Accurate segmentation of spinal structures in X-ray images is a prerequisite for quantitative scoliosis assessment, including Cobb angle measurement, vertebral translation estimation and curvature classification. In routine practice, clinicians acquire coronal, left-bending and right-bending radiographs to jointly evaluate deformity severity and spinal flexibility. However, the segmentation step remains heavily manual, time-consuming and non-reproducible, particularly in low-contrast images and in the presence of rib shadows or overlapping tissues. To address these limitations, this paper proposes R2MF-Net, a recurrent residual multi-path encoder--decoder network tailored for automatic segmentation of multi-directional spine X-ray images. The overall design consists of a coarse segmentation network and a fine segmentation network connected in cascade. Both stages adopt an improved Inception-style multi-branch feature extractor, while a recurrent residual jump connection (R2-Jump) module is inserted into skip paths to gradually align encoder and decoder semantics. A multi-scale cross-stage skip (MC-Skip) mechanism allows the fine network to reuse hierarchical representations from multiple decoder levels of the coarse network, thereby strengthening the stability of segmentation across imaging directions and contrast conditions. Furthermore, a lightweight spatial-channel squeeze-and-excitation block (SCSE-Lite) is employed at the bottleneck to emphasize spine-related activations and suppress irrelevant structures and background noise. We evaluate R2MF-Net on a clinical multi-view radiograph dataset comprising 228 sets of coronal, left-bending and right-bending spine X-ray images with expert annotations.