Cell migration and cell division are two key processes that are associated with a wide range of biological phenomena including embryogenesis, inflammation, wound healing, tumour development etc. The study of these cellular processes has received a substantial interest from the cell and molecular scientists since the understanding of the mechanisms that stimulate and control these dynamic events has important practical implications. With the advent of modern microscopy imaging modalities the amount of information required to be analysed by the clinical experts has substantially increased and the development of computer-based automatic techniques that are able to robustly track cells in large image sequences is currently one of the most active topics of research. While cellular migration is the major source of information in describing biological processes, recent studies emphasised the growing importance of cell mitosis, as this information can be directly used in the estimation of the cell cycle and in the understanding of complex biological mechanisms. Due to the increasing clinical interest in the automatic analysis of cellular data, a substantial number of studies have been recently reported in the field of cellular imaging and in the development of robust solutions that are able to identify the cell mitosis. Following a detailed analysis of published works in the field of cellular tracking, it can be concluded that the development of automated tracking strategies proved extremely challenging due to several factors such as changes in cell morphology over time, random motion, cell division, cell interaction and low signal to noise ratio. To answer these challenges in a robust manner, several approaches have been advanced where the key task was the cellular association. In this regard, the major directions of research explored cellular tracking techniques where the cellular association was implemented using either segmentation or model-driven strategies. The methods included in the former category attempt to identify the cells in each frame of the sequence and then they are later associated by employing rules that enforce the continuity of the tracking process in the spatio-temporal domain. For these approaches the cellular association process proved particularly challenging when the cells undergo shape deformation over time and their motility is generally described by random motion patterns. To adapt to these challenges, alternative approaches where parametric or non-parametric representations that sample the cells morphologies and their intensity patterns were employed to identify the corresponding cells in consecutive frames of the sequence. These methods offer the advantage that they do not entail the segmentation of the cells in each frame, but they were also problematic in the presence of cell mitosis and cell interaction - a situation when they are likely to be either trapped in local minima or to return incorrect cell associations. A distinct category of model-driven cellular tracking techniques applied motion prediction to guide the cellular association process, but practice has indicated that the simplistic inclusion of the motion estimators in the tracking process proved troublesome since the resulting tracking strategies are not able to sample in a coherent manner the modes of motion that encompass the cell migration. In the vast majority of the published works on cell tracking, the cellular division has been approached during cellular association and often their application was restricted to particular cellular data types. The major objective of this thesis is to introduce a novel framework that is able to address the theoretical and practical challenges associated with the cell tracking and cell division (mitosis) detection in dense time-lapse image sequences. To this end, a multi-phase adaptive algorithm was developed where the cell association is carried out by evaluating the topology of the local cell structures in consecutive frames of the sequences. To allow for a detailed evaluation of the local cellular structures, the connectivity rules between the neighbouring cells are encoded using Delaunay triangulation. A particular challenge associated with phase-contrast cellular datasets is associated with the large intensity contrast variation and the relative high level of noise that is present in the image data, and the robust identification of the cells throughout the sequence proved problematic. To compensate for the inconsistent inter-frame cell segmentations, in the proposed framework, a novel approach based on the evaluation of the topology changes in the local cellular structures was developed, with substantial benefits in relation to overall tracking accuracy. The last component of the proposed algorithm addresses the mitosis detection using a backward tracking analysis that integrates the local cellular structures with a pattern matching algorithm for the identification of the mitotic cells that were missed in the forward tracking phase of the algorithm. While the major contributions that emerge from this work are associated with the proposed computational framework that has been designed to address cellular tracking and mitosis detection, it would be useful to point out that another contribution resides in the detailed performance analysis of the algorithm. Thus, to comprehensively evaluate the performance of the proposed framework, several challenging time-lapse phase-contrast cell image sequences were used in the experimental study and the results returned by the proposed automatic cell tracking algorithms were compared against the manually annotated data. To further evaluate the performance of the developed method it has also been applied to public available cellular datasets and its performance is compared against those reported by the state-of-the-art cellular tracking and mitosis detection implementations. The experimental results indicate that the proposed method is able to successfully track phasecontrast cells in the presence of random migration and detect the mitosis events, and its performance proved superior to those attained by the state-of-the-art implementations.