Lie group convolution neural networks with scale-rotation equivariance.

Area of Science:

• Computer Vision
• Deep Learning
• Geometric Deep Learning

Background:

• Convolutional Neural Networks (CNNs) exhibit translation equivariance due to weight sharing.
• Existing CNNs lack inherent equivariance to scale and rotation transformations.
• Handling geometric variations is crucial for robust image classification.

Purpose of the Study:

• To propose a SIM(2) Lie group-CNN for simultaneous scale, rotation, and translation equivariance.
• To enable robust image classification under geometric transformations.
• To address the metric definition on the SIM(2) Lie group space.

Main Methods:

• A lifting module maps input images from Euclidean space to Lie group space.
• Group convolution modules are parameterized using Lie Algebra coefficients for scale and rotation equivariance.
• A fully connected network and global pooling layer facilitate classification.

Main Results:

• The SIM(2) Lie group-CNN demonstrates verified scale-rotation equivariance.
• Achieved state-of-the-art recognition accuracy on image datasets with rotation and scale variations.
• Successfully extracted geometric features from transformed images.

Conclusions:

• The proposed SIM(2) Lie group-CNN effectively handles scale, rotation, and translation equivariance.
• This approach offers a powerful framework for equivariant image recognition.
• The explicit definition of SIM(2) metric advances geometric deep learning research.