Computational Modeling of Deep Multiresolution-Fractal Texture and Its Application to Abnormal Brain Tissue Segmentation

Computational modeling of Multiresolution- Fractional Brownian motion (fBm) has been effective in stochastic multiscale fractal texture feature extraction and machine learning of abnormal brain tissue segmentation. Further, deep multiresolution methods have been used for pixel-wise brain tissue segmentation. Robust tissue segmentation and volumetric measurement may provide more objective quantification of disease burden and offer improved tracking of treatment response for the disease. However, we posit that computational modeling of deep multiresolution fractal texture features may offer elegant feature learning. Consequently, this work proposes novel modeling of Multiresolution Fractal Deep Neural Network (MFDNN) and its computational implementation that mathematically combines a multiresolution fBm model and deep multiresolution analysis. The proposed full 3D MFDNN model offers the desirable properties of estimating multiresolution stochastic texture features by analyzing large amount of raw MRI image data for brain tumor segmentation. We apply the proposed MFDNN to estimate stochastic deep multiresolution fractal texture features for tumor tissues in brain MRI images. The MFDNN model is evaluated using 1251 patient cases for brain tumor segmentation using the most recent BRATS 2021 Challenges dataset. The evaluation of the proposed model using Dice overlap score, Husdorff distance and associated uncertainty estimation offers either better or comparable performances in abnormal brain tissue segmentation when compared to the state-of-the-art methods in the literature. Index Terms: Computational Modeling, Multiresolution Fractional Brownian Motion (fBm), Deep Multiresolution Analysis, Fractal Dimension (FD), Texture Features, Brain tumor segmentation, Deep Learning.

[1]  F. Isensee,et al.  MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation , 2023, ArXiv.

[2]  N. Suciati,et al.  Single level UNet3D with multipath residual attention block for brain tumor segmentation , 2022, J. King Saud Univ. Comput. Inf. Sci..

[3]  R. Munbodh,et al.  A Joint Graph and Image Convolution Network for Automatic Brain Tumor Segmentation , 2021, BrainLes@MICCAI.

[4]  Christos Davatzikos,et al.  The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification , 2021, ArXiv.

[5]  Khan M. Iftekharuddin,et al.  Deep learning with context encoding for semantic brain tumor segmentation and patient survival prediction , 2020, Medical Imaging.

[6]  Christos Davatzikos,et al.  Longitudinal brain tumor segmentation prediction in MRI using feature and label fusion , 2020, Biomed. Signal Process. Control..

[7]  Jianming Liang,et al.  UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation , 2019, IEEE Transactions on Medical Imaging.

[8]  Seuc Ho Ryu,et al.  Brain MRI Image Classification for Cancer Detection Using Deep Wavelet Autoencoder-Based Deep Neural Network , 2019, IEEE Access.

[9]  Hui Fan,et al.  Multifocus Image Fusion Using Wavelet-Domain-Based Deep CNN , 2019, Comput. Intell. Neurosci..

[10]  Mohammad Sohel Rahman,et al.  MultiResUNet : Rethinking the U-Net Architecture for Multimodal Biomedical Image Segmentation , 2019, Neural Networks.

[11]  Andriy Myronenko,et al.  3D MRI brain tumor segmentation using autoencoder regularization , 2018, BrainLes@MICCAI.

[12]  Nima Tajbakhsh,et al.  UNet++: A Nested U-Net Architecture for Medical Image Segmentation , 2018, DLMIA/ML-CDS@MICCAI.

[13]  Liang Lin,et al.  Multi-level Wavelet-CNN for Image Restoration , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).

[14]  Christos Davatzikos,et al.  Advancing The Cancer Genome Atlas glioma MRI collections with expert segmentation labels and radiomic features , 2017, Scientific Data.

[15]  Jong Chul Ye,et al.  Framing U-Net via Deep Convolutional Framelets: Application to Sparse-View CT , 2017, IEEE Transactions on Medical Imaging.

[16]  Toshiya Hachisuka,et al.  Wavelet Convolutional Neural Networks for Texture Classification , 2017, ArXiv.

[17]  J. C. Ye,et al.  Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems , 2017, SIAM J. Imaging Sci..

[18]  Xuan Zeng,et al.  HeartID: A Multiresolution Convolutional Neural Network for ECG-Based Biometric Human Identification in Smart Health Applications , 2017, IEEE Access.

[19]  Christos Davatzikos,et al.  Improved brain tumor segmentation by utilizing tumor growth model in longitudinal brain MRI , 2017, Medical Imaging.

[20]  Thomas Brox,et al.  3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation , 2016, MICCAI.

[21]  Seyed-Ahmad Ahmadi,et al.  V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation , 2016, 2016 Fourth International Conference on 3D Vision (3DV).

[22]  Leyun Pan,et al.  Fractal and multifractal analysis of PET/CT images of metastatic melanoma before and after treatment with ipilimumab , 2015, EJNMMI Research.

[23]  Thomas Wiatowski,et al.  A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction , 2015, IEEE Transactions on Information Theory.

[24]  Brian B. Avants,et al.  The Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) , 2015, IEEE Transactions on Medical Imaging.

[25]  Subhransu Maji,et al.  Deep filter banks for texture recognition and segmentation , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[26]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[27]  Christopher Joseph Pal,et al.  Brain tumor segmentation with Deep Neural Networks , 2015, Medical Image Anal..

[28]  Yang Lu,et al.  Hyperspectral Image Classification Based on Three-Dimensional Scattering Wavelet Transform , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[29]  Qianjin Feng,et al.  Brain Tumor Segmentation Based on Local Independent Projection-Based Classification , 2014, IEEE Transactions on Biomedical Engineering.

[30]  S. Mallat,et al.  Intermittent process analysis with scattering moments , 2013, 1311.4104.

[31]  Atiq Islam,et al.  Multifractal Texture Estimation for Detection and Segmentation of Brain Tumors , 2013, IEEE Transactions on Biomedical Engineering.

[32]  Jun Zhou,et al.  Hyperspectral Image Classification Based on Structured Sparse Logistic Regression and Three-Dimensional Wavelet Texture Features , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Nasser Kehtarnavaz,et al.  Improved Labeling of Subcortical Brain Structures in Atlas-Based Segmentation of Magnetic Resonance Images , 2012, IEEE Transactions on Biomedical Engineering.

[34]  Wankai Deng,et al.  MRI brain tumor segmentation with region growing method based on the gradients and variances along and inside of the boundary curve , 2010, 2010 3rd International Conference on Biomedical Engineering and Informatics.

[35]  Nacim Betrouni,et al.  Fractal and multifractal analysis: A review , 2009, Medical Image Anal..

[36]  A. H. Siddiqi,et al.  Wavelet based hurst exponent and fractal dimensional analysis of Saudi climatic dynamics , 2009 .

[37]  Robert J. Ogg,et al.  Efficacy of texture, shape, and intensity features for robust posterior-fossa tumor segmentation in MRI , 2009, Medical Imaging.

[38]  R. Kikinis,et al.  Automated segmentation of MR images of brain tumors. , 2001, Radiology.

[39]  P. Gonçalves,et al.  Existence test of moments: Application to Multifractal Analysis , 2000 .

[40]  Lance M. Kaplan.  Extended fractal analysis for texture classification and segmentation , 1999, IEEE Trans. Image Process..

[41]  James M. Keller,et al.  A maximum likelihood estimate for two-variable fractal surface , 1998, IEEE Trans. Image Process..

[42]  R. Watanabe,et al.  DPM2 regulates biosynthesis of dolichol phosphate‐mannose in mammalian cells: correct subcellular localization and stabilization of DPM1, and binding of dolichol phosphate , 1998, The EMBO journal.

[43]  Lawrence O. Hall,et al.  Automatic tumor segmentation using knowledge-based techniques , 1998, IEEE Transactions on Medical Imaging.

[44]  C. Martínez-A,et al.  Monocyte chemoattractant protein-1-induced CCR2B receptor desensitization mediated by the G protein-coupled receptor kinase 2. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[45]  Yuxin Liu,et al.  Image feature extraction and segmentation using fractal dimension , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[46]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[47]  D. Turcotte.  Fractals and Chaos in Geology and Geophysics , 1992 .

[48]  K. Iftekharuddin,et al.  Brain Tumor Segmentation Using UNet-Context Encoding Network , 2021, BrainLes@MICCAI.

[49]  T. Neumuth,et al.  Multi-plane UNet++ Ensemble for Glioblastoma Segmentation , 2021, BrainLes@MICCAI.

[50]  M. A. Al-masni,et al.  3D CMM-Net with Deeper Encoder for Semantic Segmentation of Brain Tumors in BraTS2021 Challenge , 2021, BrainLes@MICCAI.

[51]  Jaime S. Cardoso,et al.  Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support , 2017, Lecture Notes in Computer Science.

[52]  Jing Zheng,et al.  Fractal-based brain tumor detection in multimodal MRI , 2009, Appl. Math. Comput..

[53]  Richard Kronland-Martinet,et al.  Reading and Understanding Continuous Wavelet Transforms , 1989 .