利用偏置校正的分数阶正则化水平集分割算法

doi:10.3778/j.issn.1002-8331.2204-0449

摘要/Abstract

摘要： 针对待分割图像中含有强度不均匀性和噪声情况，传统水平集分割方法不能得到理想的分割结果且效率低、抗干扰能力弱等不足。为此，提出一种利用偏置校正的分数阶正则化水平集分割算法。该方法利用分数阶距离正则项惩罚水平集函数（level set function，LSF）与带符号符号距离函数之间的偏差，抑制LSF在平坦区域的急剧反向扩散，保证LSF平稳演化。采用（Grünwald-Letnikov，G-L）分数阶导数，设计了新的分数阶导数及其共轭覆盖模板并采用改进的边缘停止函数和偏置校正，用于驱动LSF演化曲线快速地接近目标边缘。将偏置校正和分数阶距离正则化相结合用水平集函数来定义得到了能量泛函最小化的数值解。实验结果表明，所提方法对图像分割效率和鲁棒性有明显的提升。

关键词: 图像分割, 水平集函数, 偏置校正, 分数阶距离正则化

Abstract: In the case of intensity inhomogeneity and noise in the image to be segmented, the traditional level set segmentation methods can not obtain ideal segmentation results and have low efficiency and weak anti-interference ability. Therefore, a Fractional regularized level set segmentation algorithm using bias correction is proposed. In this method, the deviation between the level set function（LSF） and the signed distance function is penalized by the fractional distance regularization term to suppress the rapid backward diffusion of LSF in the flat region and ensure the smooth evolution of LSF. A new fractional derivative and its conjugate covering template are designed by using the（Grunwald-Letnikov, G-L） fractional derivative, and the improved edge stop function and bias correction are used to drive the LSF evolution curve to the target edge rapidly. Finally, the numerical solution of energy functional minimization is obtained by using a level set function in combination with bias correction and fractional distance regularization. Experimental results show that the proposed method can improve the efficiency and robustness of image segmentation.

Key words: image segmentation, level set function, offset correction, fractional distance regularization

蔡秀梅, 贺宁宁, 吴成茂. 利用偏置校正的分数阶正则化水平集分割算法[J]. 计算机工程与应用, 2023, 59(15): 196-205.

CAI Xiumei, HE Ningning, WU Chengmao. Fractional Regularized Level Set Segmentation Algorithm Using Bias Correction[J]. Computer Engineering and Applications, 2023, 59(15): 196-205.

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