Rotation Equivariant CNNs for Digital Pathology

TL;DR

The paper addresses robust tumor detection in digital pathology by exploiting rotation and reflection symmetries in histopathology images. It introduces a G-CNN–based DenseNet (P4M-DenseNet) that achieves rotation/reflection equivariance, improving both reliability and accuracy on patch- and slide-level tasks. A new PatchCamelyon patch-level dataset is introduced to enable principled benchmarking and rigorous comparisons. Experimental results on Camelyon16, PCam, and BreakHis show superior performance and data efficiency, especially in low-data regimes, demonstrating the practical value of symmetry-aware architectures in medical image analysis.

Abstract

We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysis showing improved stability on predictions, and demonstrate that exploiting rotation equivariance significantly improves tumor detection performance on a challenging lymph node metastases dataset. We further present a novel derived dataset to enable principled comparison of machine learning models, in combination with an initial benchmark. Through this dataset, the task of histopathology diagnosis becomes accessible as a challenging benchmark for fundamental machine learning research.

Figures (4)

• Figure 1: Given a canonical input and a rotated duplicate, we demonstrate how a 2-layer G-CNN is equivariant in $p4$. Feature maps of one kernel per layer are shown, and the dashed blue arrows indicate how (intermediate) representations of the two inputs correspond. The $\mathbb{Z}^2\rightarrow p4$ convolution correlates the input with 4 rotated versions of the same kernel. The $p4\rightarrow p4$ convolution correlates the resulting feature map with the $p4$-kernel, cyclically-shifting and rotating the kernel for each orientation. The final layer demonstrates how average-pooling over the orientations produces a representation that is locally invariant and globally equivariant to rotation. Global average pooling over $p4$ would result in a representation globally invariant to both translation and rotation.
• Figure 2: The proposed equivariant DenseNet architecture for the $p4$ group, consisting of 5 Dense Blocks (D.B.) alternated with Transition Blocks (T.B.). The final layer of the model is a $p4\rightarrow\mathbb{Z}^2$ group pooling layer followed by a sigmoid activation. The four orientations in $p4$ are illustrated through primary colors. A $\mathbb{Z}^2\rightarrow p4$ kernel (left), $p4\rightarrow p4$ kernel (middle) and $p4 \rightarrow \mathbb{Z}^2$ kernel (right) illustrate how equivariance arises in the model.
• Figure 3: (a) shows a large input region spanning multiple patches, with the tumor ground truth overlayed in green. The region is predicted under 32 evenly spaced sub-$90\degree$ rotations, and prediction maps rotated back to original orientation. (b) shows the mean prediction and (c) shows the standard deviation of the predictions across all rotations, using DenseNet (left) and P4M-DenseNet (right). Both networks are trained on the 12.5% data regime.
• Figure 4: Performance on the Camelyon16 test set. The confidence bounds are obtained using a 2000-fold bootstrap regime. *Challenge winner Wang2016-yf uses 40$\times$ resolution and is not directly comparable.