Incorporating either rotation equivariance or scale equivariance into CNNs has proved to be effective in improving models' generalization performance. However, jointly integrating rotation and scale equivariance into CNNs has not been widely explored. Digital histology imaging of biopsy tissue can be captured at arbitrary orientation and magnification and stored at different resolutions, resulting in cells appearing in different scales. When conventional CNNs are applied to histopathology image analysis, the generalization performance of models is limited because 1) a part of the parameters of filters are trained to fit rotation transformation, thus decreasing the capability of learning other discriminative features; 2) fixed-size filters trained on images at a given scale fail to generalize to those at different scales. To deal with these issues, we propose the Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates steerable filters and scale-space theory. The RSESF contains copies of filters that are linear combinations of Gaussian filters, whose direction is controlled by directional derivatives and whose scale parameters are trainable but constrained to span disjoint scales in successive layers of the network. Extensive experiments on two gland segmentation datasets demonstrate that our method outperforms other approaches, with much fewer trainable parameters and fewer GPU resources required. The source code is available at: https://github.com/ynulonger/RSESF.

翻译：将旋转等变或尺度等变融入卷积神经网络已被证明能有效提高模型的泛化性能。然而，将旋转与尺度等变联合集成到卷积神经网络中尚未得到广泛探索。活检组织切片的数字组织学图像可在任意方向和放大倍数下采集，并以不同分辨率存储，导致细胞呈现不同尺度。当传统卷积神经网络应用于组织病理学图像分析时，模型的泛化性能受限，原因在于：1）滤波器参数中有一部分用于拟合旋转变换，从而降低了学习其他判别性特征的能力；2）在给定尺度图像上训练的固定尺寸滤波器无法泛化至其他尺度的图像。为解决这些问题，我们提出旋转-尺度等变可操控滤波器（RSESF），该滤波器融合了可操控滤波器与尺度空间理论。RSESF包含滤波器的多个副本，这些副本是高斯滤波器的线性组合，其方向由方向导数控制，尺度参数虽可训练但被约束为在网络连续层中覆盖不相交的尺度。在两个腺体分割数据集上的大量实验表明，我们的方法以更少的可训练参数和更低的GPU资源需求，优于其他方法。源代码见：https://github.com/ynulonger/RSESF。