Abstract: This paper aims to solve the problems of the contradiction between the registration accuracy and the efficiency, and also the small registration capture range in the current 2D/3D medical image registration research. A hierarchical registration method based on principal direction Fourier transform operator (PDFTO) is proposed. Firstly, an operator with invariance of in-plane rotation and translation, PDFTO, is proposed. Then, a PDFTO-based template matching initialization method is proposed, which can avoid the requirement of an initial value that should be close to the true value, and can significantly expand the capture range. Finally, a hierarchical registration framework based on PDFTO is proposed, which reduces the searching space of registration from O(n⁶) to O(n²), and greatly improves the efficiency of registration while ensuring the accuracy of registration. In the registration experiments, the registration accuracy of the proposed method is 0.68 mm ±0.28 mm, the registration time is 16.87 s ±3.77 s, and the capture range is larger than 100 mm. Therefore, the proposed PDFTO-based hierarchical registration method can meet the requirements for the accuracy, the efficiency and the capture range in 2D/3D image registration in related clinical applications.