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<p>Localization of two-dimensional (2D) points in heatmap-based methods is hindered by the Maximal Value Drift (MVD) problem. This issue arises because the Mean Squared Error (MSE) loss function provides insufficient distinction between the pixel with the maximum value and other pixels in the heatmap. State-of-the-art (SOTA) methods address this challenge by approximating the non-differentiable maximum operation with the expectation of the maximum value. However, such methods are biased estimators. Our key insight is that preserving the relative order of heatmap values plays a crucial role in mitigating MVD. In this paper, we propose a differentiable training method, termed Progressive Order-Preserving Regularization (POPR), which encourages the relative order of heatmap values. Specifically, POPR adopts a progressive weight training strategy that gradually introduces local order constraints throughout training, thereby guiding the network to learn from coarse to fine. As a simple yet effective method, POPR can be seamlessly integrated into existing heatmap-based frameworks. Extensive experiments on several challenging benchmark datasets (e.g., face landmark detection and human pose estimation) demonstrate the efficacy of the proposed method. The results show that the precise heatmap predictions enabled by POPR improve the accuracy of keypoint coordinate regression, a critical factor for high-performance 2D keypoint localization tasks. The code is publicly available at <a href="https://github.com/pangjunbiao/POPR">https://github.com/pangjunbiao/POPR</a>.</p>

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Handling maximal value drift in heatmap-based point localization via progressive order-preserving regularization

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Zhen Huang,
  • Jiaxin Deng,
  • Zailin Dong,
  • Junbiao Pang

摘要

Localization of two-dimensional (2D) points in heatmap-based methods is hindered by the Maximal Value Drift (MVD) problem. This issue arises because the Mean Squared Error (MSE) loss function provides insufficient distinction between the pixel with the maximum value and other pixels in the heatmap. State-of-the-art (SOTA) methods address this challenge by approximating the non-differentiable maximum operation with the expectation of the maximum value. However, such methods are biased estimators. Our key insight is that preserving the relative order of heatmap values plays a crucial role in mitigating MVD. In this paper, we propose a differentiable training method, termed Progressive Order-Preserving Regularization (POPR), which encourages the relative order of heatmap values. Specifically, POPR adopts a progressive weight training strategy that gradually introduces local order constraints throughout training, thereby guiding the network to learn from coarse to fine. As a simple yet effective method, POPR can be seamlessly integrated into existing heatmap-based frameworks. Extensive experiments on several challenging benchmark datasets (e.g., face landmark detection and human pose estimation) demonstrate the efficacy of the proposed method. The results show that the precise heatmap predictions enabled by POPR improve the accuracy of keypoint coordinate regression, a critical factor for high-performance 2D keypoint localization tasks. The code is publicly available at https://github.com/pangjunbiao/POPR.