Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation. We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art

Biologically inspired goal directed navigation for mobile robots

This project involved an investigation into low-cost navigation of mobile robots with the aim of creating and adaptive navigation system inspired by behaviour seen in animals. The navigation module developed here would need to be able to successfully localise a robot and navigate it to a defined target. A critical literature review was carried out of current localisation and path-planning architectures and a bio-inspired approach using an Echo State Network and Liquid State Machine architecture was chosen as the base for the navigation modules. The navigation module implemented in this work is trained to navigate and localise itself in different environments drawing its inspiration from the behaviour of small rodents. These architectures were adapted for use by a robot with a view on the physical implementation of these architectures on an embedded low-cost robot using a Raspberry Pi computer. This robot was then built using low-cost, noisy proximity sensors which formed the inputs to the navigation modules. Before the deployment on the embedded robot the system was tested and validated in a full physics simulator. While the training of the Echo State Networks and Liquid State Machine has been carried out in the literature by the offline method of linear regression, in this work we introduce a novel way of training these networks that is online using concepts from adaptive filters. This online method increases the adaptability of this system while significantly decreasing its memory requirements making it very attractive for low-cost embedded robots. The end result from the project was a functioning navigation module using an Echo State Network that was able to navigate the robot to a target position as well as learn new paths, either using offline or online methods. The results showed that the Echo State Network approach was valid both in simulation and practically as a base for creating navigation modules for low-cost robots and could also lead to more efficient and adaptable robots being developed if the training was carried out in an online manner. The increased computational complexity of implementing the liquid State machine on analytical machines however made it unsuitable for deployment on robots using embedded micro-controllers

CORAL: Fast, parallel multi model fitting with applications to mapping, perception and scene reconstruction and understanding

Geometry plays an important role in our understanding of the world with its uses spanning multiple fields from astronomy and art to more contemporary fields such as computer vision and robotics. However, as geometry is seldom directly observed the fitting of geometric models becomes a crucial task in these fields. This is however not trivial: as data must be clustered according to the parameters of geometric models that must also be estimated, creating a chicken and egg problem. In addition, most data in practice originates from multiple models, whose numbers are also unknown, and contain noise and clutter which makes geometric multi-model fitting more challenging. In this thesis we present a framework capable of swiftly and accurately fitting multiple geometric models to data contaminated with noise and clutter. Unlike previous greedy approaches this framework efficiently searches for a soft assignment of points to models by minimising a global energy that considers the joint classification of data points to geometric models. Additionally, the energy minimisation is performed through a COnvex Relaxation ALgorithm (CORAL) that unlike other combinatorial approaches can be efficiently parallelised which leads to an energy minimisation that is significantly faster, as the resolution of data increases, while still performing as well or better than the state-of-the-art when evaluated. While geometry and subsequently this CORAL formulation are not restricted to a single field, in this thesis we are particularly interested in how they can be used to improve various systems in contemporary robotics. We investigate this firstly through mapping wherein geometric models are incorporated to improve, in real-time, dense depth map estimation from cameras in regions where there is little texture. We see that when these improved depth maps are fused there is significantly more coverage (10%) as compared to the state-of-the-art over large-scales. Following this we demonstrate how in tandem with deep learning networks understanding of the road for autonomous vehicles can be improved. In this way, the human-effort needed to obtain training data for deep networks can be reduced while still retrieving qualitatively accurate results as seen in road markings and boundary classification. Finally we present a uniform formulation that encodes relationships between different geometric models. We show that by leveraging this formulation in sparse reconstructions of both indoor and outdoor environments with low-cost LiDAR platforms, we can obtain reconstructions that are as accurate, within the laser noise (0.03m), as professional high-fidelity surveys.</p

CORAL: Fast, parallel multi model fitting with applications to mapping, perception and scene reconstruction and understanding

Geometry plays an important role in our understanding of the world with its uses spanning multiple fields from astronomy and art to more contemporary fields such as computer vision and robotics. However, as geometry is seldom directly observed the fitting of geometric models becomes a crucial task in these fields. This is however not trivial: as data must be clustered according to the parameters of geometric models that must also be estimated, creating a chicken and egg problem. In addition, most data in practice originates from multiple models, whose numbers are also unknown, and contain noise and clutter which makes geometric multi-model fitting more challenging. In this thesis we present a framework capable of swiftly and accurately fitting multiple geometric models to data contaminated with noise and clutter. Unlike previous greedy approaches this framework efficiently searches for a soft assignment of points to models by minimising a global energy that considers the joint classification of data points to geometric models. Additionally, the energy minimisation is performed through a COnvex Relaxation ALgorithm (CORAL) that unlike other combinatorial approaches can be efficiently parallelised which leads to an energy minimisation that is significantly faster, as the resolution of data increases, while still performing as well or better than the state-of-the-art when evaluated. While geometry and subsequently this CORAL formulation are not restricted to a single field, in this thesis we are particularly interested in how they can be used to improve various systems in contemporary robotics. We investigate this firstly through mapping wherein geometric models are incorporated to improve, in real-time, dense depth map estimation from cameras in regions where there is little texture. We see that when these improved depth maps are fused there is significantly more coverage (10%) as compared to the state-of-the-art over large-scales. Following this we demonstrate how in tandem with deep learning networks understanding of the road for autonomous vehicles can be improved. In this way, the human-effort needed to obtain training data for deep networks can be reduced while still retrieving qualitatively accurate results as seen in road markings and boundary classification. Finally we present a uniform formulation that encodes relationships between different geometric models. We show that by leveraging this formulation in sparse reconstructions of both indoor and outdoor environments with low-cost LiDAR platforms, we can obtain reconstructions that are as accurate, within the laser noise (0.03m), as professional high-fidelity surveys.</p