Dimensional Shuffle Transform for Point Cloud Registration
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Solution Overview
Problem
Current point cloud registration methods, such as Iterative Closest Point (ICP) and Generalized Iterative Closest Point (GICP), face inefficiencies due to expensive tree traversals and rebalancing, making real-time registration with desired precision unrealistic using tree-based approaches in 3D space searching.
Innovation Solution
The Dimensional Shuffle Transform (DST) maps a 3D space to a one-dimensional space with an implicit recursive hierarchical structure, reducing neighborhood searches to one-dimensional searches, and the Black-White Array (BWA) supports searches without tree structure traversal, enabling faster and more efficient point cloud registration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If tree-based approaches (k-d trees, octrees) are used for 3D space searching in point cloud registration, then measurement precision is improved, but productivity deteriorates due to expensive tree traversals and rebalancing operations
Solution Approach 1:
The patent transforms the 3D space search problem into a 1D array index search problem by mapping 3D coordinates to 1D array indices through a systematic transformation. This dimensionality reduction eliminates the need for complex 3D tree traversals while preserving spatial locality, achieving both high precision and speed.
Solution Approach 2:
The patent replaces the mechanical tree traversal and rebalancing operations with direct array indexing operations. Instead of navigating complex tree structures dynamically, the system uses straightforward array access with pre-computed indices, eliminating the computational overhead of tree-based methods.
2Productivity
If point cloud frames are compressed by sampling to reduce cardinality, then productivity is improved by decreasing processing costs, but measurement precision deteriorates due to loss of data points
Solution Approach 1:
The patent applies different processing strategies to different regions of the point cloud based on their importance. Critical regions retain higher density while less important regions are more aggressively sampled, optimizing the balance between processing efficiency and registration accuracy through localized quality control.
Solution Approach 2:
The patent performs preliminary organization of point cloud data into structured arrays with pre-computed spatial indices before registration. This preliminary structuring enables efficient querying and matching during registration without requiring heavy sampling, as the organized structure allows rapid access to relevant points.
3Measurement precision
If tree-based data structures are used for storing and searching point cloud data, then measurement precision is improved through organized spatial indexing, but device complexity increases due to pointer chasing and rebalancing requirements
Solution Approach 1:
The patent creates a simplified array-based copy of the spatial organization information without maintaining the full complexity of tree structures. By storing pre-computed array indices that encode spatial relationships, the system replicates the benefits of spatial indexing while eliminating the need for complex tree data structures, pointers, and rebalancing logic.
Data Source
AI summary
The current document is directed to a dimensional shuffle transform (“DST”) that maps a 3D space to a one-dimensional space that preserves 3D neighborhoods within 1D neighborhoods within an implicit recursive hierarchical structure. The search for points in a 3D subspace is reduced, by the DST, to one or more searches in the transformed 1D space. The search is performed by either recursive decomposition of the 3D region indexed by the transform into subspaces, exploiting the transformed space structure, or by direct indexing into the region of interest. The searches over the subspaces generated by recursive decomposition are independent from one another, providing many opportunities for a variety of parallel, DST-enabled search methods.