Robust Point Matching

Leo Chen

Introduction

Robust Point Matching (RPM) is an iterative and probabilistic point cloud registration approach. This method uses the technique of deterministic annealing and soft assignment. It starts with estimating the correspondence between two sets of centroids using soft assignment. Then, the method estimates the transformation parameters using coordinate descent. The resulting algorithm is a simple two step iterative approach. The outline of the algorithm is shown in Figure 1.

Figure 1: Robust Point Matching Algorithm Outline

Evaluation

The RPM is evaluated from two aspects: 1. Whether it can accurately register two polygon clouds under different translation and rotation. 2. Whether it is robust under different amount of noise and outliers. The measuring metric that is used is the mean square error between two point clouds between the closest points. A base MSE is calculated before deregistering the point clouds and compared it against the MSE for RPM registration. Two types of orchards are chosen for testing which orchard 1’s polygons are sparser while orchard 3 has denser polygons distribution as shown in Figure 4.

Figure 2: Orchard 1 with 0 confidence level threshold

Figure 3: Orchard 1 with 0.9 confidence level threshold

Figure 4: Orchard 3

Results

The results for RPM performing registration with different range of transformations are shown in Figure 5.

Figure 5: Registration MSE Difference under Different Range of Transformations

The results for RPM performing registration with different confidence level thresholds are shown in Figure 6.

Figure 6: Registration MSE Difference under Different Confidence Level Thresholds

The results can also be visually inspected as shown in Figure 7 and 8.

Figure 7: Registration results for Orchard 1 under different confidence level filtering

Figure 8: Registration results for Orchard 3 under different confidence level filtering

Conclusion

RPM can register data points under different translation and rotation accurately. However, when facing some outliers, it will decrease the accuracy with the result of some misalignment. With a significant number of outliers, the registration will be very inaccurate. The range of transformation can also have an effect on registration accuracy, with larger transformation the less accurate the registration would be. Since the requirement from Aerobotics is that only small amount of transformations need to be considered. And since the smaller the transformations the more accurate the registration is. Thus the RPM algorithm can fulfil the need for orchard registration. The algorithm has a time complexity of O(n^2). When data points are a lot, it can take up to one hour to register two images.