## Dimensionality reduction with subpixel refinement for SLAM

thesis

posted on 02.03.2017 by Gamage, Dinesh Srikantha#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

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.