HNSF Log‐Demons: Diffeomorphic demons registration using hierarchical neighbourhood spectral features

Abstract Many biomedical applications require accurate non‐rigid image registration that can cope with complex deformations. However, popular diffeomorphic Demons registration algorithms suffer from difficulties for complex and serious distortions since they only use image greyscale and gradient information. To address these difficulties, a new diffeomorphic Demons registration algorithm is proposed using hierarchical neighbourhood spectral features namely HNSF Log‐Demons in this paper. In view of three important properties of hierarchical neighbourhood spectral features based on line graph such as rotation invariance, invariance of linear changes of brightness, and robustness to noise, the hierarchical neighbourhood spectral features of a reference image and a moving image is first extracted and these novel spectral features are incorporated into the energy function of the diffeomorphic registration framework to improve the capability of capturing complex distortions. Secondly, the Nyström approximation based on random singular value decomposition is employed to effectively enhance the computational efficiency of HNSF Log‐Demons. Finally, the hybrid multi‐resolution strategy based on wavelet decomposition in the registration process is utilised to further improve the registration accuracy and efficiency. Experimental results show that the proposed HNSF Log‐Demons not only effectively ensures the generation of smooth and reversible deformation field, but also achieves better performance than state‐of‐the‐art algorithms.