We present a new algorithm for detecting filamentary structure FilFinder. The algorithm uses the techniques of mathematical morphology for filament identification, presenting a complementary approach to current algorithms which use matched filtering or critical manifolds. Unlike other methods, FilFinder identifies filaments over a wide dynamic range in brightness. We apply the new algorithm to far-infrared imaging data of dust emission released by the Herschel Gould Belt Survey team. Our preliminary analysis characterizes both filaments and fainter striations. We find a typical filament width of 0.09 pc across the sample, but the brightness varies from cloud to cloud. Several regions show a bimodal filament brightness distribution, with the bright mode (filaments) being an order of magnitude brighter than the faint mode (striations). Using the Rolling Hough Transform, we characterize the orientations of the striations in the data, finding preferred directions that agree with magnetic field direction where data are available. There is a suggestive but noisy correlation between typical filament brightness and literature values of the star formation rates for clouds in the Gould Belt.