Robust estimation in computer vision: optimisation methods and applications.

Robust parameter estimation is an important area in computer vision that underpins many practical applications. Typically, the task is to estimate a generic model from unstructured observations, where the model and observed data may vary depending on the specific applications. In most cases, computer vision data inherently contains noisy measurements, multiple instances (structures) of a model, and outliers (i.e., points that do not belong to any structures). Unfortunately, standard techniques such as Least Squares (LS), Least Median Squares (LMS) are not robust to such kind of data. Over the past decades, much research effort in computer vision has been devoted to proposing more robust and efficient estimators. Among those, the estimators based on global optimisation have attracted considerable attention and increasingly showed promising results. However these optimisation based methods still are faced with a number of issues. First, for tractability these robust techniques optimise robust objective functions over a collection of randomly sampled hypotheses using combinatorial methods. The trouble is that the adequacy of the hypothesis set could not be asserted prior to the optimisation, so the overall estimation could be misleading. In addition, the process of randomly sampling the hypothesis set is very time-consuming, especially for high-order models and complex data, thus generally decreasing the fitting efficiency. Moreover, to ease the optimisation, outliers are often assumed to distribute uniformly in the data space, and measurement noise is assumed to approximately follow a Gaussian distribution. Unfortunately, such assumptions are not always valid in practice. The research conducted in this thesis follows the global optimisation approach, and makes three distinct contributions to the robust estimation field. First, we propose a novel fitting approach that simultaneously samples hypotheses and optimises the robust objective functions, such that the under- or over- hypothesis sampling issue can be avoided. In effect, our fitting approach can effectively minimise the wastage of the hypothesis sampling and objective optimisation. The second contribution is an unconventional sampling method based on Random Cluster Model (RCM) for rapidly generating accurate hypotheses. The RCM sampling method is effectively integrated into a continuous sampling-and-fitting framework to provide the superior fitting efficiency. Finally, the thesis offers a new robust estimation framework which seamlessly considers high-level geometric priors during the parameter estimation to enhance the robustness against non-uniform outliers and non-Gaussian noise. We validate the performance of the robust methods presented in this thesis on various computer vision applications ranging from estimating motions, planar homographies in image sequences to detecting geometric objects in images and 3D point clouds.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201