# Research on a Fast Image-Matching Algorithm Based on Nonlinear Filtering
## 3 Experimental Results and Analysis
### Robustness Evaluation  
Image-processing algorithms maintain their ability to accurately and reliably identify similarities between corresponding points, regions, or features in different images, achieving effective matching capabilities even when confronted with various complex environmental conditions, image rotations, deformations, changes in illumination, viewpoint variations, and scale changes, among other factors. The robustness of such algorithms is assessed by performing feature point matching across diverse scenarios, thereby gauging their resilience under a range of challenging circumstances. The following formula is used to calculate the correctness of the five algorithms to match the correctness rateand judge the robustness of the algorithm [20]:  
\[P=N_{b}/N_{c} \tag{9}\]  
where the matching correctness is \(P\), \(N_{b}\) is the correct match remaining after eliminating the incorrect matches, and the total number of coarse matches is \(N_{c}\). Figure 3: Comparative effects of different methods for constructing scale spaces. (**a**) Gaussian filtered average downsampling image. (**b**) Gaussian filtered maximum downsampling image. (**c**) Nonlinear average downsampling image. (**d**) Nonlinear maximum downsampling image. The Mikolajczyk dataset is used in our experiments, and this experiment uses the Bark, Bikes, Leuven, Boat, and Graf image sets in this dataset, which contain factors such as image rotation, distortion, illumination change, perspective change, scale change, etc., and each image set contains six images. Each algorithm uses the first image in each set as a sample image and uses the remaining five images as the images to be matched for the matching test. The following table shows the average correctness of the different algorithms on the Mikolajczyk image dataset, as well as the total average correctness. Through an analysis of the data in Table 1, it can be concluded that the proposed fast image-matching algorithm based on nonlinear filtering exhibits excellent overall performance on this dataset. The total average correctness rate of the fastimage-matching algorithm based on nonlinear filtering is higher than that of other algorithms. In the Bark dataset with clearly visible texture features, the average correctness rate of matches is 12.86% higher than that of the SIFT algorithm. In the Bikes and Leuven datasets with lighting changes, the fast image-matching algorithm based on nonlinear filtering achieves an average correctness rate 10.18% higher than that of the SIFT algorithm. In the grayscale and rotation-changed Boat dataset, the fast image-matching algorithm based on nonlinear filtering outperforms the SIFT algorithm, with an average correctness rate that is 5.22% higher. In the Graf dataset with changes in viewpoint, the fast image-matching algorithm based on nonlinear filtering achieves an average correctness rate 8.89% higher than that of the SIFT algorithm. Additionally, the improved algorithm also surpasses the other three algorithms in scenarios involving texture features, lighting changes, grayscale transformation, rotation, and changes in viewpoint. In this paper, we take the Graf image set as an example to show the matching effect of the traditional SIFT matching algorithm and the fast image-matching algorithm based on nonlinear filtering, as shown in Figure 4.  
Figure 4 shows the feature point-matching test in the Graf images, with green indicating correct matches and red indicating incorrect matches. Figure 3(a) presents the results of the SIFT feature-matching algorithm and RANSAC algorithm, while Figure 3(b) shows the results of the fast image-matching algorithm based on nonlinear filtering. In this algorithm, an adaptive RANSAC algorithm is employed. From Figure 3(a), it can be observed that there are numerous cross mismatches in the SIFT algorithm, indicating incorrect matches. Compared to SIFT, the adaptive RANSAC algorithm in the fast image-matching algorithm based on nonlinear filtering effectively reduces incorrect matches, thereby enhancing accuracy.