Estimating Surface Normals with Depth Image Gradients for Fast and Accurate Registration

We present a fast registration framework with estimating surface normals from depth images. The key component in the framework is to utilize adjacent pixels and compute the normal at each pixel on a depth image by following three steps. First, image gradients on a depth image are computed with a 2D differential filtering. Next, two 3D gradient vectors are computed from horizontal and vertical depth image gradients. Finally, the normal vector is obtained from the cross product of the 3D gradient vectors. Since horizontal and vertical adjacent pixels at each pixel are considered composing a local 3D plane, the 3D gradient vectors are equivalent to tangent vectors of the plane. Compared with existing normal estimation based on fitting a plane to a point cloud, our depth image gradients based normal estimation is extremely faster because it needs only a few mathematical operations. We apply it to normal space sampling based 3D registration and validate the effectiveness of our registration framework by evaluating its accuracy and computational cost with a public dataset.