In this paper, a new image-correction method for flange joint bolts is proposed. A checkerboard is arranged on the side of a flange node bolt, and the homography matrix can be estimated using more than four feature points, which include the checkerboard corner points. Then, the perspective distortion of the captured image and the deviation of the camera position angle are corrected using the estimated homography matrix. Due to the use of more feature points, the stability of homography matrix identification is effectively improved. Simultaneously, the influence of the number of feature points, camera lens distance, and light intensities are analyzed. Finally, based on a bolt image taken using an iPhone 12, the prototype structure of the flange joint in the laboratory is verified. The results show that the proposed method can effectively correct image distortion and camera position angle deviation. The use of more than four correction points not only effectively improves the stability of bolt image correction but also improves the stability and accuracy of bolt-loosening detection. The analysis of influencing factors shows that the proposed method is still effective when the number of checkerboard correction points is reduced to nine, and the average error of the bolt-loosening detection result is less than 1.5 degrees. Moreover, the recommended camera shooting distance range is 20 cm to 60 cm, and the method exhibits low sensitivity to light intensity.