# Bias-Compensated Integral Regression for Human Pose Estimation

arXiv: https://arxiv.org/abs/2301.10431 · HTML: https://mlsanity.com/paper/2301.10431/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 72 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [OpenPose: Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1812.08008/) (2018)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [Cascaded Pyramid Network for Multi-Person Pose Estimation](https://mlsanity.com/paper/1711.07319/) (2017)
- [RMPE: Regional Multi-person Pose Estimation](https://mlsanity.com/paper/1612.00137/) (2016)
- [Convolutional Pose Machines](https://mlsanity.com/paper/1602.00134/) (2016)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [DeepPose: Human Pose Estimation via Deep Neural Networks](https://mlsanity.com/paper/1312.4659/) (2013)
- [Integral Human Pose Regression](https://mlsanity.com/paper/1711.08229/) (2017)
- [HigherHRNet: Scale-Aware Representation Learning for Bottom-Up Human Pose Estimation](https://mlsanity.com/paper/1908.10357/) (2019)
- [Learning to Estimate 3D Hand Pose from Single RGB Images](https://mlsanity.com/paper/1705.01389/) (2017)
- [Efficient Object Localization Using Convolutional Networks](https://mlsanity.com/paper/1411.4280/) (2014)
- [Associative Embedding: End-to-End Learning for Joint Detection and Grouping](https://mlsanity.com/paper/1611.05424/) (2016)
- [Distribution-Aware Coordinate Representation for Human Pose Estimation](https://mlsanity.com/paper/1910.06278/) (2019)
- [PersonLab: Person Pose Estimation and Instance Segmentation with a Bottom-Up, Part-Based, Geometric Embedding Model](https://mlsanity.com/paper/1803.08225/) (2018)
- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation](https://mlsanity.com/paper/1406.2984/) (2014)
- [End-to-end Hand Mesh Recovery from a Monocular RGB Image](https://mlsanity.com/paper/1902.09305/) (2019)
- [Human Pose Estimation with Iterative Error Feedback](https://mlsanity.com/paper/1507.06550/) (2015)
- [Hand Pose Estimation via Latent 2.5D Heatmap Regression](https://mlsanity.com/paper/1804.09534/) (2018)
- [Wing Loss for Robust Facial Landmark Localisation with Convolutional Neural Networks](https://mlsanity.com/paper/1711.06753/) (2017)

## Built on by (most cited first, 3 of 3)

- [Human Pose-based Estimation, Tracking and Action Recognition with Deep Learning: A Survey](https://mlsanity.com/paper/2310.13039/) (2023)
- [MARCO: Navigating the Unseen Space of Semantic Correspondence](https://mlsanity.com/paper/2604.18267/) (2026)
- [Pixel-Wise Symbol Spotting via Progressive Points Location for Parsing CAD Images](https://mlsanity.com/paper/2404.10985/) (2024)

## Abstract (arXiv)

In human and hand pose estimation, heatmaps are a crucial intermediate representation for a body or hand keypoint. Two popular methods to decode the heatmap into a final joint coordinate are via an argmax, as done in heatmap detection, or via softmax and expectation, as done in integral regression. Integral regression is learnable end-to-end, but has lower accuracy than detection. This paper uncovers an induced bias from integral regression that results from combining the softmax and the expectation operation. This bias often forces the network to learn degenerately localized heatmaps, obscuring the keypoint's true underlying distribution and leads to lower accuracies. Training-wise, by investigating the gradients of integral regression, we show that the implicit guidance of integral regression to update the heatmap makes it slower to converge than detection. To counter the above two limitations, we propose Bias Compensated Integral Regression (BCIR), an integral regression-based framework that compensates for the bias. BCIR also incorporates a Gaussian prior loss to speed up training and improve prediction accuracy. Experimental results on both the human body and hand benchmarks show that BCIR is faster to train and more accurate than the original integral regression, making it competitive with state-of-the-art detection methods.