Implementation of stereo PIV (2D3C)

[Shrediquette]

Stereo PIV is a standard method to measure three velocity components in a 2D plane in fluids. It is the same as classical 2D PIV, but using a second camera mounted at an angle with respect to the first camera to derive the third velocity component.

The mathematical background of stereo PIV is described in detail in this book (pages 211 – 227). Free download:
https://www.researchgate.net/profile/M-Raffel/publication/321614380_Particle_Image_Velocimetry_A_Practical_Guide/links/5e3be9dfa6fdccd9658abb6b/Particle-Image-Velocimetry-A-Practical-Guide.pdf

Most of the features that are required seem to be available in Matlab (image acquisition toolbox) already.
An implementation of stereo PIV in PIVlab requires the following new features to be implemented (milestones):

• 1. Camera calibration, undistortion and rectification (using e.g. the existing camera calibrator app - if it can be included in deployed applications). Used for 2D PIV (see also this enhancement request: Add image undistortion and image rectification #89
• 2. Camera stereo calibration, undistortion and rectification (using e.g. the existing stereo calibrator app - if it can be included in deployed applications)
• 3. Self calibration / disparity correction using particle images recorded with the two cameras
• 4. Geometric reconstruction of the three velocity components
• 5. Expanding the calculations of magnitude / vorticity etc. to three components instead of two
• 6. Live script Example for performing Stereo-PIV using steps 1-3
• 7. Graphical interfaces for the above steps making stereo PIV attractive to novice users
• 8. Enabling the image data import for two cameras instead of one in the PIVlab GUI
• 9. Displaying 3D velocity information in the PIVlab GUI
• 10. Enabling data validation for three components in the PIVlab GUI
• 11. Furthermore, stereo image acquisition should be implemented in PIVlab too (controlling two cameras directly from PIVlab)

Help is needed for steps 1-6

[mkbosmans]

Hi William, VORtech might be able to help with the first 5 steps. Some questions:

• Do I understand correctly that undistortion and rectification is not implemented for the current 2D PIV and that it is an essential component of 3D PIV?
• Do you have example data for stereo PIV, both the 2 recorded fields and the calibration data?
• It seems the self calibration is not described in the reference you linked. Is there any description of that process available? Is it on top of or in place of the calibration with a reference image?

[Shrediquette]

Hi @mkbosmans Maarten, nice to hear from you again :)

• Undistortion + rectification: Yes, this is mandatory for stereo-PIV, and 2D PIV would also benefit a lot. E.g. in all cases where high image distortions are unavoidable, or when the camera cannot be placed perpendicular to the image plane. This is something that people usually try to avoid, but challenging experiments may require this.
• Example data: I will soon record my own with my own setup. And I would like to work with this dataset. But for now, there is an initiative called "PIV challenge" that provides stereo-PIV test data. Here is a description of the data:
  https://www.pivchallenge.org/pub14/4th_PIV-Challenge_Instructions_Case_E.pdf
  Image data: https://www.pivchallenge.org/pub14/4th_PIV-Challenge_Case_E.zip
  I can't give you velocity fields, because I think we would have to do all the calibration before it makes sense.
• Self-calibration: The reference above says on p. 218 something like "self-calibration gives the camera positions with respect to the image plane". I think this is already available in Matlab.
• Disparity correction probably is another correction step after the image rectification / undistortion: I think that two particle images from camera A and B, taken at the same time, are cross-correlated (using standard 2D PIV technique) to find remaining misalignments / distortions.
  We have a very smart guy called @ErichZimmer that is sometimes active here, and if you read this, feel free to correct me!

[Shrediquette]

Concerning the "self-calibration": I think this term is used for different things. In the book, as I mentioned above, it is used for getting the camera positions.
But here, it is used for what I have called "disparity correction"...:
"First a standard Stereo-PIV calibration is done by viewing a calibration plate which does not need
to be aligned exactly with the light sheet. Then the recorded particle images themselves are used to
calculate the misalignment between calibration plate and light sheet. Finally the mapping function
is corrected accordingly and the recorded images are evaluated. The Stereo-PIV vector fields
are computed by LaVision’s well-known, highly accurate correlation algorithms using deformed
interrogation windows (PIV Challenge 2003). "

[mkbosmans]

@Shrediquette, could we split up the first step into two steps? First undistortion and rectification (I'm fine with making it mandatory to implement in 2D first) en second stereo camera calibration. That would have the steps we can pick up be all a bit more similar in size, which makes it easier to manage.

[Shrediquette]

Yes if course, I'll edit the text.

[Shrediquette]

For step 1, I already reveiced some code from Mathworks. It is a modified version of UndistortImage, and it does undistortion and rectification with a single interpolation. It is attached.

modifiedUndistortImage.zip

[MatTolladay]

I have been working on the first few points using the MATLAB image processing and computer vision tools and can report:

1. Image undistortion (camera based distortion) can be corrected using the tool box. A user needs to take multiple images of a calibration target with the target in different positions in the frame. If the camera settings (lens setup, aperture size etc) are fixed then the images can be taken without the camera having to be fixed in the experimental setup and the generated camera properties can be reused between experiments.
2. At the moment the code only calculates the fundamental matrix of the stereo camera system. Image features can be detected and then matched between the two cameras using the fundamental matrix and the camera properties. I have just tried this on an image of vapour and using blob detection to generate a feature set, but other schemes exist for feature detection and they may be better suited to different data such as particles. The triangulate function in MATLAB is used to produce 3-D coordinates of points of interest (based on the detected features) in the 2-D plane of the light sheet. I have approximated this using a stereo calibration image pair containing a ChArUco board with the light sheet simulated by displaying an image on a monitor:

The next step is to calculate the position and unit norm of the light sheet/monitor for both cameras. This will provide the transformations required to rectify the images for use with the cross-correlation used in PIVlab.

[Shrediquette]

I have a script version running. I will add stereo PIV to the GUI in 2026. This will include the possibility to control two cameras in PIVlab, and run the stereo analysis.
First, I'll add two Optocams, other Stereo cameras will follow later.
I'll add basic functionality first (displaying out of plane velocity component), the rest will follow later.