3.2.4. Point Cloud Smoothing

Similarly to the outlier removal operation, the smoothing of the cloud points position was implemented to improve the surface reconstruction quality. When collecting depth data, the camera may add small ripples to the description of originally flat regions, a factor caused by inaccuracies in the depth data capture. This feature contributes to a decrease in the surface reconstruction quality and description of keypoints in the surface fusion operation. The smoothing of the cloud points corrects these imperfections, providing greater accuracy in subsequent operations and in the generated model. To perform this operation the Bilateral Smoothing technique was used, composed of two parts: smoothing normals; and points repositioning based on the adjusted normals.

The Bilateral Smoothing technique needs the normal vectors to the implicit surface of the cloud points and its neighbors. These vectors are fitted, minimizing the distance to their neighbors, to describe smooth surfaces. The points are then positioned to fit the normals, so that they also form smooth surfaces. The estimation of the normal vector for each point is performed using the Principal Component Analysis (PCA) technique, which uses the eigenvalues and eigenvectors of the point covariance matrix. The smallest eigenvectors correspond to the best normal vectors with respect to the plane defined by the neighboring points, and the vector of this group with the smallest eigenvalue has the smallest direction variation and is perpendicular to the directions of greatest variation, corresponding to the normal vector to the surface [66].

The normals are iteratively adjusted, taking as a parameter the difference in distance from neighboring normals. The goal is to minimize these distances so that the discontinuities remain in separate groups, making continuous surfaces uniform and keeping the edges of the object [71]. After updating the normals, the cloud points are repositioned using the Locally Optimal Projector (LOP) technique proposed by Lipman et al. (2007) [72] and modified by Huang et al. (2013) [71] for the context of the Bilateral Smoothing technique. LOP redistributes a set of points in a way that adheres to the implicit shape described by those points. The smoothing operation can be done iteratively, allowing the control of the smoothing level. Figure 8 presents three examples of point cloud smoothing with different iteration numbers.

Point cloud smoothing. The orange point cloud indicates the smoothed point cloud, with (a) one iteration; (b) two iterations and (c) three iterations.