Dimensionality reduction with subpixel refinement for SLAM

A simultaneous localisation and mapping (SLAM) system continuously explores the environment to causally estimate the ego-motion of a robot and map the environment. Visual SLAM using a single video camera is particularly challenging. Although visual SLAM allows incorporating thousands of features into the system to improve the accuracy, this gain comes with a computational overhead. This thesis advances the state of the art in visual SLAM in terms of efficiency, accuracy and robustness. First, a sub-pixel refinement algorithm is presented to permit efficient pose estimation in monocular SLAM. The algorithm extends spatial domain Gauss-Newton parameter estimation into the frequency domain. Then corresponding features are sub-pixel refined by estimating the affine parameters between the two surrounding patches. Here, the correct frequency range is selected by identifying a direct relationship between the Gabor phase response and the frequency response of a Gaussian multiplied image patch. Further it is shown how parameter estimation can be made more accurate by operating in the frequency domain, which naturally gives rise to a multi-resolution optimisation framework. Next, a novel method is proposed to handle the dimensionality of the SLAM problem which permits the handling of a large number of parameters. The proposed method dramatically reduces the computational complexity of the Kalman-filters by reducing the dimensionality as information is acquired. The validity of the method is proved by applying it to monocular SLAM, where there are a large number of dimensions in the filter that are not subject to process noise (the landmark locations). This has the effect of reducing the cost of running a filter or allowing a single filter to process a much larger set of landmarks. Then, the dimensionality reduction is extended into a relative formulation, which is extensible into a large-scale system. The formulation uses the higher degree of linearity available with the relative formulation to build a Kalman-filter based reduced SLAM system. An un-delayed method for adding features to the filter is also introduced. Then the effect of the number of features used in the system on the final estimation uncertainty is analyzed, and it is shown that the actual number of dimensions that has to be optimised is far less than the number of original dimensions in the problem. Finally, we introduce a novel method to retrieve the pose estimation Jacobian on limited platforms through an efficient partitioning of the matrix, which removes the Jacobian computation overhead. Instead of recalculating the Jacobian every time, we show how it can be precalculated and saved for later retrieval.