## 4 Proposed Moving Object Detection Method
The distance \(d\) between the epipolar line and the feature point can be calculated by the following equation  
Figure 3:1  
where \(u\) and \(v\) are the coordinates of the feature point, and \(a\), \(b\), and \(c\) represent the coefficient of the epipolar line, \(ax+by+c=0\). The feature points of distances that are greater than the threshold are considered to be a moving object. The result of the classification may vary depending on the threshold value setting. In our test configuration, a threshold of 1.0 pixel (in \(800\times 600\) resolution image) provided the best results in the classification accuracy, which means that the feature points with more than a 1.0 pixel distance from the epipolar line are considered the moving object. Figure 6 shows the feature point classification with the example images. The red points are classified as moving feature points and the white points as background feature points. Figure 3:2 Epipolar line drawn (lower) on example images (upper). (**a**) Example image 1; (**b**) example image 2; (**c**) example image 3. Figure 3:3 Feature point classification with example images. (**a**) Example image 1; (**b**) example image 2; (**c**) example image 3. To calculate a more precise fundamental matrix, the normalized eight-point algorithm [31] is applied only to the background feature points. Then, a more accurate epipolar line can be newly drawn, and the background classification becomes more accurate. This process removes the outliers (foreground) that are initially classified as background feature points. The whole classification process can be applied iteratively until it converges to minimize the error. In addition, the RANSAC technique [33] is also applied to eliminate the outliers, if any, in the background classified feature points. After the background classification, the transformation matrix can be obtained from decomposition of the fundamental matrix. The obtained transformation matrix is applied to the image to compensate for the motion of the background in the consecutive images. The difference map of the two consecutive images then shows the foreground region. However, there exist a few outliers which are caused by a small movement in the background, such as trees shaking in the wind, etc. These outliers can be removed by denoising and image erosion. Then, the obtained foreground regions are extracted by morphological image processing [27; 30]. Figure 7 shows the example of the morphological image processing. Finally, the minimum bounding boxes are applied to the foreground region to mark the moving object. Figure 8 shows examples of the result. Figure 8 shows the result of the proposed method, and Figure 8 shows the ground truth for the example images. The proposed method detects the multiple moving objects except for the occluded objects or small (far) objects which has little feature points to detect. Figure 3:4 Bounding box on the example images. (**a**) Proposed method on example image 1; (**b**) proposed method on example image 2; (**c**) proposed method on example image 3; (**d**) ground truth of example image 1; (**e**) ground truth of example image 2; (**f**) ground truth of example image 3. Figure 3:5 Extracted foreground region with example images. (**a**) Example image 1; (**b**) example image 2; (**c**) example image 3.