We consider a certifiable object pose estimation problem, where -- given a partial point cloud of an object -- the goal is to not only estimate the object pose, but also to provide a certificate of correctness for the resulting estimate. Our first contribution is a general theory of certification for end-to-end perception models. In particular, we introduce the notion of $\zeta$-correctness, which bounds the distance between an estimate and the ground truth. We show that $\zeta$-correctness can be assessed by implementing two certificates: (i) a certificate of observable correctness, that asserts if the model output is consistent with the input data and prior information, (ii) a certificate of non-degeneracy, that asserts whether the input data is sufficient to compute a unique estimate. Our second contribution is to apply this theory and design a new learning-based certifiable pose estimator. We propose C-3PO, a semantic-keypoint-based pose estimation model, augmented with the two certificates, to solve the certifiable pose estimation problem. C-3PO also includes a keypoint corrector, implemented as a differentiable optimization layer, that can correct large detection errors (e.g. due to the sim-to-real gap). Our third contribution is a novel self-supervised training approach that uses our certificate of observable correctness to provide the supervisory signal to C-3PO during training. In it, the model trains only on the observably correct input-output pairs, in each training iteration. As training progresses, we see that the observably correct input-output pairs grow, eventually reaching near 100% in many cases. Our experiments show that (i) standard semantic-keypoint-based methods outperform more recent alternatives, (ii) C-3PO further improves performance and significantly outperforms all the baselines, and (iii) C-3PO's certificates are able to discern correct pose estimates.

翻译：我们研究可认证的物体姿态估计问题——给定物体的部分点云，目标不仅是估计物体姿态，还要为所得到的估计结果提供正确性认证。我们的第一个贡献是端到端感知模型认证的通用理论。具体而言，我们引入了ζ-正确性概念，它约束了估计值与真实值之间的距离。我们证明ζ-正确性可通过实施两类认证进行评估：(i)可观测正确性认证，用于断言模型输出是否与输入数据和先验信息一致；(ii)非退化性认证，用于断言输入数据是否足以计算唯一估计值。我们的第二个贡献是将该理论应用于实践，设计了一种新型基于学习的可认证姿态估计器。我们提出C-3PO——一种基于语义关键点的姿态估计模型，通过增加上述两种认证来解决可认证姿态估计问题。C-3PO还包含一个可微优化层实现的关键点校正器，能够纠正较大的检测误差（例如由模拟-现实差距导致）。我们的第三个贡献是一种新型自监督训练方法，该方法在训练过程中使用可观测正确性认证为C-3PO提供监督信号。在这种方法中，模型每次训练迭代仅使用可观测正确的输入-输出对进行训练。随着训练进行，可观测正确的输入-输出对逐渐增加，在许多情况下最终接近100%。实验表明：(i)标准基于语义关键点的方法优于近期替代方案；(ii)C-3PO进一步提升了性能，显著优于所有基线方法；(iii)C-3PO的认证能够有效甄别正确的姿态估计。