To address challenges involving low accuracy in feature point matching, low matching speed, cracks at the stitching points, and extended stitching time in vehicle undercarriage threat detection imaging, an optimized image-stitching algorithm is proposed. First, the corner detection (FAST) algorithm is used to extract image feature points, and then, the binary robust invariant scalable key point (BRISK) algorithm is used to describe the retained feature points. Second, the fast nearest neighbor search (FLANN) algorithm is used for coarse matching. Next, the progressive uniform sampling (PROSAC) algorithm is used for feature point purification. Finally, the Laplace pyramid algorithm is used for image fusion and stitching. The experimental results show that, when compared with SIFT, SURF, and ORB algorithms, the proposed algorithm improves the image feature matching accuracy by 13.10 percentage points, 8.59 percentage points, and 11.27 percentage points, respectively, in the image data of dangerous objects under the vehicle. The matching time is shortened by 76.26%, 85.36%, and 10.27%, respectively. The image-stitching time is shortened by 63.73%, 64.21%, and 20.07%, respectively, and there are no evident cracks at the stitching point. Therefore, the image-stitching algorithm based on the combination of FAST, BRISK, PROSAC, and Laplace pyramid is a high-quality fast image-stitching algorithm.