We aim at analysing fluorescence microscopy sequences of moving cells, so as to estimate the velocities that define the movement, the forces that drive this movement, and the pressure that characterises the material state. We use an optical flow method constrained by Stokes flow mechanics equations that define the dynamics of a fluid that is incompressible, homogeneous and viscous. We present a finite element formulation that leads to a quadratic programming problem. We apply the method to real biological data of amoebas observed by fluorescence microscopy.

Variational deformable models have proven over the past decades a high efficiency for segmentation and tracking in 2-D sequences. Yet, their application to 3-D time-lapse images has been hampered by discretization issues, heavy computational loads and lack of proper user visualization and interaction, limiting their use for routine analysis of large data-sets. We propose here to address these limitations by reformulating the problem entirely in the discrete domain using 3-D active meshes, which express a surface as a discrete triangular mesh, and minimize the energy functional accordingly. By performing computations in the discrete domain, computational costs are drastically reduced, whilst the mesh formalism allows to benefit from real-time 3-D rendering and other GPU-based optimizations. Performance evaluations on both simulated and real biological data sets show that this novel framework outperforms current state-of-the-art methods, constituting a light and fast alternative to traditional variational models for segmentation and tracking applications.