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We propose two computational approaches for improving the retrieval of planar shapes. First, we suggest a geometrically motivated quadratic similarity measure, that is optimized by way of spectral relaxation of a quadratic assignment. By utilizing state-of-the-art shape descriptors and a pairwise serialization constraint, we derive a formulation that is resilient to boundary noise, articulations and nonrigid deformations. This allows both shape matching and retrieval. We also introduce a shape meta-similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy. When applied to the MPEG-7 shape dataset in conjunction with the proposed geometric matching scheme, we obtained a retrieval rate of 92.5%.