Steerable properties dominate the design of traditional filters, e.g., Gabor filters, and endow features the capability of dealing with spatial transformations. However, such excellent properties have not been well explored in the popular deep convolutional neural networks (DCNNs). In this paper, we propose a new deep model, termed Gabor Convolutional Networks (GCNs or Gabor CNNs), which incorporates Gabor filters into DCNNs to enhance the resistance of deep learned features to the orientation and scale changes. By only manipulating the basic element of DCNNs based on Gabor filters, i.e., the convolution operator, GCNs can be easily implemented and are compatible with any popular deep learning architecture. Experimental results demonstrate the super capability of our algorithm in recognizing objects, where the scale and rotation changes occur frequently. The proposed GCNs have much fewer learnable network parameters, and thus is easier to train with an endto-end pipeline.

Abstract-In steerable filters, a filter of arbitrary orientation can be generated by a linear combination of a set of "basis filters". Steerable properties dominate the design of the traditional filters e.g., Gabor filters and endow features the capability of handling spatial transformations. However, such properties have not yet been well explored in the deep convolutional neural networks (DCNNs). In this paper, we develop a new deep model, namely Gabor Convolutional Networks (GCNs or Gabor CNNs), with Gabor filters incorporated into DCNNs such that the robustness of learned features against the orientation and scale changes can be reinforced. By manipulating the basic element of DCNNs, i.e., the convolution operator, based on Gabor filters, GCNs can be easily implemented and are readily compatible with any popular deep learning architecture. We carry out extensive experiments to demonstrate the promising performance of our GCNs framework and the results show its superiority in recognizing objects, especially when the scale and rotation changes take place frequently. Moreover, the proposed GCNs have much fewer network parameters to be learned and can effectively reduce the training complexity of the network, leading to a more compact deep learning model while still maintaining a high feature representation capacity. The source code can be found at https://github.com/bczhangbczhang .

Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group of images obtains the best performance. The idea is equivalent to estimating variable distribution based on the data sampling (bagging), which can be interpreted as finding solutions (variable distribution approximation) directly from sampled data space. However, this methodology fails to account for the variations existed in the data. In this paper, we introduce an intermediate step-solution sampling-after the data sampling step to form a subspace, in which an optimal solution can be estimated. More specifically, we propose a new method, named latent constrained correlation filters (LCCF), by mapping the correlation filters to a given latent subspace, and develop a new learning framework in the latent subspace that embeds distribution-related constraints into the original problem. To solve the optimization problem, we introduce a subspace-based alternating direction method of multipliers, which is proven to converge at the saddle point. Our approach is successfully applied to three different tasks, including eye localization, car detection, and object tracking. Extensive experiments demonstrate that LCCF outperforms the state-of-the-art methods. .

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