Experiments

In the first experiment a dataset captured from a conference room with our scan-ning system is used to evaluate different variants of the pairwise ICP matching

3.2. PAIRWISERIGID-REGISTRATION 37

(a) Two unregistered scans. (b) Registered scans.

Figure 3.5: A scanned conference room serves as input to the algorithms. The left picture shows two out of four scans coarsely aligned by wheel odometry. All methods converge to the same correct registration (right).

algorithm. Figure 3.5 depicts two out of four scans from this dataset. The scene is an easy case for most ICP variants, since it contains well defined coarse-scale geometry features which make an alignment easy. Yet it is very representative for the data acquired by our scanning system. The dataset is manually aligned to ob-tain ground truth robot poses. We then evaluate the performance of different ICP algorithms relative to this correct alignment. The metric we will use to compare the results is root-mean square point-to-point distance for the points in the test dataset and the corresponding points in the aligned reference dataset. This allows for a more objective comparisons of the performance of ICP variants than using the error metrics computed by the algorithms themselves.

We first look at the performance for different methods of the correspondence search. Figure 3.6(a) presents a comparison of convergence rates for different correspondence search methods. For the selected scene, our proposed method us-ing a combination of point, normal, and color matchus-ing produces the best results.

All methods converge to the same correct registration. However, incorporating additional clues, such as normal and color information, to the standard correspon-dence search leads to a faster convergence. We hypothesize that the reason for this is that more correct pairings are formed in early iterations. Secondly, we compare the performance of two error metrics: point-to-point and point-to-plane.

Figure 3.6(b) depicts a comparison of convergence rates for both metrics. On the choosen dataset, we see that the point-to-plane error metric performs significantly

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better than the point-to-point metric. It takes the algorithm using a point-to-point metric more than 100 iterations to converge and the residual alignment error is 1.45 mm. The alignment error of the unregistered dataset is 0.48 m. The algorithm us-ing a point-to-plane metric, however, converges to a simular residual alignment error within 5 iterations.

In the second experiment, we use ICP for a pairwise alignment of a larger dataset.

This dataset maps the first floor of Stanford’s Gates Building and it consists of 8 scans (see Figure 3.7). An initial registration of the data is performed by using the robot’s wheel odometry. This aligns the scans only coarsely but serves as a good starting point for the ICP registration. Next, we perform a registration with our ICP variant using point, normal, and color similarity for the correspondence search as well as the point-to-plane error metric. The result of this registration is presented on the right side of Figure 3.7. One will note that each pair is seemingly aligned well. However, small residual errors in this pairwise registration process accumulate and cause inconsistencies in the data. In our case, the first and the last scan are not aligned well.

3.2.5 Conclusion

In this section, we presented a pairwise ICP alignment strategy for solving the multi-view registration problem. We have shown typical results that capture the significant differences in performance using variations of the standard ICP algo-rithm. We demonstrated that ICP-based registration techniques work well for a pairwise registration of point clouds.

There are three main sources of error for ICP. The first source of error is wrong convergence: ICP can converge to a local minimum out of the attraction area of the true solution. The reasons for this behavior are the iterative nature of the al-gorithm. A coarse initial alignment of the data is essential for ICP to converge to the correct alignment. In our case, a good starting point for the ICP registration is given by the robot’s wheel odometry. The second source of error is under-constrained situations: in some environments there is not enough information to estimate the pose of the robot completely. Those situations occur when surfaces can slide in one or more directions without affecting the error function. Refer to [Gelfand et al., 2003] for a comprehensive analysis. Our strategy for finding cor-respondences by adding color and normals to the search not only leads to a better convergence but also alleviates the effect of underconstraint alignments. The third source of error is sensor noise: even though ICP arrives in the attraction area of the true solution, the outcome is different because of noise. Sensor noise is difficult to address in ICP since data points are assumed fixed and without error. Allowing

3.2. PAIRWISERIGID-REGISTRATION 39 Euclidean + normals + colors

(a) Correspondence search.

Figure 3.6: Comparison of different ICP variants on scanned data. We analyze the convergence rates using different methods of correspondence search (top) as well as different error metrics (bottom) on the conference room dataset.

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(a) Registration using odometry. (b) Registration using ICP.

Figure 3.7: Results for the registration on 8 scans. Registration based on wheel odometry (left) retrieved from the scanner leads to a highly distorted model. Using the ICP algorithm with several modifications yields good results for registering textured 3D scans (right). However, residual errors in this registration process accumulate and cause inconsistencies when scanning large loops.

data points to adjust for noise implies a fundamentally different type of non-rigid registration which we will address in Section 3.4.

When applied to a larger number of scans, an incremental registration process may result in residual errors which accumulate over time. This leads to inconsistencies especially when scanning large loops such as depicted in Figure 3.7(b). Without a global registration technique even small errors accumulate while sequentially registering the scans of those loops. Specifically, errors in orientation may cause large displacements as they act like levers in a sequential registration process.

In the following sections we will use the ICP variant using point distance, normal distance, and color similarity for the correspondence search as well as the point-to-plane error metric for pairwise scan matching.