Motion segmentation is part of the computer vision field and aims to find the moving parts in a video sequence. It is used in applications such as autonomous driving, surveillance, robotics, human motion analysis, and video indexing. Since there are so many applications, motion segmentation is ill-defined and the research field is vast. Despite the advances in the research over the years, the existing methods are still far behind human capabilities. Problems such as changes in illumination, camera motion, noise, mixtures of motion, missing data, and occlusion remain challenges. Feature-based approaches have grown in popularity over the years, especially manifold clustering methods due to their strong mathematical foundation. Methods exploiting sparse and low-rank representations are often used since the dimensionality of the data is reduced while useful information regarding the motion segments is extracted. However, these methods are unable to effectively handle large and complete occlusions as well as missing data since they tend to fail when the amount of missing data becomes too large. An algorithm based on Sparse Subspace Clustering (SSC) has been proposed to address the issue of occlusions and missing data so that SSC can handle these cases with high accuracy. A frame-to-frame analysis was adopted as a pre-processing step to identify motion segments between consecutive frames, called inter-frame motion segments. The pre-processing step is called Multiple Split-And-Merge (MSAM), which is based on the classic top-down split-and-merge algorithm. Only points present in both frame pairs are segmented. This means that a point undergoing an occlusion is only assigned to a motion class when it has been visible for two consecutive frames after re-entering the camera view. Once all the inter-frame segments have been extracted, the results are combined in a single matrix and used as the input for the classic SSC algorithm. Therefore, SSC segments inter-frame motion segments rather than point trajectories. The resulting algorithm is referred to as MSAM-SSC. MSAM-SSC outperformed some of the most popular manifold clustering methods on the Hopkins155 and KT3DMoSeg datasets. It was also able to handle complete occlusions and 50% missing data sequences, as well as outliers. The algorithm can handle mixtures of motions and different numbers of motions. However, it was found that MSAM-SSC is more suited for traffic and articulate motion scenes which are often used in applications such as robotics, surveillance, and autonomous driving. For future work, the algorithm can be optimised to reduce the execution time so that it can be used for real-time applications. Additionally, the number of moving objects in the scene can be estimated to obtain a method that does not rely on prior knowledge. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2021. / CSIR / Electrical, Electronic and Computer Engineering / MEng (Computer Engineering) / Unrestricted

En aquesta tesi s’estudia el problema de la segmentació del moviment. La tesi presenta una revisió dels principals algoritmes de segmentació del moviment, s’analitzen les característiques principals i es proposa una classificació de les tècniques més recents i importants. La segmentació es pot entendre com un problema d’agrupament d’espais (manifold clustering). Aquest estudi aborda alguns dels reptes més difícils de la segmentació de moviment a través l’agrupament d’espais. S’han proposat nous algoritmes per a l’estimació del rang de la matriu de trajectòries, s’ha presenta una mesura de similitud entre subespais, s’han abordat problemes relacionats amb el comportament dels angles canònics i s’ha desenvolupat una eina genèrica per estimar quants moviments apareixen en una seqüència. L´ultima part de l’estudi es dedica a la correcció de l’estimació inicial d’una segmentació. Aquesta correcció es du a terme ajuntant els problemes de la segmentació del moviment i de l’estructura a partir del moviment. / IN THIS STUDY THE PROBLEM OF MOTION SEGMENTATION IS DISCUSSED. MOTION SEGMENTATION STATE OF THE ART IS PRESENTED, THE MAIN FEATURES OF MOTION SEGMENTATION ALGORITHMS ARE ANALYSED, AND A CLASSIFICATION OF THE RECENT AND MOST IMPORTANT TECHNIQUES IS PROPOSED. THE SEGMENTATION PROBLEM COULD BE CAST INTO A MANIFOLD CLUSTERING PROBLEM. IN THIS STUDY SOME OF THE MOST CHALLENGING ISSUES RELATED TO MOTION SEGMENTATION VIA MANIFOLD CLUSTERING ARE TACKLED. NEW ALGORITHMS FOR THE RANK ESTIMATION OF THE TRAJECTORY MATRIX ARE PROPOSED. A MEASURE OF SIMILARITY BETWEEN SUBSPACES IS PRESENTED. THE BEHAVIOUR OF PRINCIPAL ANGLES IS DISCUSSED. A GENERIC TOOL FOR THE ESTIMATION OF THE NUMBER OF MOTIONS IS DEVELOPED. THE LAST PART OF THE STUDY IS DEDICATED TO THE DEVELOPMENT OF AN ALGORITHM FOR THE CORRECTION OF AN INITIAL MOTION SEGMENTATION SOLUTION. SUCH A CORRECTION IS ACHIEVED BY BRINGING TOGETHER THE PROBLEMS OF MOTION SEGMENTATION AND STRUCTURE FROM MOTION.