Space-Filling Curve Point Cloud Feature Generation
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Solution Overview
Problem
Existing methods for generating iso-lines from point cloud data, such as the Marching Squares approach, require rasterization, which leads to accuracy loss, interpolation, and high memory usage, especially when dealing with non-uniform data densities and large datasets.
Innovation Solution
The use of a space-filling curve, like the Hilbert curve, to transform multi-dimensional point cloud data into a single-dimensional representation, allowing for efficient identification of features without rasterization, and adapting to varying data densities by converting coordinates into Hilbert distance values and sorting points along the curve.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Marching Squares approach is used to generate iso-lines from point cloud data, then iso-lines can be generated from rasterized data, but accuracy is lost and significant main memory is required
Solution Approach 1:
The patent applies dimensionality change by mapping multi-dimensional point cloud data onto a one-dimensional space-filling curve (such as Hilbert or Peano curve). This transformation allows the system to process spatial data in a linear sequence while preserving spatial relationships, thereby avoiding the need for rasterization into multi-dimensional grids and significantly reducing memory requirements while maintaining accuracy.
Solution Approach 2:
The patent changes the parameter representation by converting spatial coordinates (x, y, z) into a single parameter along the space-filling curve. This parameter transformation enables efficient sorting and processing of points based on their position along the curve, eliminating the need for complex multi-dimensional array structures and reducing memory usage while preserving measurement precision.
2Quantity of substance
If smaller partitions are used in the Marching Squares approach, then memory requirements are reduced, but processing efficiency decreases significantly
Solution Approach 1:
By transforming the problem from multi-dimensional space to one-dimensional space along a space-filling curve, the patent enables processing of the entire point cloud in a single linear pass. This eliminates the need for partitioning into smaller spatial blocks, thereby maintaining high processing efficiency while using minimal memory to store only the sorted point sequence.
Solution Approach 2:
The space-filling curve provides a continuous traversal path through the entire point cloud, allowing the algorithm to process points in a continuous sequence without interruptions for memory management or partitioning. This continuous processing maintains high productivity while using minimal memory, as the system can stream through the data once in sorted order.
3Measurement precision
If rasterization is used to create a DEM from point cloud data, then iso-lines can be generated, but empty raster cells are created and detail is sacrificed in areas with non-uniform data density
Solution Approach 1:
The patent extracts only the essential information needed for iso-line generation by mapping points directly onto the space-filling curve parameter. This extraction eliminates the need for creating complete raster grids with their complex multi-dimensional structures, removing empty cells and unnecessary data while preserving the precision needed for accurate iso-line generation.
Solution Approach 2:
By changing from a multi-dimensional raster coordinate system to a one-dimensional space-filling curve parameter, the patent simplifies the data structure dramatically. The complex grid structure with empty cells is replaced by a simple sorted array of points indexed by their position along the curve, reducing structural complexity while maintaining measurement precision.
4Manufacturing precision
If a configurable grid density is used in rasterization, then some areas maintain detail, but holes or estimates are formed in other areas with non-uniform data density
Solution Approach 1:
The space-filling curve transformation preserves the complete set of original points without loss, regardless of their spatial distribution. By mapping all points onto the one-dimensional curve and sorting them, the method maintains data completeness for all areas while enabling uniform processing, eliminating the need for variable grid density and the resulting holes or estimates.
Solution Approach 2:
The continuous traversal along the space-filling curve ensures that every point in the point cloud is visited and processed in sequence. This continuous processing guarantees that no areas are skipped or estimated, maintaining both detail quality and data completeness across the entire dataset without requiring configurable grid density.
Data Source
AI summary
Systems, methods, and other embodiments are disclosed for identifying features within point cloud data. In one embodiment, point cloud data is read which represents multiple points of at least one point cloud in a multi-dimensional space. Each point in the point cloud data is defined by an attribute value quantifying an attribute of the point and a set of coordinates specifying a location of the point in the multi-dimensional space. The set of coordinates for each point is transformed into a space-filling distance value representing a distance along a space-filling curve. The points are sorted according to the space-filling distance values to generate a sorted order of the points. The points are traversed in the sorted order and output data points are derived, while traversing the points, based on a specified feature criterion. The output data points identify a feature within the at least one point cloud.