Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 30, Issue -, Pages 8342-8353Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2021.3115001
Keywords
Shape; Spatial resolution; Taylor series; Kernel; Standards; Network architecture; Wavelet transforms; Scale-space theory; Gaussian basis approximation; resolution learning in deep networks
Funding
- Dutch Research Council (NWO) through the Project Pixel-Free Deep Learning by the Research Program TOP [612.001.805]
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Modern convolutional neural networks often hard-code resolution hyperparameters in the network architecture, making it difficult to adjust, while the proposed N-Jet layer can automatically learn the correct resolution for each layer and performs well under various input sizes.
Resolution in deep convolutional neural networks (CNNs) is typically bounded by the receptive field size through filter sizes, and subsampling layers or strided convolutions on feature maps. The optimal resolution may vary significantly depending on the dataset. Modern CNNs hard-code their resolution hyper-parameters in the network architecture which makes tuning such hyper-parameters cumbersome. We propose to do away with hard-coded resolution hyper-parameters and aim to learn the appropriate resolution from data. We use scale-space theory to obtain a self-similar parametrization of filters and make use of the N-Jet: a truncated Taylor series to approximate a filter by a learned combination of Gaussian derivative filters. The parameter sigma of the Gaussian basis controls both the amount of detail the filter encodes and the spatial extent of the filter. Since sigma is a continuous parameter, we can optimize it with respect to the loss. The proposed N-Jet layer achieves comparable performance when used in state-of-the art architectures, while learning the correct resolution in each layer automatically. We evaluate our N-Jet layer on both classification and segmentation, and we show that learning sigma is especially beneficial when dealing with inputs at multiple sizes.
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