Graph-Theoretic Outlier Rejection: From Instance to Category-Level Perception

Abstract

In this thesis, we study the problem of outlier pruning for robust estimation. Robust estimation is the workhorse for many perception problems, from object pose estimation to robot localization and mapping. In these problems, the robot has to estimate quantities of interest in the face of outliers. Such outliers can be the result of incorrect data association, and it is not unusual to have problems where more than 90% of the input measurements are outliers.

Our first contribution is ROBIN (Reject Outliers Based on INvariants), a graphtheoretic approach that employs invariance to find mutually compatible measurements and prune outliers. ROBIN captures the mutual compatibility information by modeling measurements as vertices and mutual compatibility as edges in a compatibility graph. We generalize existing results showing that the inliers form a clique in this graph and typically belong to the maximum clique. We also provide a general definition of invariance for noisy measurements. We test ROBIN in various instance-level perception problems such as single rotation averaging and 3D point cloud registration. ROBIN boosts robustness of existing solvers (making them robust to more than 95% outliers), while running in milliseconds in large problems.

With ROBIN developed, we then 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). To solve this problem, we develop the first certifiably optimal solver for pose and shape estimation. We demonstrate that ROBIN can also be applied in this scenario, using compatibility checks based on convex hulls. We evaluate our approach through extensive experiments on both simulated and real datasets (PASCAL3D+ and ApolloScape), demonstrating that the resulting approach improves over the state of the art.