nonlinear 2d calibration of line-camera using known pattern - how to align world coordinates to points?

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arnold 2016-7-2

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评论： praveen rai 2017-12-28

I rephrased the question, see last comment

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Hi all,

I'm currently working with a highres line camera scanner and we want to use it for measurements. Therefore we need to be able to calibrate it properly in 2d.

We have an accurate test-pattern made by photolithography. We can assume it to be 'exact'. I have managed to come up with a very robust subpixel circle recognition to find the points of interest so I have no question regarding image recognition.

What is unclear to me at this point is how to use the found image coordinates together with the known spatial correlation in order to come up with a distortion map which ultimately would be used to correct the distortion.

The example shows a cropped subset of a typical image of circles with 400µm xy spacing. The recognition is already done (red circles with blue centercross) leaving out structures that are too close to the edge. Now, how do I calculate a distortion-map from that?

I played around with some algorithms like knnsearch in order to look at the lokal distances and I can see that they vary significantly. I don't want to simply create a coordinate system using arbitrary points and then measure relative distances to that system because I fear that might induce large errors over big distances.

My guess is that using a combined approach of the local information (distances) in combination with the 'far field' (straight lines, orthogonality etc.) should result in the most robst outcome but I'm stuck on how to continue. In the end we want to do many measurements in order to determine the measurement errors caused by vibration and thermal influences i.e.

I'm fairly certain this has been solved (many) times but as a non-expert on the field I just don't know what to search for exactly. I would appreciating any help!

regards

Arnold

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arnold 2016-7-5

no idea, anyone?

praveen rai 2017-12-28

@arnold can u provide me the code that how u find robust subpixel circle recognition bcz i want to find the square

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Answer 1

Image Analyst 2016-7-2

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I'd look at the average inter-row spacing as a function of row. It should be uniform. If there's a bias, you can determine that and use it to correct your real, non-calibration images. If you scan the calibration target multiple times and find that the inter-row distance is not deterministic and basically random, then there's not much you can do.

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arnold 2016-7-2

编辑：arnold 2016-7-2

ah, I see why you might be confused. Maybe I'm just not describing the problem clearly, let's try once more:

1. we like to calibrate this (and other) camera- and linear stage- systems using highly accurate calibration patterns that have well defined spacings (photolithographic masks i.e.). These can fill the entire field of view. Fiducial recognition is no problem, we know how to do that so we get the image coordinates of these teststructures. Our goal now is to get a distortion map / vector field for such an image from both inputs: real world distances/positions and image coordinates.

2. we'll repeat this process in order to get some information about the error/repeatability of such a 'camera calibration'. Naturally, one would translate/rotate the known calibration pattern. My first guess would be that one would determine a mean distortion as a result of multiple calibration runs and also a possibly location/vector based error estimation. It is to be expected, that the error along the scanning line is much smaller than along the moving stage, so be it.

3. We then want to measure samples that are non calibrated, like workpieces from a production. There are well defined fiducials/landmarks on these workpieces too. Again, we can do the recognition of these landmarks, it's already finished. The goal now is to determine the (relative) location of these points of interest in real world coordinates. .... basically, use the camera as a measurement device.

arnold 2016-7-2

编辑：arnold 2016-7-3

hehe, the problem must be in my head, I'm aware of that :)

So, where am I at:

I can extract the list with XY coordinates (image coordinates) of the test pattern. What do I do with that now? I'm lacking the knowledge of the proper algorithm to process this XY list together with the info, of constant distance. I would assume, there is a known algorithm, possibly implemented many times, to formulate a warping map, a vector fields with local offsets or something, which can then be interpolated and inversely applied in order to correct this and other images accordingly.

... but I don't have that knowledge nor can I find it. It might be that I'm confused by the fact that I only have relative coordinates for the real-life test pattern structures as to absolute image coordinates?

How would you do it? An algorithm (in plain words) or sample implementations would probably help me do it. I'm not lazy, I'll code it, but I don't know the approach and again, I'm almost certain this has to have been implemented somehow many times by now.

arnold 2016-7-3

编辑：arnold 2016-7-3

I can keep the angle more or less constant (+-5°) but this seems to be a dirty workaround though. I tried to create a point mesh with distance 400 and then use some incarnation of 'iterative closest point' to shift this template towards the best match with the found points but this wasn't robust at all. I mean, ICP shifts the measured point cloud so it has the least square error versus the template grid - that's bound to be a non-robust approach.

Attached you see heatmaps of column and row distances. The lines of the line-camera are horizontal, the stage is travelling vertically. That's why you see a clear error correlation of the VERTICAL distance heatmap - as expected.

I want a 2d calibration, not just test the line distance in one dimension. Here is the delta-vector field that I get using this ICP approach with a template of world coordinates.

My final goal is to end up with a matrix with columns x_image, y_image, dx, dy and I want to use a proven/good algorithm to allocate measured landmark-coordinates with world-coordinates....Only the distance between the landmarks is fixed, there is no DOMINANT landmark to create a coordinate system with and define an origin.

So the question might be how to create the coordinate system of the world coordinates properly (!) and align it with the image coordinate system?

arnold 2016-7-3

编辑：arnold 2016-7-3

here is an illustration of this iterative closest points approach.

1. I create a grid of points with the known world distance of the marks: 400 (µm or a.u.)

2. I overlay this synthetic grid with the found image coordinates of the marks (see upper left diagram)

3. ICP runs and tries to rigidly translate and rotate the measured point cloud to match the synthetic one (see upper right).

4. I then calculate the dx/dy from each measured point to its closest synthetic counterpart.

The first problem that comes to mind: For large samples dimensions (you only see about 1% of the image field of view), cumulated distances could end up way further than the dot distance so ICQ will fail. ...and that's just the first problem out of many I see.

dx dy vectorfield based on ICQ alignment of synthetic to measured points.

This diagram now shows the vector field created by using rigid ICP to align the measured dots with artificial template dots as shown above. So obviously, for a mostly symmetrical distortion, the errors around the center are almost zero and the peripheral ones are large. I'd be ok with that but the approach using ICP doesn't work as argued above. If the cumulative errors become larger than the point distance, i.e.

Walter Roberson 2016-7-3

I recommend posting your rephrased question here as a comment on your original question.

arnold 2016-7-3

done, see above.

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nonlinear 2d calibration of line-camera using known pattern - how to align world coordinates to points?

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nonlinear 2d calibration of line-camera using known pattern - how to align world coordinates to points?

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