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The detection of groups of parallel lines is important in applications such as form processing and text (handwriting) extraction from rule lined paper. These tasks can be very challenging in degraded documents where the lines are severely broken. In this paper, we propose a novel model-based method which incorporates high-level context to detect these lines. After preprocessing (such as skew correction and text filtering), we use trained hidden Markov models (HMM) to locate the optimal positions of all lines simultaneously on the horizontal or vertical projection profiles, based on the Viterbi decoding. The algorithm is trainable so it can be easily adapted to different application scenarios. The experiments conducted on known form processing and rule line detection show our method is robust, and achieves better results than other widely used line detection methods.