This article describes in detail the mathematical models behind the camera's internal and external parameters.

**IN THIS ARTICLE**

1. Camera external parameters

2. From 3D to 2D: Camera internal parameters

2.1 Perspective lens

2.1.1 Camera without distortion model

2.1.2 Camera with distortion model

2.2 Fisheye lens

3. Camera Rig External Parameters

Chen XingHi,

I have a question of R rotation matrix when I using Pix4D Mapper Education.

I was using omega phi and kappa to do other calculations but all results was wrong, and now I come back to double check the equation of R.

I run the whole model by using "3D MODEL", then I got "calibrated_camera_parameters.txt" (CCP)and "calibrated_external_camera_parameters.txt" (CECP) files in 1_initial folder. In CCP, I see the camera rotation R of each image, and in CECP, there is calibrated omega phi and kappa of each image.

I was trying to use MATLAB to calculate rotation matrix R by using the omega phi kappa(from CECP) through the equation mentioned in this website "1. Camera external parameters", but the result I got through the equation here was

not the samewith the one given by CCP.txt file.What caused this problem? The value should be the same...

Thank you very much!

Steven (Chen Xing)

Blaž (Pix4D)Hi,

As mentioned in the What does the Output Params Folder contain? article, the

project_name_calibrated_camera_parameterspositions and rotations of the cameras are defined in alocal coordinate system. In order to get the values in the definition mentioned in How are the Internal and External Camera Parameters defined? article, the rotation around the X-axis and the offset needs to be applied.Best,

Chen XingHi,

I reviewed those websites and the document mentioned "offset", I found the document "project_name_offset.xyz", but there was only one coordinate in that file, like xxx845.000 xxxx588.000 xx1.000.

Could you please explain how to applied the rotation around the X-axis and the offset?

Thanks!

Steven

Daniel (Pix4D)Hello,

From the article what does the output paramteres folder contain :

As it is mentioned, that folder contains "computer vision information" where the convention is to have the z-axis pointing towards the scene, while in photogrammetry we have the convention to have the z-axis pointing towards the camera. That is why it is necesary to rotate the X axis.

I hope this answer helps.

Regards.

Mughilan Thiru RamasamyHi Daniel!

Can you elaborate on how I go about doing the above? Precisely on the following grounds:

1. Do I add or subtract the offset from the coordinates in the local coordinate system?

2. Also, the rotation angle by which to rotate the X-axis comes as 'omega' from project_name_calibrated_external_camera_parameters, right?

Could you provide the equations for the same in terms of the standard parameter notations like Rm, Tm, etc.?

DENNYS MOSQUERAHello,

I am currently working with the EVO II Pro drone of the Autel, but I think that the camera parameters are not the real ones, because the size of the flown pixel does not match the one obtained in the generation of the orthophoto, the difference is up to 4 cm.

According to the camera specifications the focal length is 28.6mm, but the PIX4D mapper automatically recognizes a focal length of 10.57mm when loading images with the x705_10.6_5472x3648 camera.

Why is this difference? and please could you help me. What are all the parameters of the camera to be able to process in PIX4D Mapper?

Thanks.

Atte,

Mauricio

Momtanu (Pix4D)Hi Mauricio, Pix4D reads the focal length and other parameters from the EXIF of the images (metadata). 28.6 might be the 35 mm equivalent focal length. Some lens manufacturers give the focal length (F

_{35}) in the 35 mm equivalent. It is not the 35 mm equivalent but the real focal length that should be used in Pix4Dmapper. The camera's actual focal length is significantly smaller than 20 mm because the camera's sensor is smaller than a standard 35 mm sensor. More here: https://support.pix4d.com/hc/en-us/articles/202557469-Step-1-Before-Starting-a-Project-1-Designing-the-Image-Acquisition-Plan-b-Computing-the-Flight-Height-for-a-given-GSDYou can calculate the GSD here: https://support.pix4d.com/hc/en-us/articles/202560249-TOOLS-GSD-calculator