Fast and accurate computation of surface normals from range images

The fast and accurate computation of surface normals from a point cloud is a critical step for many 3D robotics and automotive problems, including terrain estimation, mapping, navigation, object segmentation, and object recognition. To obtain the tangent plane to the surface at a point, the traditional approach applies total least squares to its small neighborhood. However, least squares becomes computationally very expensive when applied to the millions of measurements per second that current range sensors can generate. We reformulate the traditional least squares solution to allow the fast computation of surface normals, and propose a new approach that obtains the normals by calculating the derivatives of the surface from a spherical range image. Furthermore, we show that the traditional least squares problem is very sensitive to range noise and must be normalized to obtain accurate results. Experimental results with synthetic and real data demonstrate that our proposed method is not only more efficient by up to two orders of magnitude, but provides better accuracy than the traditional least squares for practical neighborhood sizes.