Figure 2

Segmentation of cell. A. Parametrization of the active rays. Illustration of a contour curve overlaid on a real cell image. In this example, the curve is constructed using 12 nodes that are interpolated linearly. The two concentric circles mark the limits of the search space for ρ. The center c is given by the tracking procedure. B. Illustrations of the consecutive steps for computing the potential function under three different experimental conditions. The original image f(x) is first preprocessed and rescaled f_preproc(x); next, a gradient is computed in the X and Y directions, in order finally to compute the potential function ν _c (x). C. Stability of the potential function ν _c (x) with respect to variations in the position of the center c(x_c, y_c). In this illustration, the center was artificially shifted in the vertical direction and the potential function was recomputed. The shifted center is represented by a white cross. Shifts of -18, -12, -6, 0, 6, 12, and 18 pixels were considered. For translations of -18 and 18 pixels, the shifted center is placed outside the cell and the potential function does not express a clear black contour; on the contrary, for shift inferior to 12 pixels the potential function provides a clearly defined contour.