Tangent Convolution for 3D Point Clouds
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Solution Overview
Problem
Current 3D deep learning systems face challenges in processing unstructured point clouds and noisy real-world data due to the cubic complexity of voxel grids and limitations in scalability and prediction accuracy, especially when dealing with large-scale scenes and complex layouts.
Innovation Solution
Tangent convolution represents 3D data as tangent planes, enabling efficient deep learning through planar convolution, which scales to large datasets and improves prediction accuracy by projecting local surface geometry onto tangent planes, forming regular 2D grids that can be processed using conventional convolutional networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If voxel grids are used to represent 3D data for deep learning, then 3D convolution can be applied, but the computational complexity and memory consumption increase cubically
Solution Approach 1:
The patent transforms 3D spatial data into 2D tangent plane representations by projecting local surface geometry onto tangent planes at each point. This dimensionality reduction from 3D to 2D allows conventional 2D convolutional networks to process 3D data efficiently, avoiding the cubic complexity of 3D convolutions while preserving local geometric relationships through the tangent plane projection
2Productivity
If voxel grids are used to represent 3D data, then convolution can be performed, but memory consumption increases cubically
Solution Approach 1:
By representing 3D data points as 2D tangent plane images, the patent reduces the memory requirements from cubic (3D voxel grids) to quadratic (2D plane projections). Each point is represented by its local tangent plane image rather than occupying a voxel in 3D space, significantly reducing memory consumption while maintaining processing efficiency
Solution Approach 2:
The patent creates 2D tangent plane copies or projections of local 3D surface geometry around each data point. These tangent plane images serve as local representations that can be processed efficiently without storing the entire 3D voxel grid, reducing memory consumption while preserving the necessary geometric information for convolution operations
3Productivity
If hierarchical spatial data structures like octrees are used, then memory and computation efficiency improve, but prediction accuracy is limited due to upper resolution limits
Solution Approach 1:
The patent applies local tangent plane projections at each individual data point, allowing high-resolution local geometric representation without the global resolution limits of hierarchical structures. Each point gets its own high-resolution tangent plane image, preserving fine local details while maintaining computational efficiency through localized processing rather than global hierarchical decomposition
4Adaptability or versatility
If 3D convolutional networks are applied to unstructured point clouds, then 3D data can be processed, but the computational intensity increases significantly
Solution Approach 1:
The patent transforms unstructured 3D point cloud data into structured 2D tangent plane images, enabling the use of efficient 2D convolutional networks. This transformation maintains adaptability to unstructured data while reducing computational intensity by leveraging the efficiency of 2D convolutions over 3D convolutions
Solution Approach 2:
The tangent plane projection acts as an intermediary representation between unstructured 3D point clouds and conventional 2D convolutional networks. This intermediate 2D representation allows standard 2D CNNs to process 3D data efficiently without requiring complex 3D convolutional architectures, reducing computational intensity while maintaining versatility
Data Source
AI summary
To address the needs of applications that work with large-scale unstructured point clouds and other noisy data (e.g. image and video data), tangent convolution of 3D data represents 3D data as tangent planes. Tangent convolution estimates tangent planes for each 3D data point in one or more channels of 3D data. Tangent convolution further computes the tangent image signals for the estimated tangent planes. Tangent convolution precomputes the tangent planes and tangent image signals to enable convolution to be performed with greater efficiency and better performance than can be achieved with other 3D data representations.