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Feature extraction and selection are two important steps for shape retrieval. Given a data set, a set of features which describe the shape property from different aspects are extracted. Our goal is a learning-based methodology to select the features for improving retrieval performance. Our approach uses both global and local feature descriptors. The global shape features include geometric ones (elongation, eccentricity, roughness, and compactness), Fourier descriptors with complex coordinates, Fourier descriptors with Centroid Contour Distance Curve, Coefficients of Fourier Expansion of Bent function, moment invariants, and local shape features that include turn angle and Distance Across the Shape. We propose a learning-based feature selection algorithm as a strategy for optimizing retrieval performance. We provide results from the vertebra shape dataset created from our database containing spine X-rays from the National Health and Nutrition Examination Survey (NHANES II). Finally, we compare the retrieval performances of feature descriptors on ldquowhole shaperdquo and ldquocorner shaperdquo datasets. The experimental results show that various feature descriptors perform differently on different datasets, and that feature selection schemes improve the retrieval performance significantly.