Pooling second-order local feature statistics to form a high-dimensional bilinear feature has been shown to achieve state-of-the-art performance on a variety of fine-grained classification tasks. To address the computational demands of high feature dimensionality, we propose to represent the covariance features as a matrix and apply a low-rank bilinear classifier. The resulting classifier can be evaluated without explicitly computing the bilinear feature map which allows for a large reduction in the compute time as well as decreasing the effective number of parameters to be learned. To further compress the model, we propose classifier co-decomposition that factorizes the collection of bilinear classifiers into a common factor and compact per-class terms. The co-decomposition idea can be deployed through two convolutional layers and trained in an end-to-end architecture. We suggest a simple yet effective initialization that avoids explicitly first training and factorizing the larger bilinear classifiers. Through extensive experiments, we show that our model achieves state-of-the-art performance on several public datasets for fine-grained classification trained with only category labels. Importantly, our final model is an order of magnitude smaller than the recently proposed compact bilinear model, and three orders smaller than the standard bilinear CNN model.
Recently, a surprisingly simple method called bilinear pooling @cite_30 has achieved state-of-the-art performance on a variety of fine-grained classification problems. Bilinear pooling collects second-order statistics of local features over a whole image to form holistic representation for classification. Second-order or higher-order statistics have been explored in a number of vision tasks (see e.g. @cite_27 @cite_28 ). In the context of fine-grained recognition, spatial pooling introduces invariance to deformations while second-order statistics maintain selectivity.
@cite_30 @cite_27 @cite_28
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Feature extraction, coding and pooling, are important components on many contemporary object recognition paradigms. In this paper we explore novel pooling techniques that encode the second-order statistics of local descriptors inside a region. To achieve this effect, we introduce multiplicative second-order analogues of average and max-pooling that together with appropriate non-linearities lead to state-of-the-art performance on free-form region recognition, without any type of feature coding. Instead of coding, we found that enriching local descriptors with additional image information leads to large performance gains, especially in conjunction with the proposed pooling methodology. We show that second-order pooling over free-form regions produces results superior to those of the winning systems in the Pascal VOC 2011 semantic segmentation challenge, with models that are 20,000 times faster. Super-symmetric tensors – a higher-order extension of scatter matrices – are becoming increasingly popular in machine learning and computer vision for modeling data statistics, co-occurrences, or even as visual descriptors. They were shown recently to outperform second-order approaches [18], however, the size of these tensors are exponential in the data dimensionality, which is a significant concern. In this paper, we study third-order supersymmetric tensor descriptors in the context of dictionary learning and sparse coding. For this purpose, we propose a novel non-linear third-order texture descriptor. Our goal is to approximate these tensors as sparse conic combinations of atoms from a learned dictionary. Apart from the significant benefits to tensor compression that this framework offers, our experiments demonstrate that the sparse coefficients produced by this scheme lead to better aggregation of high-dimensional data and showcase superior performance on two common computer vision tasks compared to the state of the art.