Abstract
The adjustment of a straight line through a cloud of points is analyzed for the case where all coordinates are measured quantities and thus affected by random errors. The so-called Total Least-Squares Solution (TLSS) can then be obtained by solving the resulting non-linear normal equations via a newly developed iterative approximation algorithm or, equivalently, by following the smallest eigenvalue approach. After showing the superior performance of the TLS approach in the 2D-case, the procedure is extended to the 3D case where a plane is sought that best fits an observed point cloud. This procedure is implemented in surface reconstruction from a cloud of LIDAR points.
Original language | English |
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Pages (from-to) | 141-168 |
Number of pages | 28 |
Journal | Bollettino di Geodesia e Scienze Affini |
Volume | 65 |
Issue number | 3 |
State | Published - 2006 |
Keywords
- Errors-in-Variables models
- Line fitting
- Photogrammetric applications
- Three-dimensional plane fitting
- Total Least-Squares adjustment