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IEEE TRANSACTIONS ON MEDICAL IMAGING, 2013 1

Appendix: Rough Sets for Bias Field Correction inMR Images Using Contraharmonic Mean and

Quantitative IndexAbhirup Banerjee and Pradipta Maji

Abstract—One of the challenging tasks for magnetic resonance(MR) image analysis is to remove the intensity inhomogeneityartifact present in MR images, which often degrades the perfor-mance of an automatic image analysis technique. In this regard,the paper presents a novel approach for bias field correctionin MR images. It judiciously integrates the merits of roughsets and contraharmonic mean. While the contraharmonic meanis used in low-pass averaging filter to estimate the bias fieldin multiplicative model, the concept of lower approximationand boundary region of rough sets deals with vagueness andincompleteness in filter structure definition. A theoretical analysisis also presented to justify the use of both rough sets andcontraharmonic mean for bias field estimation. The integrationenables the algorithm to estimate optimum or near optimum biasfield. Some new quantitative indices are introduced to measureintensity inhomogeneity artifact present in a MR image. Theperformance of the proposed approach, along with a comparisonwith other intensity inhomogeneity correction algorithms, isdemonstrated on a set of simulated MR images for differentbias fields and noise levels and a set of real brain MR images.

I. QUALITATIVE AND QUANTITATIVE EVALUATION

Simulated images with different bias fields (20% and 40%)and noise levels (0%, 1%, 3%, 5%, 7% and 9%) have beengenerated from “BrainWeb: Simulated Brain Database” anddifferent bias field correction algorithms are applied on them.The results are reported in Fig. 1-12. The proposed algorithmRC2 [1] (rough set (RS) + contraharmonic mean (CHM) filterof order 2) has been compared with the Homomorphic Un-sharp Masking (HUM) filtering method [2], [3], nonparamet-ric nonuniform intensity normalization (N3) bias correctionmethod [4] and statistical parameter mapping (SPM8) softwaretool [5]. The effectiveness of contraharmonic mean (CHM) oforder 2 over other measures of central tendency (e.g. arithmeticmean and harmonic mean) is also established. The importanceof using rough sets is also shown in the results. Fig. 1- 6 showsthe results of the images with bias field 20% and differentnoise levels. Input images with bias field 40% and differentnoise levels and reconstructed images using different bias fieldcorrection algorithms are shown in Fig. 7-12. The root-meansquare error (RMSE) values for each of the reconstructedimages are also given.

Real T1-weighted brain MR images are downloaded from“IBSR: Internet Brain Segmentation Repository” and different

The authors are with the Machine Intelligence Unit, Indian StatisticalInstitute, Kolkata, India. E-mail: {abhirup r,pmaji}@isical.ac.in.

This work is partially supported by the Indian National Science Academy,New Delhi (grant no. SP/YSP/68/2012).

bias field correction algorithms are applied on them (RC2,RS + AM, RS + HM, NRS + CHM, HUM, N3 and SPM8).The input images along with their reconstructed images usingdifferent bias field correction algorithms are shown in Fig. 13-22.

The comparative performance of the proposed algorithmwith HUM, N3 and SPM8 over “BrainWeb” database usingdifferent quantitative indices (IoV, IoJV, IoCS and RMSE) isshown in Fig. 23 using bar diagrams. Comparison over “IBSR”database is shown in Fig. 24 using IoCS and IoJV indices.

The robustness of the proposed algorithm over different biasfield correction algorithms is checked on the unbiased imagesgenerated from “BrainWeb: Simulated Brain Database” withdifferent noise levels (0%, 1%, 3%, 5%, 7% and 9%). Theperformance is analysed using different quantitative indices inFig. 25 and the results are shown in Fig. 26-31.

REFERENCES

[1] A. Banerjee and P. Maji, “Rough Sets for Bias Field Correction inMR Images Using Contraharmonic Mean and Quantitative Index,” IEEETransactions on Medical Imaging, Submitted.

[2] L. Axel, J. Costantini, and J. Listerud, “Intensity Correction in Surface-Coil MR Imaging,” American Journal of Roentgenology, vol. 148, pp.418–420, 1987.

[3] B. H. Brinkmann, A. Manduca, and R. A. Robb, “Optimized Homomor-phic Unsharp Masking for MR Grayscale Inhomogeneity Correction,”IEEE Transactions on Medical Imaging, vol. 17, no. 2, pp. 161–171,1998.

[4] J. G. Sled, A. P. Zijdenbos, and A. C. Evans, “A Nonparametric Methodfor Automatic Correction of Intensity Nonuniformity in MRI Data,” IEEETransactions on Medical Imaging, vol. 17, no. 1, pp. 87–97, 1998.

[5] J. Ashburner and K. J. Friston, “Unified Segmentation,” NeuroImage,vol. 26, no. 3, pp. 839–851, 2005.

2 IEEE TRANSACTIONS ON MEDICAL IMAGING, 2013

(a) Input (b) RC2 : RMSE = 3.775 (c) RS + AM : RMSE = 20.711 (d) RS + HM : RMSE = 53.175

(e) NRS + CHM : RMSE = 5.828 (f) HUM : RMSE = 7.638 (g) N3 : RMSE = 9.025 (h) SPM8 : RMSE = 2.880

Fig. 1. Image of BrainWeb with 20% bias field and 0% noise and images restored by different algorithms




BANERJEE AND MAJI: ROUGH SETS AND CONTRAHARMONIC MEAN FOR BIAS FIELD CORRECTION IN MR IMAGES 3









(e) NRS + CHM: RMSE = 12.886 (f) HUM : RMSE = 13.672 (g) N3 : RMSE = 18.978 (h) SPM8 : RMSE = 12.096






(a) Input (b) RC2 (c) RS + AM (d) RS + HM

(e) NRS + CHM (f) HUM (g) N3 (h) SPM8

Fig. 13. Real image of IBSR 01 and images restored by different algorithms











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Fig. 23. Comparative performance of the proposed method, HUM algorithm of Brinkmann et al., N3 bias correction algorithm and SPM8 software tool forbias affected images from BrainWeb database


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Fig. 24. Comparative performance of the proposed method, HUM algorithm of Brinkmann et al., N3 bias correction algorithm and SPM8 software tool forbias affected images from IBSR database

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Fig. 25. Comparative performance of the proposed method, HUM algorithm of Brinkmann et al., N3 bias correction algorithm and SPM8 software tool forunbiased images from BrainWeb database

Download - IEEE TRANSACTIONS ON MEDICAL IMAGING, 2013 1 Appendix ...abhirup_r/appendix.pdf · Abhirup Banerjee and Pradipta Maji Abstract—One of the challenging tasks for magnetic resonance

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