Hierarchical Gaussian Mixture Point Cloud Registration
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Solution Overview
Problem
Conventional point cloud registration algorithms, such as ICP, perform poorly with noisy data, uneven point density, occlusions, and large displacements, and newer techniques that use statistical models are slower and offer limited improvements, making them unsuitable for real-time applications.
Innovation Solution
A registration algorithm that represents a reference point cloud using a hierarchical tree data structure and employs an Expectation-Maximization algorithm to iteratively associate points in a target point cloud with nodes of the tree, determining an estimated transformation based on maximum likelihood estimation criteria, utilizing a Mahalanobis distance and weighted least squares technique.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional ICP algorithms are used for point cloud registration, then computational speed is maintained, but registration accuracy deteriorates in noisy and complex scenarios
Solution Approach 1:
The patent segments the point cloud data processing by dividing the search space into a hierarchical tree structure (e.g., octree) where each node represents a spatial region. This segmentation allows the algorithm to focus computational effort on relevant regions rather than processing the entire point cloud uniformly, thereby improving accuracy without proportionally increasing computational cost.
Solution Approach 2:
The patent introduces a hierarchical dimension to the traditional 3D point cloud registration problem by organizing spatial regions into multiple levels of abstraction. This hierarchical dimension enables the algorithm to operate at different scales, coarse-to-fine, improving registration accuracy while maintaining computational efficiency through adaptive sampling at each level.
2Measurement precision
If statistical models are used to represent point cloud data, then registration accuracy improves, but computational speed deteriorates significantly
Solution Approach 1:
The patent segments the statistical modeling process by applying it only to selected representative points or regions identified through the hierarchical tree structure, rather than computing statistical models for all points. This selective application maintains accuracy benefits while reducing computational burden.
Solution Approach 2:
The patent applies statistical modeling partially by using it only when and where needed based on data characteristics and registration requirements, rather than universally. This partial application allows the algorithm to achieve accuracy improvements in critical scenarios without the full computational cost of universal statistical modeling.
3Measurement precision
If a detailed hierarchical tree structure is used to represent point cloud data, then registration accuracy improves, but data processing time increases
Solution Approach 1:
The patent makes the hierarchical tree structure dynamic by adaptively constructing and refining it based on the specific registration task, data characteristics, and required precision. The tree depth and granularity are adjusted dynamically rather than being fixed, allowing the algorithm to achieve necessary accuracy without unnecessary processing overhead.
Solution Approach 2:
The patent performs preliminary construction of the hierarchical tree structure before the main registration process, organizing the spatial data once and reusing this structure throughout subsequent iterations. This preliminary action avoids repeated expensive computations during the registration process while maintaining accuracy benefits.
Data Source
AI summary
Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, object/scene recognition, and augmented reality (AR). A new registration algorithm is presented that achieves speed and accuracy by registering a point cloud to a representation of a reference point cloud. A target point cloud is registered to the reference point cloud by iterating through a number of cycles of an EM algorithm where, during an Expectation step, each point in the target point cloud is associated with a node of a hierarchical tree data structure and, during a Maximization step, an estimated transformation is determined based on the association of the points with corresponding nodes of the hierarchical tree data structure. The estimated transformation is determined by solving a minimization problem associated with a sum, over a number of mixture components, over terms related to a Mahalanobis distance.