Quantification of microscopy time-series of in vitro reconstituted motor driven microtubule (MT) transport in 'gliding assays' is typically performed using computational object tracking tools. However, these are limited to non-intersecting and rod-like filaments. Here, we describe a novel computational image-analysis pipeline, KnotResolver, to track image time-series of highly curved self-intersecting looped filaments (knots) by resolving cross-overs. The code integrates filament segmentation and cross-over or 'knot' identification based on directed graph representation, where nodes represent cross-overs and edges represent the path connecting them. The graphs are mapped back to contours and the distance to a reference minimized. The accuracy of contour detection is sub-pixel with a robustness to noise. We demonstrate the utility of KnotResolver by automatically quantifying 'flagella-like' curvature dynamics and wave-like oscillations of clamped microtubules in a 'gliding assay'. The MATLAB based source code is released as OpenSource and is available at https://github.com/CyCelsLab/MTKnotResolver. Supplementary data are available at Bioinformatics.