## 4 Experiments and Analysis
### Experiment 1: DAH Pattern Performance  
The first experiment investigates the viability of the proposed DAH pattern. In order to assess its effectiveness, we conducted a performance comparison between the proposed DAH pattern and the extensively employed fiducial marker. Noteworthy examples of  
Figure 4: The hardware design of the FiMa-Reader system. fiducial markers commonly applied in practical scenarios encompass AprilTag, ArUco, DM codes, and QR codes. ArUco and AprilTag are both variants of ARTag, sharing identical pattern designs and appearances. ArUco also supports the AprilTag dictionary. The differences between them lie in image preprocessing and candidate region search methods. Compared to AprilTag, ArUco exhibits significantly faster detection and decoding speeds, a crucial metric for real-time calculations on embedded platforms. Hence, we consider AprilTag and ArUco as equivalent, with ArUco being the superior choice. This is the reason we selected ArUco as a comparative option. Similarly, QR codes and DM codes are both traditional codes used for storing substantial information. The only difference lies in the Finder pattern. QR codes have three concentric rectangles as their Finder pattern, while DM codes have an L-shaped Finder pattern. This means DM codes can accommodate more valid information in a smaller area, which is one reason we chose DM codes as a control group. Another reason is that in open-source detection algorithms, DM codes consistently exhibit better recognition accuracy than QR codes. Building upon the aforementioned deliberations, we have selected ArUco, DM codes, and a pattern wherein the DM is enveloped by a homocentric square (referred to as the DM with Box) as the designated control groups. All markers were same size of 50 mm and the same surface material was used for printing. We employed the ArUco library ([[https://sourceforge.net/projects/aruco/files/](https://sourceforge.net/projects/aruco/files/)]([https://sourceforge.net/projects/aruco/files/](https://sourceforge.net/projects/aruco/files/)), accessed on 22 October 2022) to detect the ArUco marker, and the ZXing library ([[https://github.com/glassechidna/zxing-cpp](https://github.com/glassechidna/zxing-cpp)]([https://github.com/glassechidna/zxing-cpp](https://github.com/glassechidna/zxing-cpp)), accessed on 22 October 2022) to detect the DM. For the DM with the Box pattern, we used the framework described in Section 3.1.2 for detection, with the difference being that DM with Box pattern detection did not require detecting the ArUco and integrating the region into the DAH pattern. We created four different backgrounds to simulate the markers placed on different surfaces: clean, cage-like textured, line textured, and usual indoor background, as shown in Figure 5. For each background, we captured 25 images of each marker at different distances and angles. The hardware settings in all the following experiments are illustrated in Section 3.2. Considering the effective light range of the infrared fill-light, the maximum distance between the camera and marker was approximately 250 mm, while the minimum distance was approximately 50 mm. We also created random occlusion images from the original images by generating ten random circles within the manually labeled ROI for each original image, an occlusion image example can be found in Figure 5e-h.  
Figure 5: The origin and occlusion image dataset of the four different markers: the markers in (**a**) are the DAH pattern, Data Matrix, Data Matrix with Box, and ArUco in clockwise order, starting from the top left one. (**a**,**d**) are the original images. (**e**–**h**) are random occlusion images. (**a**,**e**): clean background. (**b**,**f**): cage-like textured background. (**c**,**g**): line texture background. (**d**,**h**): usual indoor background. The red circles in (**e**–**h**) represent randomly generated occlusion features by the computer.