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This paper proposes a novel feature-based invariant descriptor termed Radon composite features (RCFs) for planar shapes. Instead of analyzing shapes directly in the spatial domain, some shape features are extracted from the Radon transform plane using statistical and spectral analysis. The proposed method overcomes the drawbacks of existing shape representation techniques since it accomplishes the invariances to common geometrical transformations without any normalization process, which usually causes inaccuracies. A novel hierarchical strategy with RCFs can achieve low complexity and coarse-to-fine retrieval, and perform accurately when retrieving shapes, while remaining robust against variations. Experiments demonstrate that RCF provides a higher degree of discrimination as compared with several state-of-the-art approaches.