Cracks are one of the main distresses that occur on concrete surfaces. Traditional methods for detecting cracks based on two-dimensional (2D) images can be hampered by stains, shadows, and other artifacts, while various three-dimensional (3D) crack-detection techniques, using point clouds, are less affected in this regard but are limited by the measurement accuracy of the 3D laser scanner. In this study, we propose an automatic crack-detection method that fuses 3D point clouds and 2D images based on an improved Otsu algorithm, which consists of the following four major procedures. First, a high-precision registration of a depth image projected from 3D point clouds and 2D images is performed. Second, pixel-level image fusion is performed, which fuses the depth and gray information. Third, a rough crack image is obtained from the fusion image using the improved Otsu method. Finally, the connected domain labeling and morphological methods are used to finely extract the cracks. Experimentally, the proposed method was tested at multiple scales and with various types of concrete crack. The results demonstrate that the proposed method can achieve an average precision of 89.0%, recall of 84.8%, and F1 score of 86.7%, performing significantly better than the single image (average F1 score of 67.6%) and single point cloud (average F1 score of 76.0%) methods. Accordingly, the proposed method has high detection accuracy and universality, indicating its wide potential application as an automatic method for concrete-crack detection.