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

arXiv: https://arxiv.org/abs/2306.04754 · HTML: https://mlsanity.com/paper/2306.04754/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation](https://mlsanity.com/paper/1912.05074/) (2019)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [3D MRI brain tumor segmentation using autoencoder regularization](https://mlsanity.com/paper/1810.11654/) (2018)
- [MultiResUNet : Rethinking the U-Net Architecture for Multimodal Biomedical Image Segmentation](https://mlsanity.com/paper/1902.04049/) (2019)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation](https://mlsanity.com/paper/2303.09975/) (2023)
- [Brain Tumor Segmentation with Deep Neural Networks](https://mlsanity.com/paper/1505.03540/) (2015)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction](https://mlsanity.com/paper/1512.06293/) (2015)
- [Domain-adversarial neural networks to address the appearance variability of histopathology images](https://mlsanity.com/paper/1707.06183/) (2017)
- [Wavelet Convolutional Neural Networks for Texture Classification](https://mlsanity.com/paper/1707.07394/) (2017)
- [Intermittent process analysis with scattering moments](https://mlsanity.com/paper/1311.4104/) (2013)
- [A Joint Graph and Image Convolution Network for Automatic Brain Tumor Segmentation](https://mlsanity.com/paper/2109.05580/) (2021)

## Built on by (most cited first, 1 of 1)

- [XMorph: Explainable Brain Tumor Analysis Via LLM-Assisted Hybrid Deep Intelligence](https://mlsanity.com/paper/2602.21178/) (2026)

## Abstract (arXiv)

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.