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Register a new userWhy Convolutional Networks Learn Oriented Bandpass Filters: Theory and Empirical Support
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Isma Hadji
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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It has been repeatedly observed that convolutional architectures when applied to image understanding tasks learn oriented bandpass filters. A standard explanation of this result is that these filters reflect the structure of the images that they have been exposed to during training: Natural images typically are locally composed of oriented contours at various scales and oriented bandpass filters are matched to such structure. We offer an alternative explanation based not on the structure of images, but rather on the structure of convolutional architectures. In particular, complex exponentials are the eigenfunctions of convolution. These eigenfunctions are defined globally; however, convolutional architectures operate locally. To enforce locality, one can apply a windowing function to the eigenfunctions, which leads to oriented bandpass filters as the natural operators to be learned with convolutional architectures. From a representational point of view, these filters allow for a local systematic way to characterize and operate on an image or other signal. We offer empirical support for the hypothesis that convolutional networks learn such filters at all of their convolutional layers. While previous research has shown evidence of filters having oriented bandpass characteristics at early layers, ours appears to be the first study to document the predominance of such filter characteristics at all layers. Previous studies have missed this observation because they have concentrated on the cumulative compositional effects of filtering across layers, while we examine the filter characteristics that are present at each layer.
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Image demoireing is a multi-faceted image restoration task involving both texture and color restoration. In this paper, we propose a novel multiscale bandpass convolutional neural network (MBCNN) to address this problem. As an end-to-end solution, MBCNN respectively solves the two sub-problems. For texture restoration, we propose a learnable bandpass filter (LBF) to learn the frequency prior for moire texture removal. For color restoration, we propose a two-step tone mapping strategy, which first applies a global tone mapping to correct for a global color shift, and then performs local fine tuning of the color per pixel. Through an ablation study, we demonstrate the effectiveness of the different components of MBCNN. Experimental results on two public datasets show that our method outperforms state-of-the-art methods by a large margin (more than 2dB in terms of PSNR).
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Convolutional neural networks (CNNs) have been successfully used in a range of tasks. However, CNNs are often viewed as black-box and lack of interpretability. One main reason is due to the filter-class entanglement -- an intricate many-to-many correspondence between filters and classes. Most existing works attempt post-hoc interpretation on a pre-trained model, while neglecting to reduce the entanglement underlying the model. In contrast, we focus on alleviating filter-class entanglement during training. Inspired by cellular differentiation, we propose a novel strategy to train interpretable CNNs by encouraging class-specific filters, among which each filter responds to only one (or few) class. Concretely, we design a learnable sparse Class-Specific Gate (CSG) structure to assign each filter with one (or few) class in a flexible way. The gate allows a filters activation to pass only when the input samples come from the specific class. Extensive experiments demonstrate the fabulous performance of our method in generating a sparse and highly class-related representation of the input, which leads to stronger interpretability. Moreover, comparing with the standard training strategy, our model displays benefits in applications like object localization and adversarial sample detection. Code link: https://github.com/hyliang96/CSGCNN.
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