Abstract

Due to the introduction of the shape parameter, generalized Gaussian has better modelling capabilities than the Gaussian distribution. Therefore it is broadly used in various fields. Based on this, we established a statistical framework for the data-weighted multivariate generalized Gaussian mixture model (WMGGMM). By extending the traditional EM algorithm, we obtain the model parameters in non-closed forms and then apply an iterative method employing the fixed point equation to get the values of the components' mean and covariance. The Newton-Raphson approach is used to update the shape parameters. The complexity of the model is automatically determined by the minimum message length (MML) criterion. This thesis implements the proposed framework to two challenging tasks: point clouds registration and single-target visual tracking. The data weighting approach considers different techniques depending on the specific application's needs. In the first application, we adopt k-nearest neighbours to supply greater weight to points with high density, highlighting the main structure of the entity point cloud object while reducing noise. In the second application, the distance significance is based on the spatial kernel, which means pixels closer to the center of the target candidate ellipse have more contributions.

In the first application, WMGGMMs describe the target point cloud and the point cloud to be registered. Then the KL divergence between these two models will be used as the loss function for the stochastic optimization to obtain the best transformation model parameters, decreasing the probability of falling into a local optimum. The self-built point cloud is utilized to evaluate the performance of the algorithm on rigid registration. The results show that the algorithm significantly reduces the influence of outliers, enhances the robustness and accuracy of the algorithm, and effectively extracts the critical features of the object. In the second application, the preprocessing step of colour compression (image segmentation) improves the adaptability of the generalized Gaussian mixture model to the data while preserving the original image information as much as possible. According to the ratio of each pixel's responsiveness to the target and background model, segmentation weights of the pixels are obtained to guide the location and size update of the target. The performance of the proposed approach is experimentally verified on a public dataset and compared with other algorithms.