  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.
