# A Non-Contact Measurement of Animal Body Size Based on Structured Light
## 3 Results
Figure 14: (**a**) Goat specimen front body point cloud obtained via our equipment; (**b**) goat specimen back body point cloud obtained via our equipment; (**c**) goat specimen front body point cloud obtained via depth camera; (**d**) goat specimen back body point cloud obtained via depth camera; (**e**) goat specimen front body point cloud obtained via 3D Scanner. Figure 13: (**a**) Fox specimen front body point cloud obtained via our equipment; (**b**) fox specimen back body point cloud obtained via our equipment; (**c**) fox specimen front body point cloud obtained via depth camera; (**d**) fox specimen back body point cloud obtained via depth camera; (**e**) fox specimen front body point cloud obtained via 3D scanner; (**f**) fox specimen back body point cloud obtained via 3D scanner. The experiment results for the error evaluations are shown in Figure 15. Different numbers of images were used in the calibration stage to show how the camera and light plane accuracy affect the measuring precision. For the camera, the parameter used for error evaluation is the reprojection error, which indicates the difference between the pixels captured directly and the pixels calculated using Equation (1). The reprojection error can be calculated using Equation (7), where \((u,v)^{\mathrm{T}}\) is the pixel captured directly, \((u^{\prime},v)^{\mathrm{T}}\) is the pixels calculated using Equation (1) and \(n_{c}\) is the number of calibration points. For the light plane, firstly, all light plane equations were transformed into the form of \(Ax+By-z=-C\) and combined as \(\mathbf{Ax=b}\). Then, we solved the system of equations by using the least squares method. And last, the least squares solution was substituted into the system of equations to calculate a new non-homogeneous term. We used the original non-homogeneous term as a benchmark to calculate the standard deviation, regarded as an error evaluation parameter for the light plane. This standard deviation represented the fluctuation of the intersection points of all light planes. If the standard deviation was less than the size of the DMD, it pointed out that all light planes could intersect on the projector's DMD, indicating that the calibration of the light planes was relatively accurate. The algorithm is shown in Algorithm 4. For the measuring precision, the difference between the manual measurement result and our equipment's result was used to represent the measuring accuracy, including absolute error and relative error. The camera calibration error and light plane calibration error are shown in Figure 15a,b, from which we can conclude that with an increase in the number of calibration images, the calibration accuracy of both the camera and the light plane has improved. Figure 15c,d show the variation of measuring error of goat specimen's body length with the increasing number of calibration images. The error evaluation result shows that as the calibration accuracy improves, the measurement error gradually decreases and converges. \[E_{1}=\frac{1}{n_{c}}\sum_{i=1}^{n_{c}}\sqrt{\left(u_{i}-u_{i}^{\prime}\right) ^{2}+\left(v_{i}-v_{i}^{\prime}\right)^{2}} \tag{7}\]  
Figure 15: (a) Camera calibration error; (b) light plane error; (c) absolute measuring error; (d) relative measuring error.