Traditional techniques for visualizing anatomical structures are based on planar sections from volume images, like images obtained by computed tomography (CT) or magnetic resonance imaging (MRI). However, planar slices taken in the coordinate system of the 3D image often do not provide sufficient or qualitative enough diagnostic information. The reason is that because planar slices do not follow curved anatomical structures (e.g. arteries, colon, spine, etc.), not all important details can be shown simultaneously. For better visualization of curved structures, reformatted images in the coordinate system of a structure must be created (an operation called curved planar reformation). In this paper we focus on automated curved planar reformation (CPR). The obtained spine-based 3D coordinate system is determined by the natural curvature of the spine, described by a curve that is parameterized by a polynomial model. The model is optimized to fit the curvature of the spine basing on the values of a pre-calculated distance map. The first coordinate is defined by the resulting spine curve, while the other two coordinates are defined by the natural rotations of the vertebrae around the spine curve. The proposed approach benefits from reduced structural complexity in favor of improved feature perception of the spine, and is not only important for extracting diagnostically important images, but also for easier navigation, manipulation and orientation in 3D space, which is helpful for morphometric analysis, automated image analysis (e.g. segmentation), and normalization of spine images.