# Complex Wavelet Mutual Information Loss: A Multi-Scale Loss Function for Semantic Segmentation

arXiv: https://arxiv.org/abs/2502.00563 · HTML: https://mlsanity.com/paper/2502.00563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 1 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [VM-UNet: Vision Mamba UNet for Medical Image Segmentation](https://mlsanity.com/paper/2402.02491/) (2024)
- [ResUNet-a: a deep learning framework for semantic segmentation of remotely sensed data](https://mlsanity.com/paper/1904.00592/) (2019)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024)
- [Region Mutual Information Loss for Semantic Segmentation](https://mlsanity.com/paper/1910.12037/) (2019)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Loss Functions in the Era of Semantic Segmentation: A Survey and Outlook](https://mlsanity.com/paper/2312.05391/) (2023)
- [Brain Tumor Segmentation and Survival Prediction using 3D Attention UNet](https://mlsanity.com/paper/2104.00985/) (2021)
- [blob loss: instance imbalance aware loss functions for semantic segmentation](https://mlsanity.com/paper/2205.08209/) (2022)
- [Y-net: Multi-scale feature aggregation network with wavelet structure similarity loss function for single image dehazing](https://mlsanity.com/paper/2003.13912/) (2020)
- [Machine learning of hierarchical clustering to segment 2D and 3D images](https://mlsanity.com/paper/1303.6163/) (2013)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [Training Transformer Models by Wavelet Losses Improves Quantitative and Visual Performance in Single Image Super-Resolution](https://mlsanity.com/paper/2404.11273/) (2024)
- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [Wavelet-based Loss for High-frequency Interface Dynamics](https://mlsanity.com/paper/2209.02316/) (2022)

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

- [Steerable Pyramid Weighted Loss: Multi-Scale Adaptive Weighting for Semantic Segmentation](https://mlsanity.com/paper/2503.06604/) (2025)

## Abstract (arXiv)

Recent advancements in deep neural networks have significantly enhanced the performance of semantic segmentation. However, class imbalance and instance imbalance remain persistent challenges, where smaller instances and thin boundaries are often overshadowed by larger structures. To address the multiscale nature of segmented objects, various models have incorporated mechanisms such as spatial attention and feature pyramid networks. Despite these advancements, most loss functions are still primarily pixel-wise, while regional and boundary-focused loss functions often incur high computational costs or are restricted to small-scale regions. To address this limitation, we propose the complex wavelet mutual information (CWMI) loss, a novel loss function that leverages mutual information from subband images decomposed by a complex steerable pyramid. The complex steerable pyramid captures features across multiple orientations and preserves structural similarity across scales. Meanwhile, mutual information is well-suited to capturing high-dimensional directional features and offers greater noise robustness. Extensive experiments on diverse segmentation datasets demonstrate that CWMI loss achieves significant improvements in both pixel-wise accuracy and topological metrics compared to state-of-the-art methods, while introducing minimal computational overhead. Our code is available at https://github.com/lurenhaothu/CWMI