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Robust Optimization for Deep Regression
Vasileios Belagiannis, Christian Rupprecht, Gustavo Carneiro, Nassir Navab
TL;DR
ConvNet regression commonly uses L2 loss despite its sensitivity to outliers. This paper trains ConvNet regressors with Tukey’s biweight loss and adds a coarse-to-fine cascade, reporting faster convergence, better generalization, and competitive pose-estimation results. The method is evaluated on pose and age estimation, with limitations tied to residual-scaling assumptions and low-resolution image refinement.
Problem
L2-based ConvNet regression is sensitive to outliers, which can impair generalization when rare samples or inaccurate annotations occur during training.
Method
The paper uses Tukey’s biweight M-estimator as the ConvNet regression loss and introduces a coarse-to-fine cascade that refines predictions from higher-resolution image regions.
Results
The robust loss yields faster convergence and better generalization than L2, while its combination with the cascade produces comparable or better state-of-the-art results on four public pose datasets.
Takeaways & Limitations
Robust loss optimization and coarse-to-fine ConvNet processing provide an effective approach for regression-based human pose and age estimation.
Takeaways & Limitations
The 95% efficiency setting assumes unit-variance residuals, and refinement can hurt performance when cropped images originate from low-resolution inputs.
Abstract
from arXiv · showhide
Convolutional Neural Networks (ConvNets) have successfully contributed to improve the accuracy of regression-based methods for computer vision tasks such as human pose estimation, landmark localization, and object detection. The network optimization has been usually performed with L2 loss and without considering the impact of outliers on the training process, where an outlier in this context is defined by a sample estimation that lies at an abnormal distance from the other training sample estimations in the objective space. In this work, we propose a regression model with ConvNets that achieves robustness to such outliers by minimizing Tukey's biweight function, an M-estimator robust to outliers, as the loss function for the ConvNet. In addition to the robust loss, we introduce a coarse-to-fine model, which processes input images of progressively higher resolutions for improving the accuracy of the regressed values. In our experiments, we demonstrate faster convergence and better generalization of our robust loss function for the tasks of human pose estimation and age estimation from face images. We also show that the combination of the robust loss function with the coarse-to-fine model produces comparable or better results than current state-of-the-art approaches in four publicly available human pose estimation datasets.
1. Introduction
ConvNet regression commonly uses L2 loss, which is sensitive to outliers. The paper proposes Tukey’s biweight loss and a coarse-to-fine model to improve robustness, convergence, and regression accuracy.
- ConvNets are widely used for regression tasks including pose estimation, object detection, facial landmark detection, and depth prediction.
- L2 loss is sensitive to outliers, including rare poses, unlikely facial point positions, and imprecisely annotated samples.Such outliers can produce poor generalization when present during training.
- The paper proposes Tukey’s biweight function as a robust ConvNet regression loss that downweights samples with unusually large errors without a hard inlier–outlier threshold.The estimator integrates sample weighting and loss minimization in one function.
- The proposed evaluation covers 2D human pose estimation and age estimation from face images, using four public human-pose datasets and one age-estimation dataset.
- The coarse-to-fine model first estimates all outputs, then refines subsets from higher-resolution image regions extracted using the first-stage results.The design targets improved accuracy of localized body skeletons and other regressed values.
- The authors report faster convergence and better generalization than L2, while the combined robust-loss and cascade model matches or exceeds state-of-the-art results on four pose datasets.
2. Related Work
Prior ConvNet regression methods generally rely on L2-based objectives or auxiliary objectives rather than directly robust losses. This work introduces Tukey’s biweight optimization for ConvNet regression and combines it with a cascade-based holistic pose model.
- Regression-based deep learning: Regression-based deep learning predicts interdependent continuous values such as bounding-box coordinates, body-joint positions, and facial-point locations.
- Regression-based deep learning: Existing ConvNet regression approaches commonly train with L2 loss, while some combine L2 with softmax, segmentation, action-detection, or other objective terms.
- Regression-based deep learning: Prior work sought L2 robustness through complex objectives or multiple L2 losses, but did not directly use a robust loss function to handle outliers during deep-network training.
- Human pose estimation: Holistic pose estimation maps image features directly to body poses and has been revisited with ConvNets after historically producing less competitive results than part-based models.
- Human pose estimation: The paper’s holistic approach is close to the cascade of ConvNets from Toshev et al., but replaces its L2 objective with Tukey’s biweight loss.
3. Robust Deep Regression
The paper trains ConvNet regressors with Tukey’s biweight loss to reduce outlier influence, and adds a coarse-to-fine cascade that refines outputs from higher-resolution regions.
- Robust loss: Tukey’s biweight function is used as the ConvNet loss to make regression training robust to outliers.The loss downweights samples with unusually large residuals during training.
- Convolutional Neural Network Architecture: The base architecture contains five convolutional layers followed by two fully connected layers and a regression output.The implementation uses smaller kernels and fewer filters than the cited classification-oriented architecture, with dropout to prevent overfitting.
- Robust loss: L2 loss can let large-residual outliers dominate backpropagation because their gradients have high magnitude.This may adapt the ConvNet to outliers while deteriorating performance for inliers.
- Robust loss: Tukey’s biweight suppresses outlier influence by reducing their gradient magnitude close to zero without requiring a hard residual threshold.The loss instead uses a tuning constant to control suppression of large residuals.
- Robust loss: MAD scales residuals and fixes the tuning constant, making the resulting Tukey loss free of parameters.The paper notes that c = 4.6851 gives approximately 95% asymptotic efficiency as L2 under standard-normal residuals, assuming unit variance.
- Coarse-to-fine model: The coarse-to-fine model first predicts all outputs, then uses higher-resolution cropped regions and separate ConvNets to refine output subsets.Regions and subsets are task-specific; for human pose estimation they can follow body anatomy.
4. Experiments
The experiments evaluate Tukey’s biweight loss against L2 loss for pose and age estimation, then assess a ConvNet cascade against related methods across four pose datasets. Results generally favor refinement with the cascade, though low-resolution Volleyball images produce a negative refinement effect.
- Experimental setup: The evaluation uses four pose datasets—PARSE, LSP, Football, and Volleyball—plus apparent age estimation, with convergence, generalization, and PCP or MAE comparisons.Pose experiments use mean pixel error and strict or loose PCP scores; age experiments compare MAE in years.
- Comparison with other methods: On PARSE, the single-ConvNet full-body score is 68.5%, improving by around 5% with the cascade and achieving the best full-body result.The method also achieves the best score for most body parts.
- Comparison with other methods: On LSP, cascade refinement raises the full-body PCP score from 63.9% to 68.8%, while using four ConvNets versus 29 in the compared method.The paper reports that Tukey’s biweight loss performs better in combination with the cascade than the compared L2-based cascade.
- Comparison with other methods: On Football, one ConvNet reaches a PCP score of 95.8%, leaving less numerical room for cascade improvement despite effective refinements in the examples.The refinement is demonstrated visually in Figures 7 and 8.
- Comparison with other methods: On Volleyball, one ConvNet reaches a PCP score of 81.7%, but refinement negatively affects results because cropped-image interpolation is attributed to the original images’ low resolution.The Volleyball evaluation uses the loose PCP score.
5. Conclusion
The paper introduces Tukey’s biweight loss for robust ConvNet regression and evaluates it with 2D human pose estimation and age estimation. Combined with a ConvNet cascade, the approach achieves comparable or better results than state-of-the-art methods on four public pose datasets.
- Tukey’s biweight loss was introduced for robust optimization of ConvNets in regression-based problems.
- The method was evaluated using 2D human pose estimation and age estimation from face images.
- The robust loss produced faster convergence and better generalization than standard L2 loss.
- Combining the robust loss with a cascade of ConvNets produced comparable or better results than state-of-the-art methods on four public human pose estimation datasets.