Removing visual bias in filament identification: a new goodness-of-fit measure

Different combinations of input parameters to filament identification algorithms, such as Disperse and FilFinder, produce numerous different output skeletons. The skeletons are a one pixel wide representation of the filamentary structure in the original input image. However, these output skeletons may not necessarily be a good representation of that structure. Furthermore, a given skeleton may not be as good a representation as another. Previously there has been no mathematical `goodness-of-fit' measure to compare output skeletons to the input image. Thus far this has been assessed visually, introducing visual bias. We propose the application of the mean structural similarity index (MSSIM) as a mathematical goodness-of-fit measure. We describe the use of the MSSIM to find the output skeletons most mathematically similar to the original input image (the optimum, or `best', skeletons) for a given algorithm, and independently of the algorithm. This measure makes possible systematic parameter studies, aimed at finding the subset of input parameter values returning optimum skeletons. It can also be applied to the output of non-skeleton based filament identification algorithms, such as the Hessian matrix method. The MSSIM removes the need to visually examine thousands of output skeletons, and eliminates the visual bias, subjectivity, and limited reproducibility inherent in that process, representing a major improvement on existing techniques. Importantly, it also allows further automation in the post-processing of output skeletons, which is crucial in this era of `big data'.