A Generalised Formulation for Collaborative Representation of Image Patches (GP-CRC)

Collaborative Representation based Categorization (CRC) represents query samples collaboratively as an optimal weighted average of training samples across all classes. It has been shown to be effective for recognition problems, but its performance degrades in presence of high variation in image background. We present a generalization mathematical reformulation of a patch based CRC approach. The proposed method (GP-CRC) analytically overcomes the problem in the cost function itself and provides a closed form solution. Experiments are carried out on two face recognition (AR and LFW) and two species recognition (Oxford-102 Flowers and Oxford-IIIT Pets) benchmarks. The proposed method outperforms the original CRC as well as basic patch based CRC consistently across all the datasets (with statistical significance in majority of the cases) and comparable or marginally higher accuracy than the state of the art probabilistic CRC. It is also demonstrated experimentally that our method is more robust to background variations than its competitors.