We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given category (e.g. a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e. different car models have different shapes). We consider an active shape model, where -- for an object category -- we are given a library of potential CAD models describing objects in that category, and we adopt a standard formulation where pose and shape estimation are formulated as a non-convex optimization. Our first contribution is to provide the first certifiably optimal solver for pose and shape estimation. In particular, we show that rotation estimation can be decoupled from the estimation of the object translation and shape, and we demonstrate that (i) the optimal object rotation can be computed via a tight (small-size) semidefinite relaxation, and (ii) the translation and shape parameters can be computed in closed-form given the rotation. Our second contribution is to add an outlier rejection layer to our solver, hence making it robust to a large number of misdetections. Towards this goal, we wrap our optimal solver in a robust estimation scheme based on graduated non-convexity. To further enhance robustness to outliers, we also develop the first graph-theoretic formulation to prune outliers in category-level perception, which removes outliers via convex hull and maximum clique computations; the resulting approach is robust to 70%-90% outliers. Our third contribution is an extensive experimental evaluation. Besides providing an ablation study on a simulated dataset and on the PASCAL3D+ dataset, we combine our solver with a deep-learned keypoint detector, and show that the resulting approach improves over the state of the art in vehicle pose estimation in the ApolloScape datasets.

翻译：本文研究类别级感知问题：给定描绘某类别（如汽车）物体的三维传感器数据，需在类内变异（即不同汽车模型具有不同形状）条件下重建物体位姿与形状。我们采用主动形状模型——针对物体类别，提供描述该类物体的潜在CAD模型库，并采用将位姿与形状估计构造为非凸优化的标准范式。本文首要贡献是首次提出可认证最优的位姿与形状求解器。具体而言，我们证明旋转估计可与物体平移及形状估计解耦，并论证：(i) 最优物体旋转可通过紧致（小规模）半定松弛计算获得，(ii) 平移与形状参数可在已知旋转时以闭式解形式计算。第二项贡献是为求解器添加异常值剔除层，使其对大量误检测具有鲁棒性。为此，我们基于渐进非凸性将最优求解器包裹在鲁棒估计框架中。为进一步强化对异常值的鲁棒性，我们还提出首个用于类别级感知的图论异常值剪枝方法，通过凸包与最大团计算剔除异常值；所得方法可容忍70%-90%的异常值。第三项贡献是开展广泛实验评估。除在模拟数据集及PASCAL3D+数据集上进行消融研究外，我们将求解器与深度学习关键点检测器结合，实验表明该方法在ApolloScape数据集的车辆位姿估计中显著优于当前最优技术。