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This paper deals with the spatio-temporal analysis of two-dimensional deformation and motion of cells from time series of digitized video images. A parametric motion approach based on an affine model has been proposed for the quantitative characterization of cellular movements in different experimental areas of cellular biology including spontaneous cell deformation, cell mitosis, individual cell migration and collective migration of cell populations as cell monolayer. The accuracy and robustness of the affine model parameter estimation, which is based on a multiresolution algorithm, has been established from synthesized image sequences. A major interest of the authors' approach is to follow with time the evolution of a few number of parameters characteristic of cellular motion and deformation. From the time-varying eigenvalues of the affine model square matrix, a precise quantification of the cell pseudopodial activity, as well as of cell division has been performed. For migrating cells, the motion quantification confirms that cell body deformation has a leading role in controlling nucleus displacement, the nucleus itself undergoing a larger rotational motion. At the cell population level, image motion analysis of in vitro wound healing experiments quantifies the heterogeneous cell populations dynamics.