3D point cloud registration based on local features is a core problem in the field of computer vision and robotics, and most of the existing 3D local feature descriptors are of floating-point type. In this paper, a binary local feature descriptor, the Binary Depth Image Descriptor (BDIF), is proposed for describing 3D local features, and a registration algorithm based on the BDIF is also put forward for point cloud registration of large scenes. The BDIF encodes the local structure as a bit string based on the distance of the local surface to the projection plane. Specifically, the BDIF descriptor establishes a local reference frame near the keypoints to achieve rotational invariance, and then encodes the spatial information on three orthogonal projection surfaces. After that, binarization is completed based on the thresholding method and the segmentation threshold is determined using the maximum inter-class variance. An efficient point cloud registration algorithm is developed based on BDIF, which employs the adaptive scale Welsch to estimate the spatial variation parameters, and can effectively deal with the point cloud data collected from large scenes. Finally, extensive experiments are conducted on Retrieval and WHU-TLS datasets, respectively, and the experimental results demonstrate the effectiveness and overall superiority of the BDIF and BDIF-based point cloud registration algorithm proposed in this paper.