# Significance of Camera Pixel Error in the Calibration Process of a Robotic Vision System
## 4 Case Study: Measuring Dimension of 3D Parts  
In this section, a 3D printed car part is considered for estimating its dimension through a robotic vision system under variable camera settings. The objective behind choosing different camera resolutions is to observe the proposed proposition in real world scenario which can replicate error in image pixels by capturing low resolution image.  
Figure 5(a) shows an image of a car door with a planner edge-to-edge dimension of \(2.37\times 0.98\) m\({}^{2}\) that has been captured from the top-left position occupying whole frame of a door in the image. Note that in Figure 5(a), 42 colourful circular stickers of 1 cm diameter are affixed at the different door locations, which is helpful in estimating the error propagation as the pixel error increases.  
To predict the door size and diameter of stickers, initially the image is manually extracted from its background and is then merged with a respective depth image, which is shown in Figure 5(c). Note that in the depth image, the gray shaded region indicates the variation in the distance of the camera sensor from the local door regions. The darker the depth image, the farther the camera sensor is; hence more chances for uncertainty in pixel estimation as compared to light gray regions. Further, the variation in the shades of gray in the door region also indicates the existence of the combination of rotational and translational variation. Such variations are very common in industrial settings where large objects are inspected in the production belt.  
Figure 5: Error norms associated with rotation matrix and translation vector estimated using: (**a,b**) [PERSON]–Dornaika method; (**c,d**) [PERSON]–Lenz method; (**e,f**) Andreff et al. method.  
Figure 7 illustrates the diameter of all stickers captured under three different camera resolution i.e., \(1392\times 1040\), \(1044\times 780\), and \(696\times 520\). A falling trend in Figure 7 indicates that as the resolution of camera decreases the capability of estimating accurate size of object also decreases. It can be noted that as the resolution is dropped to 25% from its original value, the average error in estimating diameter of sticker also dropped by 21%. Further, a relation between sticker diameter estimation and distance of sticker can be established in a similar way under all three resolution settings, i.e., as the distance from sensor to object increases, the error in estimating sticker diameter decreases. Similarly, the dimension of door estimated using three camera settings, i.e., \(1392\times 1040\), \(1044\times 780\), and \(696\times 520\) is coming out to be, \(2.36\times 0.98\) m\({}^{2}\), \(2.33\times 0.96\) m\({}^{2}\), and \(2.31\times 0.95\) m\({}^{2}\), respectively.  
Figure 6: Image of 3D printed car door captured under different camera resolution, i.e., \(1392\times 1040\), \(1044\times 780\), and \(696\times 520\). (**a**) Original image, (**b**) Manually extracted image, (**c**) Respective depth image.  
Figure 7: Variation in estimation of sticker diameter under different camera settings.