A Variational Approach to Simultaneous Image Segmentation and Bias Correction

This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

[1]  Zhihui Wei,et al.  An improved variational level set method for MR image segmentation and bias field correction. , 2013, Magnetic resonance imaging.

[2]  Huihui Song,et al.  A Globally Statistical Active Contour Model for Segmentation of Oil Slick in SAR Imagery , 2013, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[3]  Jerry L. Prince,et al.  Adaptive fuzzy segmentation of magnetic resonance images , 1999, IEEE Transactions on Medical Imaging.

[4]  Chunming Li,et al.  Active contours driven by local Gaussian distribution fitting energy , 2009, Signal Process..

[5]  Julien Milles,et al.  MRI intensity nonuniformity correction using simultaneously spatial and gray-level histogram information , 2004, SPIE Medical Imaging.

[6]  S. Arridge,et al.  Sources of intensity nonuniformity in spin echo images at 1.5 T , 1994, Magnetic resonance in medicine.

[7]  Koenraad Van Leemput,et al.  Automated model-based bias field correction of MR images of the brain , 1999, IEEE Transactions on Medical Imaging.

[8]  Bostjan Likar,et al.  Retrospective Correction of MR Intensity Inhomogeneity by Information Minimization , 2000, MICCAI.

[9]  Xuelong Li,et al.  A Unified Tensor Level Set for Image Segmentation , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  John C. Gore,et al.  A robust parametric method for bias field estimation and segmentation of MR images , 2009, CVPR.

[11]  Bostjan Likar,et al.  A Review of Methods for Correction of Intensity Inhomogeneity in MRI , 2007, IEEE Transactions on Medical Imaging.

[12]  Chunming Li,et al.  A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities With Application to MRI , 2011, IEEE Transactions on Image Processing.

[13]  Aly A. Farag,et al.  A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data , 2002, IEEE Transactions on Medical Imaging.

[14]  Alan C. Evans,et al.  A nonparametric method for automatic correction of intensity nonuniformity in MRI data , 1998, IEEE Transactions on Medical Imaging.

[15]  Chunming Li,et al.  MRI Tissue Classification and Bias Field Estimation Based on Coherent Local Intensity Clustering: A Unified Energy Minimization Framework , 2009, IPMI.

[16]  Prashanthi Vemuri,et al.  Coil Sensitivity Estimation for Optimal SNR Reconstruction and Intensity Inhomogeneity Correction in Phased Array MR Imaging , 2005, IPMI.

[17]  M. Bronskill,et al.  Phase and sensitivity of receiver coils in magnetic resonance imaging. , 1986, Medical physics.

[18]  Xuelong Li,et al.  Spectral Segmentation via Midlevel Cues Integrating Geodesic and Intensity , 2013, IEEE Transactions on Cybernetics.

[19]  Martin Styner,et al.  Parametric estimate of intensity inhomogeneities applied to MRI , 2000, IEEE Transactions on Medical Imaging.

[20]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  David Zhang,et al.  Reinitialization-Free Level Set Evolution via Reaction Diffusion , 2011, IEEE Transactions on Image Processing.

[22]  Weili Zheng,et al.  Evaluation of performance metrics for bias field correction in MR brain images , 2009, Journal of magnetic resonance imaging : JMRI.

[23]  John W. Fisher,et al.  A Unified Variational Approach to Denoising and Bias Correction in MR , 2003, IPMI.

[24]  Lei Zhang,et al.  A variational multiphase level set approach to simultaneous segmentation and bias correction , 2010, 2010 IEEE International Conference on Image Processing.

[25]  J. Mangin,et al.  Entropy minimization for automatic correction of intensity nonuniformity , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[26]  Daniel Cremers,et al.  On Local Region Models and the Statistical Interpretation of the Piecewise Smooth Mumford-shah Functional , 2007 .

[27]  Jagath C. Rajapakse,et al.  Statistical approach to segmentation of single-channel cerebral MR images , 1997, IEEE Transactions on Medical Imaging.

[28]  Karl J. Friston,et al.  Unified segmentation , 2005, NeuroImage.

[29]  Richard A. Robb,et al.  Optimized homomorphic unsharp masking for MR grayscale inhomogeneity correction , 1998, IEEE Transactions on Medical Imaging.

[30]  Tianhu Lei,et al.  Statistical analysis of MR imaging and its applications in image modeling , 1994, Proceedings of 1st International Conference on Image Processing.

[31]  Rachid Deriche,et al.  Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation , 2002, International Journal of Computer Vision.

[32]  Lei Zhang,et al.  Active contours with selective local or global segmentation: A new formulation and level set method , 2010, Image Vis. Comput..

[33]  Chunming Li,et al.  Image segmentation with simultaneous illumination and reflectance estimation: An energy minimization approach , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[34]  W. Eric L. Grimson,et al.  Adaptive Segmentation of MRI Data , 1995, CVRMed.

[35]  Xavier Bresson,et al.  Fast Global Minimization of the Active Contour/Snake Model , 2007, Journal of Mathematical Imaging and Vision.

[36]  Brian B. Avants,et al.  N4ITK: Improved N3 Bias Correction , 2010, IEEE Transactions on Medical Imaging.

[37]  Frithjof Kruggel,et al.  Segmentation of MR images with intensity inhomogeneities , 1998, Image Vis. Comput..

[38]  Xuelong Li,et al.  A Relay Level Set Method for Automatic Image Segmentation , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[39]  Benoit Mory,et al.  Fuzzy Region Competition: A Convex Two-Phase Segmentation Framework , 2007, SSVM.

[40]  J. Haselgrove,et al.  An algorithm for compensation of surface-coil images for sensitivity of the surface coil , 1986 .

[41]  Michael Brady,et al.  Estimating the bias field of MR images , 1997, IEEE Transactions on Medical Imaging.

[42]  Lei Zhang,et al.  Active contours driven by local image fitting energy , 2010, Pattern Recognit..

[43]  Xuelong Li,et al.  A Nonlinear Adaptive Level Set for Image Segmentation , 2014, IEEE Transactions on Cybernetics.

[44]  Xuelong Li,et al.  Adaptive Shape Prior Constrained Level Sets for Bladder MR Image Segmentation , 2014, IEEE Journal of Biomedical and Health Informatics.