Uncertainty analysis for optimum plane extraction from noisy 3D range-sensor point-clouds

Abstract

We utilize a more accurate range noise model for 3D sensors to derive from scratch the expressions for the optimum plane fitting a set of noisy points and for the combined covariance matrix of the plane's parameters, viz. its normal and its distance to the origin. The range error model used by us is a quadratic function of the true range and also the incidence angle. Closed-form expressions for the Cramér-Rao uncertainty bound are derived and utilized for analyzing four methods of covariance computation: exact maximum likelihood, renormalization, approximate least-squares, and eigenvector perturbation. The effect of the simplifying assumptions inherent in these methods are compared with respect to accuracy, speed, and ease of interpretation of terms. The approximate least-squares covariance matrix is shown to possess a number of desirable properties, e.g., the optimal solution forms its null-space and its components are functions of easily understood terms like the planar-patch's weighted centroid and scatter. It is also fast to compute and accurate enough in practice. Its experimental application to real-time range-image registration and plane fusion is shown by using a commercially available 3D range sensor.

Global Registration of 3D LiDAR Point Clouds Based on Scene Features: Application to Structured Environments

“…In indoor environments, planes have already been used to perform a registration by Pathak et al [33,34], whose work is inspired by the NDT, but uses walls to determine the probability density function. The walls are extracted as sets of points.…”

Beyond points: Evaluating recent 3D scan-matching algorithms

“…Each plane patch is represented by the unit normaln and the distance d from the origin, along with the polygonal boundary. Using a noise model of the 3D sensor model, a 4 × 4 covariance matrix of the plane parameters is also computed [17] for each patch. …”

Fast and accurate computation of surface normals from range images

“…In the robotics and automotive domain, the points are usually organized in graphs or range images, and the computation of surface normals focuses almost exclusively on least squares solutions [9], [10], [16], [21], [22], [24], [28]. Alternative methods for computing normals from organized point clouds rely on averaging the normals of adjacent triangles [2], [13], [19], [26], but the obtained normals are sensitive to noise and to the proper construction of the graph.…”

“…Alternative methods for computing normals from organized point clouds rely on averaging the normals of adjacent triangles [2], [13], [19], [26], but the obtained normals are sensitive to noise and to the proper construction of the graph. Least squares and some of these averaging methods were compared in quality and computation time in [13], [21], [27]. In all these experiments, least squares shows the best results in terms of accuracy and speed.…”

“…The component d is found as the normal distance to the plane, i.e., d =p T n. This is the most widely used method in the literature [10], [11], [14], [16], [18], [21], [22], [23], [24], [28].…”