Selecting or Ranking: Point Localization With Order-Preserving Regularization

The heatmap-based methods for determining key-point positions face the problem of maximal value drift. The expectation of error or error of expectation attempts to address this issue by converting the non-differentiable max operation into a differentiable one. However, they still encounter the challenge of estimating the underlying distribution. In this paper, we address the problem by directly preserving the order of values rather than complexly estimating the underlying distribution. Concretely, the proposed order-preserving constraint (OPC) is a differentiable training method that imposes implicit constraints on the order of the probability map. The proposed unconventional OPC is simple, yet by approximating the nature of the max operation, our approach outperforms traditional methods which involve careful design and complex steps. Furthermore, we show that OPC can seamlessly replace the conventional soft-argmax operation on various localization tasks. Comprehensive experiments have demonstrated the effectiveness and flexibility of this method in the field of pose estimation.