Multifractal texture estimation for detection and segmentation of brain tumors

Abstract

A stochastic model for characterizing tumor texture in brain magnetic resonance (MR) images is proposed. The efficacy of the model is demonstrated in patient-independent brain tumor texture feature extraction and tumor segmentation in magnetic resonance images (MRIs). Due to complex appearance in MRI, brain tumor texture is formulated using a multiresolution-fractal model known as multifractional Brownian motion (mBm). Detailed mathematical derivation for mBm model and corresponding novel algorithm to extract spatially varying multifractal features are proposed. A multifractal feature-based brain tumor segmentation method is developed next. To evaluate efficacy, tumor segmentation performance using proposed multifractal feature is compared with that using Gabor-like multiscale texton feature. Furthermore, novel patient-independent tumor segmentation scheme is proposed by extending the well-known AdaBoost algorithm. The modification of AdaBoost algorithm involves assigning weights to component classifiers based on their ability to classify difficult samples and confidence in such classification. Experimental results for 14 patients with over 300 MRIs show the efficacy of the proposed technique in automatic segmentation of tumors in brain MRIs. Finally, comparison with other state-of-the art brain tumor segmentation works with publicly available low-grade glioma BRATS2012 dataset show that our segmentation results are more consistent and on the average outperforms these methods for the patients where ground truth is made available.

Fig. 1

Simulation of fBm process with different H values; (a) H = 0.01; (b) H = 0.5; (c) H = 0.99.

Fig. 2

Algorithm to compute multi-FD in brain MRI.

Fig. 3

Proposed modified AdaBoost algorithm.

Fig. 4

Simplified overall flow diagram.

Fig. 5

Multimodality MRI slices showing different preprocessing steps: (a) original T1, (b) original T2, (c) original FLAIR, (e) T1 after realign, unwarp, and bias field correction, (f) T2 after realign, unwarp, co-registration with T1 and biasfield correction, (g) FLAIR after realign, unwarp, co-registration with T1 and bias field correction, (h) intensity normalized T1, (i) intensity normalized T2, and (j) intensity normalized FLAIR.

Fig. 6

(a) Original T2 MRI. Arrow shows the tumor location. Features plots for (b) FD (PTPSA) versus intensity; (c) multi-FD versus intensity; (d) multi-FD versus intensity versus FD (PTPSA). Black points represent feature values in tumor regions, while white points represent feature values in nontumor regions.

Fig. 7

Comparison of segmentation results using (intensity, PTPSA and multi-FD) versus (intensity and texton) feature combination for astrocytoma (PXXX) patients.

Fig. 8

Comparison of segmentation results using (intensity, PTPSA and multi-FD) versus (intensity and texton) feature combination for medulloblastoma (MXXX) patients.

Fig. 9

Sagittal slice: (a) T1 contrast enhanced; (b) ground Truth; (c) Segmented tumor cluster.

Fig. 10

Coronal slice: (a) T1 contrast enhanced; (b) ground truth; (c) segmented tumor cluster.

Fig. 11

Change in classification error as classifiers are added in the ensemble.

Fig. 12

Change in total diversity as classifiers are added in the ensemble.

Fig. 13

ROC curve obtained from astrocytoma patients with: (a) intensity and PTPSA, (b) intensity and multi-FD, (c) intensity, PTPSA, and multi-FD, (d) intensity and texton, and (e) intensity, PTPSA, multi-FD, and texton.

Fig. 14

Box plot of modified AdaBoost prediction values for tumor (1) and nontumor (0) samples. Classifiers are trained with different feature combinations (IP: intensity+PTPSA, IM: intensity+multi-FD, IPM: intensity+PTPSA+multi-FD, IT: intensity+texton, IPMT: intensity+ PTPSA+multi-FD+texton).