## 2 Materials and Methods
### Algorithm Performance Testing  
To test the effectiveness and robustness of the algorithm, we designed a testing experiment. In this experiment, we divided 260 images into three categories: low, medium, and high concentrations (low concentration: 0-50 \(\upmu\)g/mL, medium concentration: 80-500 \(\upmu\)g/mL, and high concentration: 800-1500 \(\upmu\)g/mL). We randomly applied salt-and-pepper noise, Gaussian noise, and Poisson noise to the images, as shown in Figure 13. Subsequently, we tested these noisy images using the algorithm proposed in this paper. At the same time, we tested  
Figure 11: SVM fitting of feature values and concentrations.  
Figure 12: Fitting error parameter chart.  
the accuracy of the algorithm on the samples without any noise added. The test results are shown in Table 3.  
After adding noises, the accuracy of the algorithm in detecting light-colored test strips with a low concentration drops from 88% to 71%. However, it still maintains a high accuracy for test strips with medium and high concentrations. This indicates that the algorithm performs better in detecting test strips with darker colors and higher concentrations. Despite the added noises, it still achieves an accuracy of 85% in detecting the test strips. This demonstrates the effectiveness of the algorithm, but further improvements are needed to enhance its ability to detect targets with low concentrations.  
Traditional image processing and machine learning methods, like KNN, CNN, and U-net, are widely used to analyze and detect LFIA images, but they require large training data sets and are sensitive to parameter changes, thus limiting their practical use. To address these issues, this study proposed a quantitative detection method for LFIA images based on image processing technology, which combines multiple image processing techniques and mathematical methods to effectively optimize LFIA imaging, thereby improving the accuracy and reliability of detection. The specific performance of the proposed algorithm and other common algorithms is shown in Table 4.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Algorithm** & **Accuracy (\%)** & **Sample Size** & **Goodness of Fit** \\ \hline This paper & 94.1 & 205 & 0.995 \\ \hline KNN & 95.56 & 1500 & 0.960 \\ \hline CNN & 92 & 120 & 0.987 \\ \hline U-net & 97.46 & 942 & \textgreater{}0.9 \\ \hline Image Processing & 94.5 & N/A & 0.993 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance of common algorithms.  
Figure 13: Example of adding salt-and-pepper noise, Gaussian noise, and Poisson noise to an image.  
A comparison was made on the performance of several algorithms in various applications. The KNN classifier developed by [PERSON] et al. achieved an accuracy of 95.56% in the quantification of Salmonella LFIA images with a large sample size of 1500 [19]. [PERSON] et al., using convolutional neural network (CNN), achieved an accuracy of 92% when detecting images of performance-enhancing drugs with a small sample size of 120 [20]. [PERSON] et al. adopted the U-net algorithm in deep learning and achieved the highest accuracy of 97.46% with 942 samples [21]. [PERSON] et al. proposed a multi-strip detection algorithm using image processing, which achieved an accuracy of 94.5% [22]. Compared to traditional image processing algorithms, the accuracy is slightly lower than KNN and U-net but slightly higher than CNN with insufficient sample size. The proposed algorithm shows better performance in cases with smaller sample sizes. Additionally, the proposed algorithm can be trained faster and demonstrates more stable performance in fitting.