A correlation-based approach to calculate rotation and translation of moving cells

We present a noniterative image cross-correlation approach to track translation and rotation of crawling cells in time-lapse video microscopy sequences. The method does not rely on extracting features or moments, and therefore does not impose specific requirements on the type of microscopy used for imaging. Here we use phase-contrast images. We calculate cell rotation and translation from one image to the next in two stages. First, rotation is calculated by cross correlating the images´ polar-transformed magnitude spectra (Fourier magnitudes). Rotation of the cell about any center in the original images results in translation in this representation. Then, we rotate the first image such that the cell has the same orientation in both images, and cross correlate this image with the second image to calculate translation. By calculating the rotation and translation over each interval in the movie, and thereby tracking the cell´s position and orientation in each image, we can then map from the stationary reference frame in which the cell was observed to the cell´s moving coordinate system. We describe our modifications enabling application to nonidentical images from video sequences of moving cells, and compare this method´s performance with that of a feature extraction method and an iterative optimization method.