Efficient Change Detection in 3D Environment for Autonomous ...

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for the person’s head and that in the lower members, a hole appeared separating the two legs. Given a threshold h, we will consider a normalized global density function G(p) = h − G(p), where zero value defines the boundary surface, negative and positive values define interior and exterior regions of the cluster, respectively. The use of G allows, without loss of generality, for the efficient use of Boolean operations on implicit volumes. C. Boolean Operations Let two point clouds P1 and P2 represent current and reference data, respectively. It is hard to perform Boolean operations such as P1 ∩ P2 or P1 − P2. However, using their associated normalized global density functions, given by G1, G2 : R 3 → R, each Boolean operation constructs a new normalized global density function G3 in a simple step, as shown in [8], using the following operations: P1 ∪ P2 ⇒ G3 (p) = min (G1 (p) , G2 (p)) P1 ∩ P2 ⇒ G3 (p) = max (G1 (p) , G2 (p)) P1 − P2 ⇒ G3 (p) = max (G1 (p) , −G2 (p)) The above Boolean operation is defined for implicit data only. In order to take advantage of this procedure to compute changes from our discrete point clouds, we obtain G3 (p) = max (G1 (p) , −G2 (p)), which is a new density function whose negative values define a volume where points belonging to the portion where there is a change should lie. Finally, points p ∈ P1 are detected as a change if G3(p) < 0, which is computed in linear time. Figure 1 shows an example of an operation of difference between two point clouds. Algorithm 1 details our method. Algorithm 1 ChangeDetect( P1, P2, h ) 1: Compute G1 from P1 2: Compute G2 from P2 3: Compute G3 = max(G1, −G2) 4: D = ∅ 5: for each p ∈ P1 do 6: if G3(p) < 0 then 7: D = D ∪ {p} 8: end if 9: end for 10: return D Notice that, as it is, Algorithm 1 computes change points that shows up. Disappearing change points can be computed as well by swapping P1 and P2 in the input. IV. EXPERIMENTAL RESULTS In order to obtain statistical quantitative assessment of the proposal method, we use the methodology proposed by Vieira Neto and Nehmzow [12] to evaluate change detection. They propose the use of contingency tables to relate the system response with ground truth information to obtain three different statistical indicators based on χ 2 analysis. In our work, the ground truth data was manually segmented by the authors. Vieira Neto and Nehmzow propose the use of three metrics: Cramer’s V , uncertainty coefficient U(0 ≤ V, U ≤ 1) and κ index of agreement. Those methods were used to quantify the strength of data association, where small values indicate weaker associations and values closer to one represent stronger associations. The index κ varies between [−1; 1], where values smaller than 0.1 indicate no agreement, values between 0.1 and 0.4 indicate a weak agreement, values between 0.4 and 0.6 indicate a clear agreement and values larger than 0.6 indicate a strong agreement. Due to the similarity between these metrics, we show only the κ index of agreement in order to show the accuracy of our method. The κ index can be computed using Equation 1, where A represents inliers, B represents detection failure, C represents outliers, and D represents correct detection of the absence of change. More details on these metrics can be found in [12]. κ = 2(AD − BC) (A + C)(C + D) + (A + B)(B + D) A. Evaluation of robustness and parameters sensitivity The experiments to evaluate robustness of our method used a 3D dataset acquired in an office environment as reference map and 10 different datasets of the same environment modified with objects of different sizes and shapes. A Pioneer 2-AT Robot equipped with a Microsoft Kinect sensor was used to obtain the data, and each data set has about 76k points. The environment and 10 different changes are shown in Fig. 5-a and 5-b. The tests were executed on a PC with a Core 2 Duo CPU running at 2.0 GHz and with 2 GB RAM. Our algorithm obtains a discrete sampling for the global density function by computing its values for a 3D grid defined for the bounding box of the point clouds. Larger grid size leads to dense sampling, which improves robustness but decreases performance, as shown in Fig. 6. Firstly, Fig. 6-a depicts the statistical results using the κ index with mean and standard deviation (error bar). These results were generated on a grid 40 × 40 × 40 to 320 × 320 × 320, with a step of 40. The result shows that high accuracy is obtained from grid size 120 × 120 × 120 and that this accuracy is stable for higher values. Considering values greater than 0.6 as good (a) (b) Fig. 5. Experimental Setup 1: (a) Environment and experimental setup composed of a Pioneer Robot equipped with a Kinect sensor used to acquire 3D data. (b) Ten different changes inserted in the office environment, with varies size, pose and shape. (1)
TABLE I COMPARATIVE STUDY OF DIFFERENT CHANGE DETECTION ALGORITHMS. Number of Points Build Ref. Map Build Cur. Map Detection Dataset Ref. Map Cur. Map Nuñez et al. Our Nuñez et al. Our Nuñez et al. Our Real Data - Test Area 1 79171 79633 177.21 1.12 164.56 1.07 0.014 0.146 Real Data - Test Area 2 79171 81134 177.36 1.16 110.86 1.05 0.014 0.149 Real Data - Test Area 3 79171 80112 167.88 1.14 109.22 1.06 0.028 0.166 detection, we are able to detect changes even for small sized changes (see Figure 5-b). Figure 6-b, shows the processing time of the proposed algorithm. The processing time is obtained considering the total time for each of the three steps: (1) building implicit volume for reference point cloud, (2) building implicit volume for the point cloud with changes and, (3) performing the Boolean operation (change detection). The results are shown with mean time and standard deviation. This graph shows that increasing grid size, increases computational time without any gain in accuracy for grid sizes greater than 80 × 80 × 80, for which high accuracy is obtained in less than half a second. (a) (b) Fig. 6. Results obtained using different datasets acquired with the Kinect device, with objects of different sizes and shapes and for different poses. a) The statistical assessment κ index of agreement for grid size changes. b) Processing time for each dataset change in the grid size. In order to experimentally show the linear time complexity of our method, we computed changes for point clouds with different sizes. For this experiment, nine sets were used for which the number of points varyed from 17k to 144k. For each dataset, five different acquisitions were processed to Fig. 7. Computation time for different point cloud sizes. Nine sets with different sizes from 17k to 144k were used to show the linear time complexity in the number of points. present the mean and standard deviation of the processing time as shown in Figure 7. B. Comparison with a state-of-art approach We use compare our method with the one presented in [6] on their dataset. That dataset was acquired in the hallways of a building of the Minas Gerais Federal University using a Pioneer 2-AT Robot equipped with two SICK LMS-200 mounted orthogonally, in order to localize and acquire 3D maps. For the experiments, three different novelties were included in the robot’s workspace: An identification cylinder, a person and a printer box. The environment and the objects used are shown in Fig. 8-a and 8-b. Considering the results shown in [6], we are able to compare only the processing time. The accuracy of the method is not available because different metrics were used in the evaluation processes of each method. As in [6], we are also capable to detect changes in all three scenarios, (a) (b) Fig. 8. Experimental Setup 2: (a) Environment and experimental setup composed of a Pioneer 2-AT Robot equipped with two orthogonally mounted laser scanners acquiring 3D data. (b) Three different changes were inserted in the robot’s environment.
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