Shape-based retrieval of vertebral x-ray images is a challenging task because of high similarity among the vertebral shapes. Most techniques, such as global shape properties or scale space filtering, lose or fail to detect local details. As the result of this shortfall, the number of retrieved images is so high that the retrieval result is sometimes meaningless. To retrieve a small number of best matched images, shape representation and similarity measurement techniques must distinguish shapes with minor variations. The main challenge of shape-based retrieval is to define a shape representation method that is invariant with respect to rotation, translation, scaling, and the curve starting point shift. In this research, a polygon curve evolution technique was developed for smoothing polygon curves and reducing the number of data points while preserving the significant pathology of the shape. The x and y coordinates of the simplified boundary points were then converted into a bend angle versus normalized curvature length function to represent the curve. Finally, the Fourier descriptors of the shape representation were calculated for similarity measurement. This approach meets the invariance requirements and has been proved to be efficient and accurate.