The relative orientation between filamentary structures in molecular clouds and the ambient magnetic field provides insight into filament formation and stability. To calculate the relative orientation, a measurement of filament orientation is first required. We propose a new method to calculate the orientation of the one pixel wide filament skeleton that is output by filament identification algorithms such as textsc{filfinder}. We derive the local filament orientation from the direction of the intensity gradient in the skeleton image using the Sobel filter and a few simple post-processing steps. We call this the `Sobel-gradient method. The resulting filament orientation map can be compared quantitatively on a local scale with the magnetic field orientation map to then find the relative orientation of the filament with respect to the magnetic field at each point along the filament. It can also be used in constructing radial profiles for filament width fitting. The proposed method facilitates automation in analysis of filament skeletons, which is imperative in this era of `big data.
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