# How to simulate Unity Pinhole Camera from its intrinsic parameters

We have a real camera for which its intrinsic parameters are estimated, based on the calibration toolbox of Bouget: Perona Lab - Home
We assume that there is no a non-linear optical distortion and estimate parameters:
Focal length: The focal length in pixels is stored in the 2x1 vector fc.
Principal point: The principal point coordinates are stored in the 2x1 vector cc
as described in http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html

According to the classic theory presented in the book of Zisserman “Multiple View Geometry in Computer Vision Second Edition” (chapter 6), the projection matrix in this case is given by:

P = [fc(1), 0, cc(1), 0;
0, fc(2), cc(2), 0;
0, 0, 1, 0]
This matrix is 3x4 and it acts on the homogenous coordinates (X,Y,Z,1)’ to get projective homogenous coordinates; (x,y, z)’ = P*(X,Y,Z,1)'. The corresponding image pixel coordinates are then calculated based on xp= x/z and yp=y/z.

Does anyone can help us to simulate exactly the same camera in the Unity. We would like to know how the classic matrix P above is related to Camera.projectionMatrix that is of dimensionality [4x4] and we would like to save the obtained rendered scene that has the same number of pixels as images from the real camera.

Or another way around, what is the mathematical expression that relates between (XYZ)-coordinates in the camera coordinate system and (xp,yp)- projective pixel coordinates and Camera.projectionMatrix of the Unity?

It’s late answer, but there is nothing to do with projection matrix.

you have to play with Sensor Size & Lens Shift by using Physical Camera option

ax 0 px

0 ay py

0 0 1

say this is Intrinsic matrix K, then

SensorSizeX = f * resolution_width / ax

SensorSizeY = f * resolution_height / ay

LensShiftX = - (px - width / 2.0f) / width // somehow this is apposite sign …

LensShiftY = (py - height / 2.0f) / height

Here, you have to set screen resolution as yout image’s resolution (if you work in Unity editor you can do this by changing player option or in script and set Game view as Standalone).

I tested this by setting these camera value with given intrinsic K, placing checkerboard, capturing images and run camera calibration using opencv. Calibration gives less than 1% error. I’d say, it works.

@jungguswns Thank you so much! I’ve been looking all around for this answer! For e.g - > https://forum.unity.com/threads/how-to-use-opencv-camera-calibration-to-set-physical-camera-parameters.704120/

That said, is there a web link/source where I can verify the formulae - the SensorX, SensorY, lens-shift, etc or if not some source where I can read up this info, and maybe figure out the formula by my own?

Much appreciated!

Hi,
i have the same problem. i have the real camera parameters and i wanna integrate them into Unity could u help me please with the program ??

``````<?xml version="1.0"?>
<opencv_storage>
<calibration_time>"Mon Oct  5 11:15:14 2020"</calibration_time>
<nr_of_frames>25</nr_of_frames>
<image_width>640</image_width>
<image_height>480</image_height>
<board_width>9</board_width>
<board_height>7</board_height>
<square_size>26.</square_size>
<fix_aspect_ratio>1.</fix_aspect_ratio>
<!-- flags: +fix_aspectRatio +fix_principal_point +zero_tangent_dist +fix_k4 +fix_k5 -->
<flags>6158</flags>
<fisheye_model>0</fisheye_model>
<camera_matrix type_id="opencv-matrix">
<rows>3</rows>
<cols>3</cols>
<dt>d</dt>
<data>
6.5977387082509961e+02 0. 3.1950000000000000e+02 0.
6.5977387082509961e+02 2.3950000000000000e+02 0. 0. 1.</data></camera_matrix>
<distortion_coefficients type_id="opencv-matrix">
<rows>5</rows>
<cols>1</cols>
<dt>d</dt>
<data>
1.9198627770868830e-03 3.0317553019619008e-02 0. 0.
-4.5730418705509945e-01</data></distortion_coefficients>
<avg_reprojection_error>3.4177707564715609e-01</avg_reprojection_error>
<per_view_reprojection_errors type_id="opencv-matrix">
<rows>25</rows>
<cols>1</cols>
<dt>f</dt>
<data>
2.22406134e-01 2.11091563e-01 3.18504691e-01 2.39104092e-01
3.09625685e-01 4.70417738e-01 2.05981627e-01 1.47743702e-01
3.89496386e-01 3.60383183e-01 2.33502612e-01 2.22289190e-01
3.13145518e-01 6.48265600e-01 3.21525455e-01 4.54577595e-01
2.84252644e-01 2.78994173e-01 1.51937529e-01 2.13156864e-01
3.06999326e-01 7.31929719e-01 1.81998357e-01 3.35410535e-01
2.63880163e-01</data></per_view_reprojection_errors>
<!-- a set of 6-tuples (rotation vector + translation vector) for each view -->
<extrinsic_parameters type_id="opencv-matrix">
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<image_points type_id="opencv-matrix">
<rows>25</rows>
<cols>63</cols>
<dt>"2f"</dt>
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</opencv_storage>
``````

,Hi Sir,

i have same problem. i have the parameter matrix of my camera and i wann visualise it in Unity could u help me please with the program anf thank u