张桂梅, 徐继元, 刘建新. 一种新的基于自适应分数阶的活动轮廓模型[J]. 计算机研究与发展, 2017, 54(5): 1045-1056.
 引用本文: 张桂梅, 徐继元, 刘建新. 一种新的基于自适应分数阶的活动轮廓模型[J]. 计算机研究与发展, 2017, 54(5): 1045-1056.
Zhang Guimei, Xu Jiyuan, Liu Jianxin. A New Active Contour Model Based on Adaptive Fractional Order[J]. Journal of Computer Research and Development, 2017, 54(5): 1045-1056.
 Citation: Zhang Guimei, Xu Jiyuan, Liu Jianxin. A New Active Contour Model Based on Adaptive Fractional Order[J]. Journal of Computer Research and Development, 2017, 54(5): 1045-1056.

## A New Active Contour Model Based on Adaptive Fractional Order

• 摘要: 区域可调拟合(region scalable fitting, RSF)活动轮廓模型在分割弱纹理、弱边缘图像时，优化易陷入局部极小导致曲线演化速度缓慢；同时该模型中的局部拟合项为高斯核函数，导致目标的边界模糊，影响分割精度.针对该问题，提出了一种基于自适应分数阶的活动轮廓模型，用于图像的分割.首先将全局G-L(Grünwald-Letnikov)分数阶梯度融合到RSF模型中，以增强灰度不均匀和弱纹理区域的梯度信息,从而提高对曲线初始位置选择的鲁棒性，并提高了图像分割的精度和速度；然后用双边滤波函数替换局部拟合项中的高斯核函数，解决了高斯核函数在演化过程中造成的边界模糊问题;最后根据图像的梯度模值和信息熵构建自适应分数阶阶次的数学模型，并计算出最佳分数阶阶次.理论分析和实验结果均表明:提出的算法可以用于灰度不均匀和弱纹理、弱边缘区域的图像分割，并能根据图像的特征自适应计算最佳分数阶阶次，避免曲线演化陷入局部最优.用多幅图像进行实验，得出该方法的分割精度和分割效率都有较大提高.

Abstract: Region scalable fitting (RSF) active contour model has limitation in segmenting image with weak texture and weak edge, troubled by inclining to local minimum and slow evolution speed. Aiming at the problem, this paper proposes a new active contour model with fractional order derivative operator capable of adjusting degree adaptively. Firstly, the global Grünwald-Letnikov (G-L) fractional gradient is integrated with the RSF model, which can strengthen the gradient of regions with intensity inhomogeneity and weak texture. As a result, both the robustness to initial location of evolution curve and efficiency of image segmentation are improved. Secondly, the Gaussian kernel function in local fitting term is replaced by bilateral filtering, and the blurred boundary caused by Gaussian kernel function in the process of curve evolution can be tackled. Lastly, an adaptive fractional order mathematical model is constructed based on the gradient magnitude and information entropy of image, therefore the optimal fractional degree is adjusted adaptively. Theoretical analysis and experimental results show that the proposed algorithm is capable of segmenting images with intensity inhomogeneity and weak texture. And the optimal degree of fractional order derivative operator can be calculated adaptively. Furthermore, the presented method is capable of avoiding falling into local optimum, thus the efficiency of image segmentation can be improved.

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