# PixelGame: Infrared small target segmentation as a Nash equilibrium

arXiv: https://arxiv.org/abs/2205.13124 · HTML: https://mlsanity.com/paper/2205.13124/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 80 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [GCNet: Non-local Networks Meet Squeeze-Excitation Networks and Beyond](https://mlsanity.com/paper/1904.11492/) (2019)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Semi-Supervised Semantic Segmentation with High- and Low-level Consistency](https://mlsanity.com/paper/1908.05724/) (2019)
- [Asymmetric Contextual Modulation for Infrared Small Target Detection](https://mlsanity.com/paper/2009.14530/) (2020)
- [Attentional Local Contrast Networks for Infrared Small Target Detection](https://mlsanity.com/paper/2012.08573/) (2020)
- [M2Det: A Single-Shot Object Detector based on Multi-Level Feature Pyramid Network](https://mlsanity.com/paper/1811.04533/) (2018)
- [Rotate to Attend: Convolutional Triplet Attention Module](https://mlsanity.com/paper/2010.03045/) (2020)
- [Finding Tiny Faces](https://mlsanity.com/paper/1612.04402/) (2016)
- [Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium](https://mlsanity.com/paper/2104.12761/) (2021)
- [EigenGame: PCA as a Nash Equilibrium](https://mlsanity.com/paper/2010.00554/) (2020)
- [Asymmetric Loss Functions and Deep Densely Connected Networks for Highly Imbalanced Medical Image Segmentation: Application to Multiple Sclerosis Lesion Detection](https://mlsanity.com/paper/1803.11078/) (2018)
- [Effective Use of Dilated Convolutions for Segmenting Small Object Instances in Remote Sensing Imagery](https://mlsanity.com/paper/1709.00179/) (2017)
- [Infrared Small-Dim Target Detection with Transformer under Complex Backgrounds](https://mlsanity.com/paper/2109.14379/) (2021)
- [Multi-Task Driven Feature Models for Thermal Infrared Tracking](https://mlsanity.com/paper/1911.11384/) (2019)
- [Fast and Robust Small Infrared Target Detection Using Absolute Directional Mean Difference Algorithm](https://mlsanity.com/paper/1810.03173/) (2018)

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

- [Position-Aware Relation Learning for RGB-Thermal Salient Object Detection](https://mlsanity.com/paper/2209.10158/) (2022)

## Abstract (arXiv)

A key challenge of infrared small target segmentation (ISTS) is to balance false negative pixels (FNs) and false positive pixels (FPs). Traditional methods combine FNs and FPs into a single objective by weighted sum, and the optimization process is decided by one actor. Minimizing FNs and FPs with the same strategy leads to antagonistic decisions. To address this problem, we propose a competitive game framework (pixelGame) from a novel perspective for ISTS. In pixelGame, FNs and FPs are controlled by different player whose goal is to minimize their own utility function. FNs-player and FPs-player are designed with different strategies: One is to minimize FNs and the other is to minimize FPs. The utility function drives the evolution of the two participants in competition. We consider the Nash equilibrium of pixelGame as the optimal solution. In addition, we propose maximum information modulation (MIM) to highlight the tar-get information. MIM effectively focuses on the salient region including small targets. Extensive experiments on two standard public datasets prove the effectiveness of our method. Compared with other state-of-the-art methods, our method achieves better performance in terms of F1-measure (F1) and the intersection of union (IoU).