Feature pooling is a key component in modern visual classification system. However, the conventional two prevailing pooling techniques, namely average and max poolings, are not theoretically optimal, due to the unrecoverable loss of the spatial information during the statistical summarization and the underlying over-simplified assumption about the feature distribution. Addressing these issues, this paper proposes to generalize previous pooling methods toward a weighted ℓ p -norm spatial pooling function tailored for class-specific feature spatial distribution. Optimizing such a pooling function toward discriminative class separability that is subject to a spatial smoothness constraint yields a so-called geometric ℓ p -norm pooling (GLP) method. Furthermore, to handle the variation of object scale/position, which would affect not only the learning of discriminative pooling weights but also the applicability of the learned weights, we propose a simple yet effective self-alignment step during both learning and testing to adaptively adjust the pooling weights for individual images. Image segmentation and visual saliency map are utilized to construct a directed pixel adjacency graph. The discriminative pooling weights are diffused using random walk on the constructed graph and therefore the discriminative pooling weights are propagated onto the salient and foreground region. This leads to a robust version of GLP (RGLP) which can cope with the misalignment of object position and scale in images. Comprehensive experiments validate the effectiveness of the proposed GLP feature pooling framework. The proposed random walk based self-alignment step can effectively alleviate the image misalignment issue and further boost classification accuracy. State-of-the-art image classification and action recognition performances are attained on several benchmarks. 
Robust geometric ℓ p -norm feature pooling for image classification and action recognition