基于偏移场校正的图像分割问题

Image segmentation based on bias field correction

摘要

针对低对比度图像分割中灰度不均匀性导致的性能下降问题，本文提出图像分割和偏移场校正联合模型，实现对乘性偏移场，加性偏移场和真实图像的联合估计。在此基础上，设计一种交替极小化方法（alternating minimization method，ADM）来求解此类含多个未知函数的变分泛函极小化问题。在给定条件下，证明 ADM 方法的收玫性。实验结果表明，本文所构建的图像分割方法在处理低对比度、边界模糊及灰度不均匀图像时具有显著优势。

Abstract

To address the performance degradation caused by intensity inhomogeneity in low－contrast image segmentation，this paper proposes a joint model for image segmentation and bias field correction，which achieves simultaneous estimationof the multiplicative bias field，additive bias field，and the true image．On this basis，an alternating minimization method（ADM）is designed to solve the variational functional minimization problem involving multiple unknown functions．Under given conditions，we prove the convergence of the proposed ADM．Experimental results demonstrate that the proposed image segmentation method has significant advantages in handling low－contrast，blurred boundary，and intensity inhomogeneous images．

关键词

图像分割 / 低对比度 / 偏移场校正 / 凸优化 / 交替极小化

Key words

image segmentation / low－contrast / bias field correction / convex optimization / alternating minimization

参考文献

[1] YEN J C, CHANG F J, CHANG S. A new criterion for automatic multilevel thresholding[J]. IEEE Transactions on Image Processing, 1995, 4(3):370-378.

[2] KASS M, WITKIN A, TERZOPOULOS D. Snakes:active contour models[J]. International Journal of Computer Vision, 1988, 1:321-331.

[3] CASELLES V, KIMMEL R, SAPIRO G. Geodesic active contours[J]. International Journal of Computer Vision, 1997, 22: 61-79.

[4] XU C Y, PRINCE J L. Gradient vector flow:a new external force for snakes[C]//Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,1997:66-71.

[5] XU C Y, PRINCE J L. Generalized gradient vector flow external forces for active contours[J]. Signal Processing, 1998, 71 (2):131-139.

[6] XU C Y, PRINCE J L. Snakes,shapes,and gradient vector flow[J]. IEEE Transactions on Image Processing, 1998, 7(3): 359-369.

[7] MUMFORF D, SHAH J. Optimal approximations by piecewise smooth functions and associated variational problems[J]. Communications on Pure and Applied Mathematics, 1989, 42(5):577-685.

[8] CHAN T F, VESE L A. Active contours without edges[J]. IEEE Transactions on Image Processing, 2001, 10(2):266-277.

[9] ACHANTA R, SHAJI A, SMITH K, et al. SLIC superpixels compared to state-of-the-art superpixel methods[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(11):2274-2281.

[10] ROTHER C, KOLMOGOROV V, BLAKE A. ＂GrabCut＂-interactive foreground extraction using iterated graph cuts[J]. ACM Transactions on Graphics, 2004, 23(3):309-314.

[11] LI C M, KAO C Y, GORE J C, et al. Implicit active contours driven by local binary fitting energy[J]. IEEE Conference on Computer Vision and Pattern Recognition,2007:1-7.

[12] GAO Shangbing, YANG Jian, YAN Yunyang. A local modified chan-vese model for segmenting inhomogeneous multiphase images[J]. International Journal of Imaging Systems and Technology, 2012, 22(2):103-113.

[13] ZHANG K H, ZHANG L, LAM K, et al. A level set approach to image segmentation with intensity inhomogeneity[J]. IEEE Transactions on Cybernetics, 2015, 46(2):546-557.

[14] WU Yongfeng, LI Meng, ZHANG Qifeng, et al. A retinex modulated piecewise constant variational model for image segmentation and bias correction[J]. Applied Mathematical Modelling, 2018, 54:697-709.

[15] WENG Guirong, DONG Bin, LAI Yu. A level set method based on additive bias correction for image segmentation[J]. Expert Systems with Applications, 2021, 185(15):115633.

[16] HSIEH P W, TSENG C L, YANG S Y. Additive-bias-correction variational model for noisy and intensity-inhomogeneous image segmentation[J]. SIAM Juornal On Imaging Sciense, 2025, 18(2):1235-1259.

[17] RAN Yanjun, LI Dong, TANG Liming. A variational level set model based on additive decomposition for segmenting noisy images with intensity inhomogeneity[J]. Signal Processing, 2023, 212:109169.

[18] LI Chunming, HUANG Rui, DING Zhaohua, et al. A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI[J]. IEEE Transactions on Image Processing, 2011, 20(7):2007-2016.

[19] CAI Qing, QIAN Yiming, ZHOU Sanping, et al. AVLSM:adaptive variational level set model for image segmentation in the presence of severe intensity inhomogeneity and high noise[J]. IEEE Transactions on Image Processing, 2022, 31:43-57.

[20] VERMA N, COWPERTHWAITE M C, MARKEY M K. Variational level set approach for automatic correction of multiplicative and additive intensity inhomogeneities in brain MR images[J]. IEEE Engineering in Medicine and Biology Society, 2012, 8:98-101.

[21] PANG Zhifeng, GUAN Zhenyan, LI Yue, et al. Image segmentation based on the hybrid bias field correction[J]. Applied Mathematics and Computation, 2023, 452:128050.

[22] THELJANI A, CHEN K. A nash game based variational model for joint image intensity correction and registration to deal with varying illumination[J]. Inverse Problems, 2020, 36(3):034002.

[23] CHAN T F, ESEDOGLU S, NIKNLOVE M. Algorithms for finding global minimizers of image segmentation and denoising models[J]. SIAM Journal on Applied Mathematics, 2006, 66(5):1632-1648.

[24] DEMENGEL F, DEMENGEL G. Functional spaces for the theory of elliptic partial differential equations[M]. New York: Springer, 2012.

[25] CHAMBOLLE A. An algorithm for total variation minimization and applications[J]. Journal of Mathematical Imaging and Vision, 2004, 20(1):89-97.

[26] GOLDSTEIN T, OSHER S. The split Bregman method for L1-regularized problems[J]. SIAM Journal on Imaging Sciences, 2009, 2( 2 ):323-343.

[27] YANG Yijie, ZHONG Qiuxiang, DUAN Yuping, et al. A weighted bounded hessian variational model for image labeling and segmentation[J]. Signal Processing, 2020, 173:107564.

[28] ALPERT S, GALUN M, BASRI R, et al. Image segmentation by probabilistic bottom-up aggregation and cue integration[C/OL]. IEEE Conference on Computer Vision and Pattern Recognition(CVPR).( 2007-06-17)[ 2026-05-11]. https://www.wisdom.weizmann.ac.il/-vision/Seg_Evaluation_DB/.

[29] WANG Dong, WANG Xiaoping. The iterative convolution-thresholding method(ICTM)for image segmentation[J]. Pattern Recognition, 2022, 130:108794.

[30] DING Keyan, XIAO Linfang, WENG Guirong. Active contours driven by region-scalable fitting and optimized laplacian of gaussian energy for image segmentation[J]. Signal Processing, 2017, 134:224-233.

基金资助

国家自然科学基金项目(12471484)