Linear objects convey substantial information about document structure, but are challenging to detect accurately because of degradation (curved, erased) or decoration (doubled, dashed). Many approaches can recover some vector representation, but only one closedsource technique introduced in 1994, based on Kalman filters (a particular case of Multiple Object Tracking algorithm), can perform a pixelaccurate instance segmentation of linear objects and enable to selectively remove them from the original image. We aim at re-popularizing this approach and propose: 1. a framework for accurate instance segmentation of linear objects in document images using Multiple Object Tracking (MOT); 2. document image datasets and metrics which enable both vector-and pixel-based evaluation of linear object detection; 3. performance measures of MOT approaches against modern segment detectors; 4. performance measures of various tracking strategies, exhibiting alternatives to the original Kalman filters approach; and 5. an open-source implementation of a detector which can discriminate instances of curved, erased, dashed, intersecting and/or overlapping linear objects.