Purpose - This paper aims to present the spherical entropy image (SEI), a novel global descriptor for the scan registration of three-dimensional (3D) point clouds. This paper also introduces a global feature-less scan registration strategy based on SEI. It is advantageous for 3D data processing in the scenarios such as mobile robotics and reverse engineering. Design/methodology/approach - The descriptor works through representing the scan by a spherical function named SEI, whose properties allow to decompose the six-dimensional transformation into 3D rotation and 3D translation. The 3D rotation is estimated by the generalized convolution theorem based on the spherical Fourier transform of SEI. Then, the translation recovery is determined by phase only matched filtering. Findings - No explicit features and planar segments should be contained in the input data of the method. The experimental results illustrate the parameter independence, high reliability and efficiency of the novel algorithm in registration of feature-less scans. Originality/value - A novel global descriptor (SEI) for the scan registration of 3D point clouds is presented. It inherits both descriptive power of signature-based methods and robustness of histogram-based methods. A high reliability and efficiency registration method of scans based on SEI is also demonstrated.