Multiview Point Cloud Registration Based on Minimum Potential Energy for Free-Form Blade Measurement

TL;DR

This work tackles the challenge of globally robust registration for free-form blade point clouds corrupted by noise and outliers. It introduces the negative full inverse (NFI) criterion as a robust, globally oriented objective and reformulates registration as a minimum potential energy (MPE) problem, yielding a convex-like energy landscape that prioritizes inliers. A physics-inspired motion-control scheme computes per-point gravitational forces and torques to guide the template toward alignment, with axis-angle rotation and mutation-based stride adaptation, followed by a Trimmed ICP refinement for fine-tuning. Empirical results on four blade models and a blade-measurement system demonstrate superior accuracy, noise resistance, and computational efficiency, supporting practical automated blade reconstruction in industrial settings. $E_I(R,t) = -\sum_{i=1}^{N}\sum_{j=1}^{M} \frac{1}{\| y_j - (R x_i + t) \| + \varepsilon^2}$ and $\phi = \sum_{i=1}^{N}\sum_{j=1}^{M} -\frac{G m_i m_j}{r}$ with $r = \| y_j - (R x_i + t) \| + \varepsilon^2$ are key formulations linking the robust loss to the energy-based optimization.$

Abstract

Point cloud registration is an essential step for free-form blade reconstruction in industrial measurement. Nonetheless, measuring defects of the 3D acquisition system unavoidably result in noisy and incomplete point cloud data, which renders efficient and accurate registration challenging. In this paper, we propose a novel global registration method that is based on the minimum potential energy (MPE) method to address these problems. The basic strategy is that the objective function is defined as the minimum potential energy optimization function of the physical registration system. The function distributes more weight to the majority of inlier points and less weight to the noise and outliers, which essentially reduces the influence of perturbations in the mathematical formulation. We decompose the solution into a globally optimal approximation procedure and a fine registration process with the trimmed iterative closest point algorithm to boost convergence. The approximation procedure consists of two main steps. First, according to the construction of the force traction operator, we can simply compute the position of the potential energy minimum. Second, to find the MPE point, we propose a new theory that employs two flags to observe the status of the registration procedure. We demonstrate the performance of the proposed algorithm on four types of blades. The proposed method outperforms the other global methods in terms of both accuracy and noise resistance.

Figures (13)

• Figure 1: Schematic diagram of the reconstruction system. The fixed camera scans multiple views of the blade with transformations. The green areas denote the visible parts of the camera view, which are then reconstructed to a complete model for quality evaluation with the standard model.
• Figure 2: Framework of the proposed MPE method.
• Figure 3: One-dimensional illustration of the registration error with the NFI metrics. (a) 1D data, the blue template set and the red reference set. The hollow circle in the reference set denotes an outlier. (b)-(e) The curve of the NFI loss function with the 1D translation of the template set.
• Figure 4: One-dimensional illustration of the registration error with the traditional $\ell_2$ error and the NFI metrics with a value of $\varepsilon^2$. Each column represents the loss function map with an outlier in the reference set. The first row (a)-(d) presents the data with four different outlier values. Each 1D data set consists of a blue template set and a red reference set. The hollow circle in the reference set denotes an outlier. The second row (e)-(h) presents the corresponding NFI error, and the last row presents the $\ell_2$ error. For a better illustration of the difference, we enlarge the local map in an extra window around the optimal translation $+5$.
• Figure 5: Two-dimensional illustration of the registration error with traditional $\ell_2$ and NFI metrics. The rows from top to bottom present the data, the error contour map using the NFI metric, and using the $\ell_2$ metric. The columns present the noiseless and corrupted data registrations with the 2D cross-section point set of the blade. The relative positions (abbreviated as Pt.) of the registration are represented as a star, rhombus, and triangle. The four contour maps of the last two columns share the same coordinate system with rotation $\theta$ and translation $t$.