The promising achievement of sparse ranking in image-based recognition gives rise to a number of development on person re-identification (Re-ID) which aims to reconstruct the probe as a linear combination of few atoms/images from an over-complete dictionary/gallery. However, most of the existing sparse ranking based Re-ID methods lack considering the geometric relationships between probe, gallery, and cross-modal images of the same person in multi-shot Re-ID. In this paper, we propose a novel joint graph regularized dictionary learning and sparse ranking method for multi-modal multi-shot person Re-ID. First, we explore the probe-based geometrical structure by enforcing the smoothness between the codings/coefficients, which refers to the multi-shot images from the same person in probe. Second, we explore the gallery-based geometrical structure among gallery images, which encourages the multi-shot images from the same person in the gallery making similar contributions while reconstructing a certain probe image. Third, we explore the cross-modal geometrical structure by enforcing the smoothness between the cross-modal images and thus extend our model for the multi-modal case. Finally, we design an APG based optimization to solve the problem. Comprehensive experiments on benchmark datasets demonstrate the superior performance of the proposed model. The code is available at https://github.com/ttaalle/Lhc.
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