# Efficient Model-Based Object Pose Estimation Based on Multi-Template Tracking and PnP Algorithms
## 5 Experimental Results
### Quantitative Evaluation  
To evaluate the estimation accuracy of the proposed algorithm quantitatively, a protractor and a ruler were used in the experiments to measure the orientation angle and the translation distance of the target along an axis manually, respectively. These measures were used as the ground truth of  
Figure 3: Pose estimation results of the proposed algorithm in tracking the OOI with the three templates shown in Figure 2: 3D pose estimation by tracking (**a**) the template No. 1, (**b**) the two templates No.1 and No. 3, (**c**) the template No. 3, (**d**) the two templates No.1 and No. 3 again, (**e**) the template No. 1, (**f**) the two templates No. 1 and No. 2, (**g**) the template No. 2 and (**h**) the template No. 1 with a rotation on the \(z\)-axis. the target poses. Figure 4 illustrates the translation estimation results of the proposed algorithm. The experimental results of target translations along the \(x-\), \(y\)- and \(z\)-axes are shown in Figure 4a1-h1, Figure 4a2-h2 and Figure 4a3-h3, respectively. From Figure 4a1-h1, it is clear that the maximum absolute translation error (defined by 1 Ground Truth-Estimation 1) is less than 0.8 cm on the \(x\)-axis. In Figure 4a2-h2, the maximum absolute translation error along the \(y\)-axis is about 1.0 cm when the target is close to the boundary of the image. In Figure 4a3-h3, the maximum absolute translation error along the \(z\)-axis is less than 0.6 cm. Therefore, the accuracy of the target translation estimation of the proposed algorithm is verified. Figure 5 presents the rotation estimation results of the proposed algorithm. Similarly, the experimental results of target rotation estimation in the \(x\)-, \(y\)-, and \(z\)-axes are shown in Figure 5a1-h1, Figure 5a2-5h2 and Figure 5a3-h3, respectively. From Figure 5, the maximum absolute rotation error  
Figure 4: Experimental results of the proposed algorithm to estimate the translation motions of the OOI along the (**a1–h1**) \(x\)-axis, (**a2–h2**) \(y\)-axis and (**a3–h3**) \(z\)-axis. is less than 1.8 degrees across the \(x\)-axis, 1.9 degrees across the \(y\)-axis and 0.9 degrees across the z-axis. Hence, the accuracy of the target rotation estimation of the proposed algorithm is also verified. Based on the above experimental results, two estimation error criteria were employed to quantitatively evaluate the estimation performance of the proposed algorithm as follows:  
\[e_{R_{\Omega}}=\left(R_{\Omega}-\hat{R}_{\Omega}\right)^{2}\text{ and }e_{T_{\Omega}}=\left(T_{\Omega}-\hat{T}_{\Omega}\right)^{2}, \tag{20}\]  
where \(\Omega=\{x\),\(y\),\(z\}\) denotes one of the three axes of the 3D Cartesian coordinate system; \(R_{\Omega}\) and \(T_{\Omega}\) denote the ground truths of the rotation angle and translation distance on the \(\Omega\)-axis, respectively; \(\hat{R}_{\Omega}\) and \(\hat{T}_{\Omega}\) denote the corresponding estimates of the rotation angle and translation distance obtained from the proposed algorithm, respectively. Table 1 records the estimation errors of the experimental results shown in Figures 4 and 5. The last row in Table 1 shows the average estimation error of the experiments. From Table 1, it is clear that  
Figure 5: Experimental results of the proposed algorithm to estimate the rotation angles of the (**a1–h1**) \(x\)-axis, (**a2–h2**) \(y\)-axis and (**a3–h3**) \(z\)-axis of the OOI. the rotation estimation in \(y\)-axis has the largest estimation error of about 1.64 degrees on average. By contrast, the average rotation estimation errors in both the \(x\)- and \(z\)-axis are smaller than 0.82\({}^{\circ}\) and 0.23\({}^{\circ}\), respectively. Moreover, the translation estimation errors in the three axes are all smaller than 0.33 cm on average. In other words, the average percentage error of the translation estimation results is lower than 3.3% when compared to the real dimensions of the object.