3D Body Pose Estimation With Möbius Graph Convolution
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Solution Overview
Problem
Existing graph convolutional networks (GCNs) for 3D human pose estimation fail to explicitly model the rotation between joints, leading to inefficiencies and a high computational burden, limiting their application to mobile devices.
Innovation Solution
The MöbiusGCN architecture operates in the complex domain, leveraging the Möbius transformation of the graph Laplacian to encode both rotation and translation between joints, reducing the model's parameter count and computational requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional GCNs are used for 3D pose estimation, then the model can process graph-structured 2D joint data, but the computational burden is high and rotation between joints is not explicitly modeled
Solution Approach 1:
The patent transitions from real-valued graph convolutions to complex-valued graph convolutions by introducing the Möbius transformation. This dimensional change allows the model to simultaneously encode both rotation and translation transformations between joints in the complex domain, achieving explicit rotation modeling without increasing computational complexity. The complex domain provides an additional dimension for representing rotational information through phase angles.
Solution Approach 2:
The patent changes the mathematical domain from real to complex numbers, fundamentally altering how transformations are represented. By using complex-valued filters in the spectral domain, the model can encode rotation angles as phase information and translation as magnitude, efficiently capturing both transformation types with fewer parameters compared to conventional approaches that treat them separately.
2Loss of information
If conventional spectral GCNs are used, then the model operates in the real domain, but it cannot encode all transformation distributions between joints explicitly
Solution Approach 1:
By moving to the complex domain through Möbius transformation, the patent adds an imaginary dimension that enables simultaneous encoding of rotation (phase) and translation (magnitude) transformations. This single complex-valued representation captures complete transformation distributions between joints, eliminating information loss without requiring separate real and imaginary network branches.
3Productivity
If a compact model is used to reduce parameters, then the network can run on mobile devices, but achieving accurate 3D pose from 2D input becomes more difficult
Solution Approach 1:
The patent changes the representation domain to complex numbers, which allows more information to be packed into the same parameter space. The complex-valued MöbiusGCN achieves better feature representation with fewer parameters by encoding both rotation and translation in a unified complex domain, maintaining high accuracy while enabling deployment on resource-constrained mobile devices.
Data Source
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AI summary
A computer implemented method for determining a pose of a body model in 3D space from a 2D input includes acquiring an input graph representation of a body model in 2D space, the input graph representation comprising a plurality of joints with associated joint positions and interconnections between the joints, and processing the input graph representation with a sequential Mobius graph convolution, MGC, chain comprising one or more MGC blocks. Each MGC block determines a set of graph signals from its respective block input and applies a weight matrix and a graph filter on the set of graph signals, wherein the graph filter is based on a Mobius parameter set and is applied in a spectral graph convolutional network. The block input is the input graph representation in 2D space if the MGC block is a first MGC block of the sequential MGC chain, or else is an output graph representation of a preceding MGC block of the sequential MGC chain. A last MGC block of the sequential MGC chain provides the output graph representation of the body model in 3D space as an output.