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Orientation parameters

 Hello everyone

I recently created an ortho using Pix4D. I am trying to write a program that projects an image point onto the orthophoto. Does anyone know exactly what equations I have to use. I know they should be collinearity equations, but I am not sure about the conventions (coordinate systems, orientation angles and the order they are used to form the orientaiton matrix)  pix4d uses.




If I understand well, you want to click on a point in one image and get its correspondence in the ortho.

If that is the case, what you have to do is:

  • Compute the “ray” which is defined by the projection center and the point you click in the image. You need the interior and exterior orientation to compute that “ray”.

  • Intersect that “ray” with the DTM/DSM which was used for the orthorectification and compute the X,Y coordinates of the intersection point.

Please note that if you use a DTM instead of a DSM, a point on the top of a building will be located in different positions depending on the photo you click.

I hope this information helps.



Thank you. Yes that is exactly what I want to do. The only thing I need are the equations. In other words, I am going to get the orientation parameters, which are the internal and external parameters computed by Pix4D, and put them into collinearity equations you have used. I just need them or other form of equations you use in Pix4D, so when I say insert a ground point coordinates into the equations, I will be able to get the corresponding image coordinates. 


The only trouble I have is that I do not know exactly, what equations you use. Could you please help me?

Hi again,

These are the colinearity equations:


You can find the photocoordinates (x,y) of a point in the terrain (X,Y,Z) by knowing the external and internal orientations of the photo.

I guess that is what you want.

External parameters (position and rotations of each camera)  and rotations can be found in the file …calibrated__camera_parameters.txt located at …\1_initial\params


I hope this information helps you.