# The Method of Multi-Camera Layout in Motion Capture System for Diverse Small Animals
## 2 The Parameters of Multi-Camera System
### The Depth of Field of Multi-Camera  
The accuracy of motion capture also depends on the depth of field of the multi-camera system. According to the principle of geometric optics, the farthest plane that can be clearly imaged on the image plane is called the far scene, while the nearest plane is called the near scene. The sum of the two is called the depth of field and the plane of the image is called the scene plane. It should be noted that, the conjugate plane is also called the alignment plane [32] (Figure 4a, the detailed calculation of the depth of field is detailed in the Supporting Documents S5). The front depth of field is less than the back depth of field, that is, after precise focusing, the scenery within a short distance in front of the focus can be clearly imaged but the scenery within a long distance at the back of the focus is clear. Image processing is a key step of the motion capture technique based on a video sequence.  
Figure 3: (**a**) Projections of three typical camera layouts and their field of view intersection areas in the horizontal and vertical planes; (**b**) Volumetric representations of the intersections of three typical camera layouts in the field of view are the simplest cubic representations (in units of length \(L\)), the width \(W\) and the height \(H\) are proportional to the long \(L\), respectively) and their shape matching with the typical capture object.  
The position of the markers was identified from the picture to acquire corresponding 3-D coordinates at each moment. It is well-known that the clearer the image, the more recognizable the markers.  
The depth of field has a significant correlation with the layout of the camera. Seen in Figure 4a, the depth of field (the yellow area), which is covered by the visual angle of the camera, has intersecting volume characteristics that are the same as a multi-camera system. As shown in Figure 4b, the half-annular layout has a significantly larger depth of field than the other layouts. It can be directly determined that the corresponding depth of field is determined by _WD_ and \(f\) (Figure 4c). The length (\(L\)) represents the depth of field area segmented by the motion plane and increases as \(\alpha\) increases, while the field of view volume decreases as \(\alpha\) increases when the camera's field of view is divided by the work plane. Therefore, the relationship between the depth of field and the field of view volume should be balanced according to the different motion characteristics of the small animal of interest. When the sampling motion area of the small animal is a long channel, a relatively small angle of pitch is sufficient. The selection of the motion area of different small animals is restrictive and it needs to be considered comprehensively based on the locomotion characteristics, the camera's depth of field and the pitch angle of the camera.  
We proposed the layout method of multi-camera based on a rectangular planar 3D force measuring platform (length 300 mm). Since the pitch angle imposed limitations on the depth of field, it was necessary to select an appropriate pitch angle. According to the size constraint of the target motion plane, the working distance could be adjustable within the range from 350 mm to 700 mm. When _WD_ was 350 mm, the depth of field was about 120 mm. To ensure that \(L\) was greater than 300 mm, \(\alpha\) should be greater than or equal to 66.5\({}^{\circ}\). In addition, when _WD_ was greater than or equal to 540 mm, the depth of field could be more than 300 mm and then, \(\alpha\) could optionally be any value within the defined domain.  
Figure 4: Relationship between camera depth of field and remaining work planes (**a**) Depth of camera area; (**b**) Depth of field area in the form of three camera layouts; (**c**) With the same depth of field, the intersection of the field of view of two cameras with different pitch angles and the working plane.