DISCO: accurate Discrete Scale Convolutions

TL;DR

This paper introduces DISCO, a novel discrete scale convolution method that achieves accurate scale equivariance in CNNs, improving performance on scale-sensitive vision tasks like classification and tracking.

Contribution

We derive exact constraints for discrete scale-convolution to ensure equivariance, enabling high-precision scale handling in CNNs for various vision applications.

Findings

State-of-the-art results on MNIST-scale classification

Improved STL-10 classification accuracy

Enhanced efficiency of scale-equivariant Siamese tracking

Abstract

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.