Monday, February 19, 2018

WebApp for calculating the 4x4 transformation matrix between 2 corresponding sets of 3D points

In working with 3D point clouds, one of the task may be to register or transform the point cloud to known ground control points (GCPs) on the ground with corresponding control points in the point cloud. For instance, the screen shot below shows the point cloud with four control points p1, p2, p3, and p4.

Note: At least 3 corresponding set of points are needed to calculate a rigid transformation matrix.

From the point cloud, the from-control points can be measured:

On the ground, the actual ground control points can be obtained, perhaps from a GPS receiver:


With the measured points from the point cloud and the corresponding control points on the ground, a 4x4 homogeneous transformation matrix can be calculated and used to rigidly transform the point cloud to the actual ground coordinate system. 

This WebApp calculator at https://dominoc925-pages.appspot.com/webapp/calc_transf3d/default.html can be used to calculate the 4x4 transformation matrix, as well as the root mean square error (RMSE) as an indicator of the quality of the control points i.e. the smaller the RMSE, the better they are. The WebApp uses the Numeric Javascript matrix library from http://www.numericjs.com/ for performing the required SVD decomposition to calculate the transformation matrix. Note that the library has some unfixed bugs in the SVD decomposition for certain cases and I may probably replace this with an alternative solution in future.  
  1. Paste the "from control points" into the Source Points text area field. 

  2. Paste the ground control point values into the Destination Points text area field.
  3. Click the Calculate button.



    The resultant transformation matrix appears in the 4x4 Transformation Matrix field. The RMSE for the calculation is displayed in the RMSE field.

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