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According to the World Health Organisation, 285 million people live with a visual impairment. Despite the fact that many efforts have been made recently, there is still no computer-guided system that is reliable, robust and practical enough to help these people to increase their mobility. Motivated by this shortcoming, we propose a novel obstacle detection system to assist the visually impaired. This work mainly focuses on indoor environments and performs classification of typical obstacles that emerge in these situations, using a 3D sensor. A total of four classes of obstacles are considered: walls, doors, stairs and a residual class (which covers loose obstacles and bumpy parts on the floor). The proposed system is very reliable in terms of the detection accuracy. In a realistic experiment, stairs are detected with 100% true positive rate and 8.6% false positive rate, while doors are detected with 86.4% true positive rate and 0% false positive rate.