**Feng Yang 1,2, Mingyue Ding <sup>1</sup> and Xuming Zhang 1,\***


Received: 15 August 2019; Accepted: 23 October 2019; Published: 28 October 2019

**Abstract:** The non-rigid multi-modal three-dimensional (3D) medical image registration is highly challenging due to the difficulty in the construction of similarity measure and the solution of non-rigid transformation parameters. A novel structural representation based registration method is proposed to address these problems. Firstly, an improved modality independent neighborhood descriptor (MIND) that is based on the foveated nonlocal self-similarity is designed for the effective structural representations of 3D medical images to transform multi-modal image registration into mono-modal one. The sum of absolute differences between structural representations is computed as the similarity measure. Subsequently, the foveated MIND based spatial constraint is introduced into the Markov random field (MRF) optimization to reduce the number of transformation parameters and restrict the calculation of the energy function in the image region involving non-rigid deformation. Finally, the accurate and efficient 3D medical image registration is realized by minimizing the similarity measure based MRF energy function. Extensive experiments on 3D positron emission tomography (PET), computed tomography (CT), T1, T2, and proton density (PD) weighted magnetic resonance (MR) images with synthetic deformation demonstrate that the proposed method has higher computational efficiency and registration accuracy in terms of target registration error (TRE) than the registration methods that are based on the hybrid L-BFGS-B and cat swarm optimization (HLCSO), the sum of squared differences on entropy images, the MIND, and the self-similarity context (SSC) descriptor, except that it provides slightly bigger TRE than the HLCSO for CT-PET image registration. Experiments on real MR and ultrasound images with unknown deformation have also be done to demonstrate the practicality and superiority of the proposed method.

**Keywords:** medical image registration; similarity measure; non-rigid transformation; computational efficiency; registration accuracy
