Abstract
Point normal calculation and cloud registration are two of the most common operations in point cloud processing. However, both are vulnerable to issues of numerical precision and loss of significance. This paper documents how loss of significance in the open-source Point Cloud Library can create erroneous point normals and cause cloud registration to fail. Several test clouds are used to demonstrate how the loss of significance is caused by tight point spacing and clouds being shifted far from the origin of their coordinate system. The results show that extreme loss of significance can cause point normals to be calculated with a random orientation, and cause meters of error during cloud registration. Depending on the structure of the point cloud, loss of significance can occur when the cloud is at hundreds or even tens of meters from the origin of its coordinate system. Shifting to larger data types (e.g., from 32-bit “floats” to 64-bit “doubles”) can alleviate the problem but will not solve it completely. Several “best practice” recommendations for avoiding this issue are proposed. But the only solution guaranteed to eliminate loss of significance is de-meaning the entire cloud, or clusters of points before processing.
Highlights
Much research has been done to date on the development of point cloud registration and normal calculation algorithms
In many cases involving real-world data such as that produced by a LiDAR unit, this mesh is not available and the point normals must be calculated from the structure of the cloud itself
When Iterative Closest Point (ICP) is used with a double data type instead of float, its result is more consistent still often worse than the initial error
Summary
Much research has been done to date on the development of point cloud registration and normal calculation algorithms. While many algorithms for point cloud processing have infinite precision in theory, in practice they often require making compromises between precision and computation speed. This can introduce problems with loss of significance (LoS), where errors can be introduced that may have consequences for every down-stream process. This is of particular significance for normal calculation since it is often a precursor to other cloud processing operations such as feature identification or surface reconstruction. In many cases involving real-world data such as that produced by a LiDAR unit, this mesh is not available and the point normals must be calculated from the structure of the cloud itself
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