Subcellular filament networks (e.g. actin or microtubules) play important roles in many cellular processes, including wound healing and cancer metastasis, for example. Modern imaging techniques, such as confocal fluorescence microscopy, can be used to obtain detailed images of these structures. Subcellular filament distributions, however, are often too complex to be analysed and understood visually. In this paper, we describe a new computational algorithm that is able to detect the presence of filamentous distributions in microscopy images as well as extract their exact location (centrelines) without the need for visual or manual analysis of the data. Our goal is to describe a method relatively robust with respect to small variations in the input data or algorithm parameters. Experiments using real and simulated data, including acting and DNA filaments, are used to quantify the robustness of the new method.