Neck pain is one of the most common symptoms of cervical spine disease, and segmenting neck muscles to create volumetric measurements may assist clinical diagnosis. While image registration is used to segment medical images, registration is highly challenging for neck muscles due to their tight proximity, shape and size variations among subjects, and similar appearance. These challenges cause conventional multi resolution-based registration methods to be trapped in local minima due to their low degree of freedom geometrical transforms. This article presents a novel object-constrained hierarchical registration framework for aligning inter-subject neck muscles. First, to handle large scale local minima, the proposed framework uses a coarse registration technique, which optimizes the new edge position difference (EPD) similarity measure, to align large mismatches. Also, a new transformation based on the discrete periodic spline wavelet (DPSW), affine and free-form-deformation (FFD) transformations are exploited. Second, to avoid monotonous nature of using transformations in multiple stages, a fine registration technique is designed for aligning small mismatches. This technique uses a double-pushing system by changing edges in the EPD and switching transformation resolutions. The EPD helps in both coarse and fine techniques to implement object-constrained registration via controlling edges, which is not possible when using traditional similarity measures. Experiments are performed on clinical 3D magnetic resonance imaging (MRI) scans of the neck, with the results showing that the EPD is more effective than the mutual information (MI) and sum of squared difference (SSD) measure in terms of volumetric dice similarity coefficient (DSC). Additionally, the proposed method is compared with the diffeomorphic Demons and SyN state-of-the-art approaches with ablation studies in inter-subject deformable registration. The proposed method achieves better accuracy, robustness and consistency than the reference methods, with an average volumetric DSC of 0.7029 compared to 0.6654 and 0.6606 for the Demons and SyN methods, respectively.