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Computational modeling of Multiresolution- Fractional Brownian motion (fBm)has been effective in stochastic multiscale fractal texture feature extractionand machine learning of abnormal brain tissue segmentation. Further, deepmultiresolution methods have been used for pixel-wise brain tissuesegmentation. Robust tissue segmentation and volumetric measurement may providemore objective quantification of disease burden and offer improved tracking oftreatment response for the disease. However, we posit that computationalmodeling of deep multiresolution fractal texture features may offer elegantfeature learning. Consequently, this work proposes novel modeling ofMultiresolution Fractal Deep Neural Network (MFDNN) and its computationalimplementation that mathematically combines a multiresolution fBm model anddeep multiresolution analysis. The proposed full 3D MFDNN model offers thedesirable properties of estimating multiresolution stochastic texture featuresby analyzing large amount of raw MRI image data for brain tumor segmentation.We apply the proposed MFDNN to estimate stochastic deep multiresolution fractaltexture features for tumor tissues in brain MRI images. The MFDNN model isevaluated using 1251 patient cases for brain tumor segmentation using the mostrecent BRATS 2021 Challenges dataset. The evaluation of the proposed modelusing Dice overlap score, Husdorff distance and associated uncertaintyestimation offers either better or comparable performances in abnormal braintissue segmentation when compared to the state-of-the-art methods in theliterature. Index Terms: Computational Modeling, Multiresolution FractionalBrownian Motion (fBm), Deep Multiresolution Analysis, Fractal Dimension (FD),Texture Features, Brain tumor segmentation, Deep Learning.

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