Optimal Observability and Maximal Cardinality

Abstract: Uses the good features for SLAM concept to propose a deterministic process for inlier estimation that matches RANSAC performance while having a more consistent time cost relative to RANSAC.
Measurement selection and outlier rejection use feature condition scoring and hypothesis testing. The outcomes suggest that randomized methods can be superceded by bounded or fixed time-cost deterministic methods based on feature point scoring.

Motivation and Background

Methods to address robustness and time-cost of filter-based, indirect SLAM tended to be at odds, whereby improving one would compromise the other. As a case in point, robustness using randomized model fitting in the form of RANSAC-based methods increases the computational cost and variance through repeated model fitting tests. The number of model estimation and fitting iterations is unknown since RANSAC uses data-driven termination condition. Bounding the iterations will bound the runtime, but without the same robusness guarantees as meeting the termination condition. We were interested in exploring whether good features observability scoring could be used to not only prioritize the points to test, but to provide a deterministic selection process with a fixed set of tests for better runtime properties.

OOMC Approach

Our earlier work on good features suggested that an alternative scheme to RANSAC could be used to perform outlier rejection within a model fitting framework. The key result was related to the observability analysis, which found that three features tracked over two frames provided sufficient information to render the system observable. This property is known by the computer vision community in the static context, as it is the number of measurements needed when seeking to solve camera displacement with known measured and associated world points). If we could establish a fast mechanism to generate many tracked triplets with good observability scores, then these triplets would serve as the model fitting elements of the sampling process of RANSAC. If the mechanism was deterministic, then the randomized nature could be removed without loss of performance (given that the triplets have better estimation properties than randomly selected points). The resulting publication was the ICRA 2015 paper “Optimally Observable and Minimal Cardinality Monocular SLAM” ¹.

Post-Facto

Our intent behind good features was to show that (1) using the conditioning to actively manage the estimation process has value, and (2) the concept was extensible and flexible regarding existing SLAM solutions. Since a theoretical proof is not on the horizon, both of these assertions require proof by overwhelming evidence, in that the bruden of proof is on us to demonstrate the value and the flexibility. As a step in that direction, a similar concept was applied to the bundle-adjustment based SLAM method known as ORB-SLAM. After feature matching, the BA optimization conditioning of feature points was tested to identify the most robust set for camera pose estimation. Again, the aim was to improve the pose estimation error by identifying the best set of feature points to use in the local pose optimization step. Unlike outlier rejection methods, we consider the technique to be an inlier selection method. More details can be found here