The progress in staining of living cells together with advances in confocal microscopy devices has allowed detailed studies of the behavior of intracellular components including the structures inside the cell nucleus. The typical number of investigated cells in one study varies from tens to hundreds in order to achieve a reasonable statistical significance of the result. One gets time-lapse series of two or three dimensional images as an output from the microscope. The manual analysis of such large data sets is very inconvenient and annoying. This is especially true for 3D series. Moreover, there is no guarantee on the accuracy of the result. Therefore, there is a natural demand for computer vision methods which can help with the analysis of time-lapse image series. Estimation or correction of global as well as local motion belongs to the main tasks in this field.
We have implemented the latest optical flow methods which we use for local motion estimation in live-cell image series. Up to our best knowledge, nobody has investigated the application of the state-of-the-art methods in the field of live-cell imaging yet.
Let the two consecutive frames of image sequence be given. Optical flow methods compute the displacement vector field which maps all voxels from the first frame into their new position in the second frame. We study and implement the three-dimensional variants of following methods:
Variational optical flow methods determine the desired displacement as the minimizer of suitable energy functional. Particular energy functional consists of data term and smoothness term. Data term ensures that certain image properties (e.g. grey value, gradient magnitude) remain constant in time. Smoothness term regularises the non-unique solution by certain smoothness constraint.
We study common as well as the state-of-the-art variational optical flow methods published recently by Andr\xE9s Bruhn. We focus our interest on the multiscale warping based methods. These methods can handle motion larger than one pixel. This situation often occurs in live-cell image series. We implement and extend to three dimensions several variational optical flow methods, namely the following:
We present some results and screenshots from our programs here. In the first example you can see two 2D frames of HL-60 cell nucleus. In the right picture is the example output of our optic flow demo program. The flow is visualised in color representation (top frame color codes direction, intensity length of the flow vector) and in vectors (bottom frame). Size of input frames is 400x400 pixels. The flow was computed with warping based method for large displacements.