Image calibration and rectification

An important step, perhaps the most important step, in using the Particle Imaging Velocimetry method is the calibration/rectification of the views of the model.

At it simplest the calibration assigns a scale to the images, allowing displacements in the image space (in pixel) to be converted to displacements in the physical world. However, the images are usually distorted and a single scale can not be applied uniformly. The distortions must be assessed and removed, in order to have such spatially uniform simple scale. This is the role of the calibration / rectification procedure.

In TecPIV the calibration / rectification for 2D PIV employs one single view of a calibration board with a known checkerboard pattern. For a surface view, the calibration board can be placed horizontally above the surface of the model, or above where the surface of the model will be, and then the camera can be lowered precisely to compensate this height difference. What matters is the relative position of the calibration board / model surface and camera.

img_20190117_095823-s

Experimental set-up with checkerboard calibration board placed in order to constrain images of the model surface. The camera can be displaced vertically, and take oblique views of the calibration board / model surface.

Control points are found in the views of the calibration board. The relative positions of the control points is know. For example, the calibration board can have 30 by 30 squares that are 15 mm wide. The Harris corner detector allows finding the control points with subpixel precision. The positions are then evaluated against a target, ideal, position calculated using the position of the central point and the image resolution around this central point.

cpc

Image of the calibration board with control points (red crosses) before rectification. The four corners are selected by the user (pink circles), and the control points are found with sub-pixel precision. A dimension of the squares and number of squares are provided by the user. 

cp-1c

Projective rectification of the calibration view. The control points are now in a position that is much closer to the target regular grid, but the error on the rectification is still important. For example, some cushioning can be seen along the top and bottom lines.

cp-2c

Polynomial 3 rectification after the projective rectification. Polynomial corrections after projection allow the removal of the non-linear distortion. Now the error on the correction is about 1.2 pixels, while the resolution is 15.58 pixels / mm.

Linear (projective) and non-linear function are used sequentially to move all the control points towards their target positions. The error is calculated for the user to select the best projection method.

Here 875 control points have been employed to constrain a large portion of the image space, where the model will be.

It is important to note that only the area covered by the control points is calibrated. The model deformation should not be analyzed outside of the calibrated area.

The model views can be rectified using the functions defined during the calibration procedure, using the calibration board, and cropped such that the model outside the calibrated area is removed.

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