Abstract
AbstractTransformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points.
Highlights
Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision
Simulated annealing algorithm for 3D coordinate transformation 493 caused a shift in the way we look at estimation tasks and the algorithms used for those purposes
Despite the significant disadvantage resulting from the placement of common points the Simulated annealing (SA) procedure was able to deliver angular transformation parameters that were good enough, so that the subsequently introduced least squares (LS) procedure was able to provide the exact solution after a few iterations
Summary
Abstract: Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. There are many algorithms used to determine transformation parameters based on the coordinates of common points They can be divided into two groups: analytical procedures and iterative numerical procedures. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods This is true for large angles of rotation. A rotation matrix corresponding to the quaternion (Rodrigues’ matrix) can be defined as follows: a2 + b2 − c2 − d2 2(bc − ad)
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