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 for inputs at multiple sizes.

使用 N-Jet 层，通过学习 Gaussian 导数滤波器的组合来自动学习每层正确的分辨率，优化连续参数 σ 从而实现有效的分类和分割。