SO(3) Rotation Equivariant Feature Maps for Pose Estimation
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Solution Overview
Problem
Computer vision systems face challenges in accurately estimating the pose of an image sensor in medium to large environments due to the need for a large set of training images covering various positions and orientations, making it impractical.
Innovation Solution
A neural network is configured to generate a rotation equivariant feature map indexed in the SO(3) space from omnidirectional images, allowing for efficient training with a single orientation while achieving high accuracy in pose estimation by using an encoder network that converts omnidirectional images to SO(3) indexed feature maps and a decoder network that determines the pose from these feature maps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional pose estimation methods are used with omnidirectional images, then accurate pose estimation can be achieved, but a large set of training images spanning various positions and orientations is required, making it impractical for medium or large sized environments
Solution Approach 1:
The patent changes the parameter space by transforming images from standard 2D Euclidean space to SO(3) rotation group space. This transformation allows the network to learn rotationally equivariant features, where a single training image can generalize to multiple orientations through the mathematical properties of SO(3) convolution, drastically reducing the number of training images needed while maintaining pose estimation accuracy
Solution Approach 2:
The patent introduces a new dimensional framework by using SO(3) indexed feature maps instead of traditional 2D feature maps. This adds a rotational dimension to the feature representation, allowing the network to capture orientation information inherently through the SO(3) group structure, thereby reducing dependence on multiple oriented training samples
2Adaptability or versatility
If traditional neural networks are trained with multiple orientations, then rotation robustness can be achieved, but training time and computational resources increase significantly
Solution Approach 1:
By changing the parameter space to SO(3), the network inherently learns rotationally equivariant representations. The SO(3) convolution operation is designed to be equivariant to rotations by construction, meaning the network automatically adapts to different orientations without requiring explicit rotation augmentation or retraining, thus achieving rotation robustness efficiently
Solution Approach 2:
The SO(3) convolution layer serves multiple functions simultaneously: it extracts features, encodes rotation information, and provides rotational equivariance all in a single operation. This multi-functionality eliminates the need for separate modules or training procedures to handle different orientations, reducing training time while maintaining adaptability
Data Source
AI summary
A computer implemented method for pose estimation of an image sensor includes receiving an omnidirectional image of a scene captured by an image sensor; using a trained neural network to generate a rotation equivariant feature map from the omnidirectional image of the scene; and determining information relating to the pose of said camera when capturing the scene from the rotation equivariant feature map. The rotation equivariant feature map is a SO(3) indexed feature map.