Network structures formed by actin filaments are present in many kinds of fluorescence microscopy images. In order to quantify the conformations and dynamics of such actin filaments, we propose a fully automated method to extract actin networks from images and analyze network topology. The method handles well intersecting filaments and, to some extent, overlapping filaments. First we automatically initialize a large number of Stretching Open Active Contours (SOACs) from ridge points detected by searching for plus-to-minus sign changes in the gradient map of the image. These initial SOACs then elongate simultaneously along the bright centerlines of filaments by minimizing an energy function. During their evolution, they may merge or stop growing, thus forming a network that represents the topology of the filament ensemble. We further detect junction points in the network and break the SOACs at junctions to obtain "SOAC segments". These segments are then re-grouped using a graph-cut spectral clustering method to represent the configuration of actin filaments. The proposed approach is generally applicable to extracting intersecting curvilinear structures in noisy images. We demonstrate its potential using two kinds of data: (1) actin filaments imaged by Total Internal Reflection Fluorescence Microscopy (TIRFM) in vitro; (2) actin cytoskeleton networks in fission yeast imaged by spinning disk confocal microscopy.