Digital histopathology slides are scanned and viewed under different magnifications and stored as images at different resolutions. Convolutional Neural Networks (CNNs) trained on such images at a given scale fail to generalise to those at different scales. This inability is often addressed by augmenting training data with re-scaled images, allowing a model with sufficient capacity to learn the requisite patterns. Alternatively, designing CNN filters to be scale-equivariant frees up model capacity to learn discriminative features. In this paper, we propose the Scale-Equivariant UNet (SEUNet) for image segmentation by building on scale-space theory. The SEUNet contains groups of filters that are linear combinations of Gaussian basis filters, whose scale parameters are trainable but constrained to span disjoint scales through the layers of the network. Extensive experiments on a nuclei segmentation dataset and a tissue type segmentation dataset demonstrate that our method outperforms other approaches, with much fewer trainable parameters.

翻译：数字组织病理学切片在不同放大倍数下扫描和观察，并以不同分辨率存储为图像。在特定尺度下训练的卷积神经网络（CNN）无法泛化到不同尺度的图像。这种局限性通常通过使用重缩放图像增强训练数据来解决，使具备足够容量的模型能够学习所需模式。另一种方法是将CNN滤波器设计为尺度等变的，从而释放模型容量以学习判别性特征。本文基于尺度空间理论，提出了用于图像分割的尺度等变UNet（SEUNet）。SEUNet包含多组滤波器，这些滤波器是高斯基滤波器的线性组合，其尺度参数可训练但受限于在网络的各层中跨越不相交的尺度。在细胞核分割数据集和组织类型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优于其他方法。