intensity inhomogeneity and is robust to the position of the initial curve.