Scale is often seen as a given, disturbing factor in many vision tasks. When
doing so it is one of the factors why we need more data during learning. In
recent work scale equivariance was added to convolutional neural networks. It
was shown to be effective for a range of tasks. We aim for accurate
scale-equivariant convolutional neural networks (SE-CNNs) applicable for
problems where high granularity of scale and small kernel sizes are required.
Current SE-CNNs rely on weight sharing and kernel rescaling, the latter of
which is accurate for integer scales only. To reach accurate scale
equivariance, we derive general constraints under which scale-convolution
remains equivariant to discrete rescaling. We find the exact solution for all
cases where it exists, and compute the approximation for the rest. The discrete
scale-convolution pays off, as demonstrated in a new state-of-the-art
classification on MNIST-scale and on STL-10 in the supervised learning setting.
With the same SE scheme, we also improve the computational effort of a
scale-equivariant Siamese tracker on OTB-13.

通过权重共享和卷积核重新缩放的方式，基于一些普遍的先决条件，建立了精确的尺度卷积等变性，并为所有情况找到了确切的解，并计算其余近似值。这种离散尺度卷积具有重要意义，能在 MNIST-scale 和 STL-10 的监督学习中达到最新分类性能，并通过 OTB-13 上尺度等变 Siamese 跟踪器改进了计算效率。