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Text line segmentation in freestyle handwritten documents remains an open document analysis problem. Curvilinear text lines and small gaps between neighbouring text lines present a challenge to algorithms developed for machine-printed or hand-printed documents. We investigate a general-purpose, knowledge-free method for the automatic detection of text lines based on a stable path approach. Lines affected by curvature and inclination are robustly detected. The proposed methodology was tested on a modern set of handwritten images made available on the ICDAR 2009 handwriting segmentation competition, with promissing results.