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Most vision-based SLAM systems utilize corner-like features, and may be unstable in non-textured environments where only a few corner features can be extracted. To cope with this problem, we employ edge points to perform SLAM with a stereo camera. The edge-point based SLAM is applicable to non-textured environments since plenty of edge points can be obtained even from a small number of lines. The proposed method estimates camera poses and builds detailed 3D maps robustly by aligning edge points between frames using the ICP algorithm. In indoor experiments, the method successfully built detailed 3D maps even under noisy condition.