Fast Low-rank Representation based Spatial Pyramid Matching for Image Classification

Recently, Spatial Pyramid Matching (SPM) with nonlinear coding strategies, e.g., sparse code based SPM (ScSPM) and locality-constrained linear coding (LLC), have achieved a lot of success in image classification. Although these methods achieve a higher recognition rate and take less time for classification than the traditional SPM, they consume more time to encode each local descriptor extracted from the image. In this paper, we propose using Low Rank Representation (LRR) in place of sparse code or vector quantization in the existing SPMs to encode the descriptors. The proposed method, called LrrSPM, calculates the lowest-rank representation by projecting each descriptor into a coordinate system; and forms a single representation based on the multiple-scale LRR. In addition, the paper proposes a fast and online method to obtain the LRR of each descriptor. Extensive experimental studies show that LrrSPM achieves competitive recognition rates and is 25– 50 times faster than ScSPM and 5–16 times faster than LLC on a range of databases.