Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets.
Bilinear models were first introduced by Tenenbaum and Freeman @cite_13 to separate style and content. Second order pooling have since been considered for both semantic segmentation and fine grained recognition, using both hand-tuned @cite_28 , and learned features @cite_33 . Although repeatedly shown to produce state-of-the art results, it has not been widely adopted; we believe this is partly due to the prohibitively large dimensionality of the extracted features.
@cite_28 @cite_13 @cite_33
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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 a 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 [8], and three orders smaller than the standard bilinear CNN model [19]. Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets. Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets. We propose bilinear models, a recognition architecture that consists of two feature extractors whose outputs are multiplied using outer product at each location of the image and pooled to obtain an image descriptor. This architecture can model local pairwise feature interactions in a translationally invariant manner which is particularly useful for fine-grained categorization. It also generalizes various orderless texture descriptors such as the Fisher vector, VLAD and O2P. We present experiments with bilinear models where the feature extractors are based on convolutional neural networks. The bilinear form simplifies gradient computation and allows end-to-end training of both networks using image labels only. Using networks initialized from the ImageNet dataset followed by domain specific fine-tuning we obtain 84.1 accuracy of the CUB-200-2011 dataset requiring only category labels at training time. We present experiments and visualizations that analyze the effects of fine-tuning and the choice two networks on the speed and accuracy of the models. Results show that the architecture compares favorably to the existing state of the art on a number of fine-grained datasets while being substantially simpler and easier to train. Moreover, our most accurate model is fairly efficient running at 8 frames sec on a NVIDIA Tesla K40 GPU. The source code for the complete system will be made available at http: vis-www.cs.umass.edu bcnn.