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 filter sizes are required. Current SE-CNNs rely on weight sharing and filter 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 improving the results on STL-10. 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。

DISCO：精准离散尺度卷积