The first half part of this thesis concerns optic-flow (OF) based motion estimation. Recent advances in OF regularisation approaches have emphasised the three important aspects, exploring new motion-integration strategies, looking for improvements or replacements of existing motion spaces, and investigating more suitable motion-distribution priors (MDPs) that can better fit or describe the statistics of a particular motion space. Motivated by that, two motion regularisation approaches, making up the first core contribution of this thesis, have been proposed. First, an oriented geodesic distance based non-local regularisation approach. At the heart of this approach is a novel pairwise feature-affinity measurement. The new non-local OF approach has been demonstrated particular useful in dealing with two situations: accurately recovering object boundary motion and estimating motion for nearby similar-appearance objects. Experimental results, comparing to leading-edge non-local regularisation schemes, have confirmed the superior performance of the proposed approach. Second, a sparsity&non-sparsity constraint based prior-adaptive regularisation approach, the proposal of which is motivated by that globally fixed MDPs based regularities do not respect local variances of OF statistics. Due to the particular challenge of minimising the involved OF energy functional, a novel Iteratively Reweighted Least Squares (IRLS) and Generalised Cross Validation (GCV) based strategy has also been developed, that can simultaneously optimise the solutions for the flow field as well as the hyperparameter fields involved. Moreover, an exhaustive literature survey on OF regularisation approaches have been provided. This has finally led to a new generalised regularisation formulation, which has been formally clarified, for the first time, in the literature. The second half part of this thesis focuses on the problem of tracking dense cell populations over phase-contrast image sequences. Quantitative analysis on whole populations of cells, and identification of cell division events plays vital roles in the biomedical research domain. Driven by that, the second major contribution in this work is a model and motion based cell tracking framework. A novel strategy that seamlessly integrates the snake and the OF technique is designed, by enforcing a soft coherence constraint between the model and motion based tracking techniques. And, the directional gradient vector flow technique is, for the first time, applied to the segmentation and tracking of dense cell populations. The outstanding advantages of the proposed approach are reflected in the following aspects: accurately segmenting ambiguous cell boundaries, correctly tracking partially overlapped cells, consistently tracking elongated cells, and the efficient tracking of large displacement cells. By testing the proposed approach on challenging real cellular datasets, qualitative and quantitative experimental results have indicated that the proposed approach can achieve superior performance, in comparison with the state-of-the-art cell segmentation and tracking approaches. In addition, a third major contribution of this thesis is the development of a motion-occlusion analysis based, automated cell-division detection approach. Through experimentation on different types of cellular datasets, the proposed approach can successfully detect dividing cells with a variety of division behaviour.