Deformable medical image registration is essential in medical image analyses. Recent transformer-based registration methods have achieved high registration accuracy. However, these methods often rely on patch embedding at the beginning of encoding, resulting in limited ability to capture detailed anatomical structural information in the images and explore local semantic relationships within individual patches. Here, we proposed a novel Dual-feet Encoder (DFEnc) to asynchronously model semantic information from moving and fixed images at various scales through two separate branches in three steps. For each step, features from adjacent resolution levels were processed by a Single Step Hybrid Extractor (SSHExt), which performed patch convolution to preserve local information, followed by several transformer blocks to capture global context. Dense connections were employed to enhance semantic awareness across adjacent feature resolution levels. Additionally, we introduced a Feature Fusion-based Decoder (FFDec) to progressively fuse features related to the fixed and moving images and to generate intermediate deformation fields at each stage, enabling accurate image alignment through stepwise warping and alignment refinement. Extensive ablation studies demonstrated the effectiveness of the proposed DFEnc, SSHExt, and FFDec. Compared to a state-of-the-art AutoFuse-Trans method, our approach yielded improvements in Dice of 1.14%, 1.77%, and 4.47% on the ACDC, OASIS, and Abdomen CT datasets, respectively, while maintaining relatively low computational cost. These results suggest the utility of the proposed approach for broad research and clinical applications.

MOTIVATION: Inferring gene networks provides insights into biological pathways and functional relationships among genes. When gene expression samples exhibit heterogeneity, they may originate from unknown subtypes, prompting the utilization of mixture Gaussian graphical model (GGM) for simultaneous subclassification and gene network inference. However, this method overlooks the heterogeneity of network relationships across subtypes and does not sufficiently emphasize shared relationships. Additionally, GGM assumes data follows a multivariate Gaussian distribution, which is often not the case with zero-inflated scRNA-seq data. RESULTS: We propose an Adaptive Joint Graphical Model (AJGM) for estimating multiple gene networks from single-cell or bulk data with unknown heterogeneity. In AJGM, an overall network is introduced to capture relationships shared by all samples. The model establishes connections between the subtype networks and the overall network through adaptive weights, enabling it to focus more effectively on gene relationships shared across all networks, thereby enhancing the accuracy of network estimation. On synthetic data, the proposed approach outperforms existing methods in terms of sample classification and network inference, particularly excelling in the identification of shared relationships. Applying this method to gene expression data from triple-negative breast cancer confirms known gene pathways and hub genes, while also revealing novel biological insights. AVAILABILITY AND IMPLEMENTATION: The Python code and demonstrations of the proposed approaches are available at https://github.com/yyytim/AJGM, and the software is archived in Zenodo with DOI: 10.5281/zenodo.14740972.