1. A system for visualizing an object in image data using a first curvilinear cross-section surface coupled to an anatomical structure model of the object, the system comprising: a model unit, executed by a microprocessor, that adapts the anatomical structure model to the object in the image data; a surface unit, executed by the microprocessor, that adapts the first curvilinear cross-section surface to the adapted anatomical structure model based on the coupling between the first curvilinear cross-section surface and the anatomical structure model, wherein the surface unit further adapts a second curvilinear cross-section surface to the anatomical structure model of the object based on the coupling between the second curvilinear cross-section surface and the anatomical structure model, wherein the surface unit further adapts a third curvilinear cross-section surface that is perpendicular to the first curvilinear cross-section surface to the anatomical structure model of the object, wherein the third curvilinear cross-section surface is elastically coupled to first, second, third, fourth and fifth control points, wherein the first control point and the second control point are located at a tip of a respective first and second transverse process, wherein the third control point is located on a right pedicle and the fourth control point is located on a left pedicle, wherein the fifth control point is located on a vertebral foramen; and a visualization unit, executed by the microprocessor, that computes an image from the image data based on the adapted first curvilinear cross-section surface, the adapted second curvilinear cross-section surface, and the adapted third curvilinear cross-section surface.