Roto-Translation Covariant Convolutional Networks for Medical Image Analysis (1804.03393v3)

Abstract: We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in a net roto-translation. We encode this geometric structure into convolutional neural networks (CNNs) via $SE(2)$ group convolutional layers, which fit into the standard 2D CNN framework, and which allow to generically deal with rotated input samples without the need for data augmentation. We introduce three layers: a lifting layer which lifts a 2D (vector valued) image to an $SE(2)$-image, i.e., 3D (vector valued) data whose domain is $SE(2)$; a group convolution layer from and to an $SE(2)$-image; and a projection layer from an $SE(2)$-image to a 2D image. The lifting and group convolution layers are $SE(2)$ covariant (the output roto-translates with the input). The final projection layer, a maximum intensity projection over rotations, makes the full CNN rotation invariant. We show with three different problems in histopathology, retinal imaging, and electron microscopy that with the proposed group CNNs, state-of-the-art performance can be achieved, without the need for data augmentation by rotation and with increased performance compared to standard CNNs that do rely on augmentation.

• The paper introduces a novel SE(2) convolutional layer that embeds rotation and translation covariance, eliminating the need for rotation augmentation.
• It employs a lifting layer to map 2D images into SE(2) space, followed by group convolution and projection layers to extract invariant features.
• Experiments show the method outperforms conventional CNNs in tasks like mitosis detection, vessel segmentation, and cell boundary mapping.

Roto-Translation Covariant Convolutional Networks for Medical Image Analysis

The paper, "Roto-Translation Covariant Convolutional Networks for Medical Image Analysis," explores the extension of convolutional neural networks (CNNs) to incorporate rotation and translation covariance via the $SE(2)$ group convolutions. The authors present a framework wherein the geometric structures inherent in medical images are encoded directly into the network architecture, thus mitigating the need for conventional data augmentation techniques such as rotation.

This research introduces a novel architectural component, the $SE(2)$ group convolutional layer, alongside two other layers: a lifting layer and a projection layer. The lifting layer expands a 2D image into an $SE(2)$ image, effectively mapping image data into a richer domain accommodating both position and orientation. Subsequently, the group convolution layer processes this $SE(2)$ image, maintaining the natural covariance in rotations and translations. Finally, a projection layer enables the network to produce rotation-invariant features via a maximum intensity projection over possible orientations.

The paper's empirical focus is solidified by applications across three distinct medical imaging tasks: mitosis detection in histopathology, vessel segmentation in retinal images, and cell boundary segmentation in electron microscopy. For each task, the $SE(2)$ G-CNN consistently outperformed its traditional CNN counterparts, establishing state-of-the-art accuracy across these varied modalities. Specifically, the performance gains are attributed to the intrinsic handling of arbitrary orientations inherent in medical imagery, which the proposed method leverages to enhance learning efficiency and stability.

Several observations are noteworthy:

1. Elimination of Rotation Augmentation: By encoding rotation covariance into the network, the documented approach obviates the need for additional data augmentation traditionally employed to achieve rotation invariance.
2. Enhanced Performance and Stability: The experiments exhibit that the networks' stability and performance metrics improved with the scaling of orientation capacity (increasing $N$ in $SE(2,N)$), suggesting a regularization effect due to advanced weight sharing.
3. Flexibility and Integration: The $SE(2)$ layers are compatible with existing CNN designs, allowing for potential integration into more complex architectures like UNets and ResNets, where further performance gains could be realized.

The paper's theoretical foundation is well-aligned with prior research on group convolutions and invariant networks, expanding the landscape of symmetry-based deep learning methods. The authors recognize the adaptability of their work, suggesting that the implemented framework could benefit other computer vision tasks where rotational variance is a factor of consideration, thus broadening the application spectrum of their findings.

In conclusion, this work significantly contributes to the domain of medical image analysis by providing a compact, rotation-invariant alternative to typical data augmentation strategies. This advancement not only supports enhanced accuracy but also fosters computational efficiency in training deep learning models for complex medical imaging tasks. Future research might delve into optimizing the kernel rotations further or exploring similar group-theoretic transformations for 3D medical imaging, thereby pushing the operational boundaries of covariance-aware deep learning frameworks.