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.