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Toward obtaining a compact and multiresolution representation of 2D range scans, a wavelet framework is proposed for encoding an orientation measure called running angle (RA). A new shrinkage algorithm is developed using discrete wavelet transform of the RA signal, which leads to a simplified polyline approximation of the initial scanned points. This approach is evaluated in terms of segmentation of 2D range scans as a line extractor. As a proof of concept, an experiment is performed in our laboratory hallway by a mobile robot equipped with two SICK laser range finders which shows that it is possible to successfully segment raw measurements of the scanner using the proposed approach and obtain proper linear abstraction. Besides a simple, fast heuristic line extraction algorithm is also proposed for the sake of comparison. It is based on thresholding the changes of the incident angles between the laser beam and the vertices of the initial polygon observed by the scanner. Despite its simplicity, this approach performs rather well and can be used in structured environments with low measurement noise. Both approaches are experimentally evaluated and compared with some well known and commonly used line extraction algorithms.