This paper presents an automated method for actin filament segmentation and tracking for measuring tip elongation rates in Total Internal Reflection Fluorescence Microscopy (TIRFM) images. The main contributions of the paper are: (i) we use a novel open active contour model for filament segmentation and tracking, which is fast and robust against noise; (ii) different strategies are proposed to solve the filament intersection problem, which is shown to be the main difficulty in filament tracking; and (iii) this fully automated method avoids the need of human interaction and thus reduces required time for the entire elongation measurement process on an image sequence. Application to experimental results demonstrated the robustness and effectiveness of this method.