GOGMA: Globally-Optimal Gaussian Mixture Alignment

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

Where infrastructure alone is not enough: developing well-functioning non-motorized transport with a focus on cycling in the 'Northern-Inner' district of Cape Town

Post-apartheid Cape Town is characterized largely by a sprawling and inequitable city form. Well-located land within the city tends to be expensive, and as a result the majority of poor residents have to travel long and time-consuming distances to employment opportunities, often spending close to half their monthly income on commuting. Current development patterns largely perpetuate this situation. Whilst non-motorized transport (NMT) often presents as a potentially equitable and efficient form of mobility, the context of long distance commuting coupled with a lack of NMT-specific connected infrastructure within metropolitan Cape Town is not conducive to NMT. The challenges and corresponding Interventions required to enable wellfunctioning NMT within cities broadly, and within the City of Cape Town in particular were explored through a variety of literature drawing on precedent from around the world, a review of NMT-related policy, and interviews with city officials and NGOs involved in promoting NMT. These challenges and interventions were then investigated in a particular context, namely the 'Northern inner' district of Cape Town, whereafter specific interventions were proposed. Key findings regarding the implementation of well-functioning NMT (and cycling in particular) indicate that there are a number of interconnected factors that need to be considered beyond the provision of NMT-specific infrastructure. At the metropolitan level, by developing high-density affordable housing opportunities in well-located areas, more compact environments with increased proximity between origins and destinations can be created. Such environments are far better suited to NMT. This can in turn begin to address the inequitable and inefficient current city form. NMT-specific infrastructure is of course very important in all NMT-enabling development (and particularly for cycling), and as such the equitable provision of NMT-prioritized intersections, paths and lanes in relation to infrastructure for motorized transport are very important. Finally, intermodal linkages between NMT and public transport, crime reduction through strategic placement and design of NMT infrastructure, and promotion of visibility and awareness of the value of NMT through public awareness campaigns constitute broader required interventions to enable well-functioning NMT. Regarding implementation, given the multiple interconnected factors involved in creating well-functioning NMT, it is important that the proposed interventions take place simultaneously, through an integrated inter-departmental approach

Georgetown County Workforce Assessment and Survey

Georgetown County is a county located on the east coast of South Carolina and just like other counties in South Carolina is experiencing workforce issues. These issues are due to a variety of situations including the most obvious occurring situation, the Covid-19 Pandemic. While working in the Georgetown County Chamber of Commerce I have been able to work on creating a workforce survey that would be distributed to many businesses within Georgetown County. By creating and distributing this survey will allow the chamber and myself to receive as much insight as possible into some of the workforce struggles in Georgetown County. This research will not only benefit Georgetown County but to any other counties experiencing the same workforce dynamics by assessing the workforce directly

Robust and Optimal Methods for Geometric Sensor Data Alignment

Geometric sensor data alignment - the problem of finding the rigid transformation that correctly aligns two sets of sensor data without prior knowledge of how the data correspond - is a fundamental task in computer vision and robotics. It is inconvenient then that outliers and non-convexity are inherent to the problem and present significant challenges for alignment algorithms. Outliers are highly prevalent in sets of sensor data, particularly when the sets overlap incompletely. Despite this, many alignment objective functions are not robust to outliers, leading to erroneous alignments. In addition, alignment problems are highly non-convex, a property arising from the objective function and the transformation. While finding a local optimum may not be difficult, finding the global optimum is a hard optimisation problem. These key challenges have not been fully and jointly resolved in the existing literature, and so there is a need for robust and optimal solutions to alignment problems. Hence the objective of this thesis is to develop tractable algorithms for geometric sensor data alignment that are robust to outliers and not susceptible to spurious local optima. This thesis makes several significant contributions to the geometric alignment literature, founded on new insights into robust alignment and the geometry of transformations. Firstly, a novel discriminative sensor data representation is proposed that has better viewpoint invariance than generative models and is time and memory efficient without sacrificing model fidelity. Secondly, a novel local optimisation algorithm is developed for nD-nD geometric alignment under a robust distance measure. It manifests a wider region of convergence and a greater robustness to outliers and sampling artefacts than other local optimisation algorithms. Thirdly, the first optimal solution for 3D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms other geometric alignment algorithms on challenging datasets due to its guaranteed optimality and outlier robustness, and has an efficient parallel implementation. Fourthly, the first optimal solution for 2D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms existing approaches on challenging datasets, reliably finding the global optimum, and has an efficient parallel implementation. Finally, another optimal solution is developed for 2D-3D geometric alignment, using a robust surface alignment measure. Ultimately, robust and optimal methods, such as those in this thesis, are necessary to reliably find accurate solutions to geometric sensor data alignment problems