Scale-Aware Network with Scale Equivariance

Abstract

The convolutional neural network (CNN) has achieved good performance in object classification due to its inherent translation equivariance, but its scale equivariance is poor. A Scale-Aware Network (SA Net) with scale equivariance is proposed to estimate the scale during classification. The SA Net only learns samples of one scale in the training stage; in the testing stage, the unknown-scale testing samples are up-sampled and down-sampled, and a group of image copies with different scales are generated to form the image pyramid. The up-sampling adopts interpolation, and the down-sampling adopts interpolation combined with wavelet transform to avoid spectrum aliasing. The generated test samples with different scales are sent to the Siamese network with weight sharing for inferencing. According to the position of the maximum value of the classification-score matrix, the testing samples can be classified and the scale can be estimated simultaneously. The results on the MNIST and FMNIST datasets show that the SA Net has better performance than the existing methods. When the scale is larger than 4, the SA Net has higher classification accuracy than other methods. In the scale-estimation experiment, the SA Net can achieve low relative RMSE on any scale. The SA Net has potential for effective use in remote sensing, optical image recognition and medical diagnosis in cytohistology.

Alias-Free Convnets: Fractional Shift Invariance via Polynomial Activations

“…It is worth mentioning that other equivariance properties have been studied as well, such as rotation, reflection and group equivariance [Delchevalerie et al, 2021, Bronstein et al, 2016, Xu et al, 2021, Ning et al, 2022, Manfredi and Wang, 2020, Romero et al, 2020, Yeh et al, 2022, Weiler and Cesa, 2019, Delchevalerie et al, 2021. This work is focused on the specific property of shift-invariance in CNNs for image classification.…”