## 4 Evaluation
### Practical Application  
The proposed approach is implemented in a visual measurement system called 3D four-wheel aligner (3 Excel, T50). The system, designed for aligning four automobile wheels, mainly consists of an upper computer and four cameras and chessboard targets (Figure 16). Each camera is equipped with infrared filter and illuminant, for ensuring a high immunity to the complicated imaging conditions at customer sites. During an initial operation, the automobile under test is driven up to a certain distance by external force. Meanwhile, the cameras C\({}_{1}\) to C\({}_{4}\) are triggered in synchronous mode to capture image sequences of the targets T\({}_{1}\) to T\({}_{4}\) mounted on the front-left, front-right, rear-left, and rear-right wheels, respectively. For each image sequence, sub-pixel corners are detected for estimating a wheel attitude with respect to the corresponding camera; two alignment parameters _toe-in/toe-out_ and _camber_ are then determined by decomposing angles of the wheel attitude unified in a global frame defined by the bodywork. During a real-time alignment, the parameters are dynamically calculated from continuous estimations of the wheel attitude changes with respect to their initial values. Figure 15: Four images of a stationary chessboard captured under (**a**) underexposed, (**b**) overexposed, (**c**) indoor light interfered, and (**d**) outdoor light interfered scenarios. \begin{table}
\begin{tabular}{c c c c c} \hline  & [16] & [20] & [24] & **Proposed** \\ \hline RMSD (pixel) & 0.419 & 0.287 & 0.396 & 0.241 \\ \hline \end{tabular}
\end{table} 
Table 3: Overall evaluation result for four different approaches. As demonstrated in Figure 17, an automobile (Ford Focus) in healthy condition is used for on-site alignment. The introduced aligner can capture chessboard images with black backgrounds due to the usage of infrared filters and illuminants. After finishing the initial operation, the alignment is carried out and divided into two periods: one performs normally, and the other is interfered by infrared pollution sources. During each period, the alignment parameters are incessantly computed based on both the proposed and built-in techniques, until the number of their recorded values reaches 120. Figure 18 shows two boxplots of total _toe-in/toe-out_ for the front and rear wheel-sets. This parameter, called _toe-in_ for positive and _toe-out_ for negative values, is defined for investigating the symmetry of each wheel-set about the geometric centerline (or thrust line). For both normal and interfered periods, the proposed method results in a median closer to zero and IQR of minor scope, compared with the built-in algorithm. Considering the fact that two total values should be pretty small because of the healthy condition of the automobile, the boxplots prove that the proposed method shows better central tendency, due to the accurate corner localization. When comparing the medians of the proposed method during two periods, the deviations between them are about 0.003\({}^{\circ}\) and 0.002\({}^{\circ}\) for the front and rear wheel-sets, significantly less than that of the built-in algorithm (0.009\({}^{\circ}\) and 0.003\({}^{\circ}\)), which also shows that the proposed method  
Figure 19 depicts four curve plots of _camber_ as a function of time stamp for the front-left, front-right, rear-left, and rear-right wheel positions, which are divided into two parts, according to two different periods of the alignment. This parameter is defined for measuring the inclination of a wheel with respect to vertical line of the bodywork. Different from _toe-in/toe-out_, it is separately investigated using the wheel attitude, and weakly restricted to the absolute symmetry about its baseline for the corresponding wheel-set and, therefore, a total value makes poor sense for the evaluation.