Denoising point clouds using pulling-back method

We propose a method for denoising a point cloud by pulling every noise point to its supposed position. In R2, suppose that the point cloud be all located on a presumed curve. However, some points are not on the curve due to noise. For every point, in a small neighborhood the presumed curve is approximated by an osculating circle. The point is then pulled to the circle, i.e., its new position is the projected point on the circle. In R3, the 2-D osculating circle is replaced by Dupin indicatrix. This Dupin indicatrix is attached to the noisy point, thus it also moves with the moving noisy point. The noisy point will move along its normal direction. Then, along the normal direction, the length of every k-nearest point to the projected point on the Dupin indicatrix is computed. The noisy point's new position is the place where the sum of squared length of all k-nearest points reaches minimum. The point cloud data are used to examine the result and found satisfactory.