Equidistant distortion model

[NikolausDemmel]

Hi, could you point me to a resource/paper explaining the equidistant distortion model? It seems to me the paper reference on [1] is not discussing that.

Am I right to assume that the standard ROS tools (image_proc) do not support that distortion model, but rather only the pinhole camera model + radtan distorition model (called plumb_bob in CameraInfo) [2,3]?

[1] https://github.com/ethz-asl/kalibr/wiki/supported-models
[2] http://wiki.ros.org/image_pipeline/CameraInfo
[3] http://docs.ros.org/api/sensor_msgs/html/msg/CameraInfo.html

[furgalep]

@rehderj, can you provide a paper with the equidistant model that you implemented?

To the best of my knowledge you are right; the ROS tools only support pinhole + radtan.

[rehderj]

Hi, please see equation 7 of the referenced paper, which should describe the equidistant distortion model employed in kalibr. While there is a more complete model including additional tangential distortion reported in that work, kalibr uses the radially symmetric model detailed on in section II.A of the paper. Note that this is consistent with the work of other groups, which can be found here, equation 3-8.
My understanding of ROS from here is that it currently does not support this model.
However, we found it to return lower reprojection errors for a wide range of optics, which again is consistent with findings in this paper.

[NikolausDemmel]

Thanks for the pointers! I will look them up and possibly come back with any additional questions.

[rehderj]

Sure, feel free to approach us with additional questions. As an addition, the last comment referred to figure 6 in the Richardson paper, which suggests (for these particular optics) a generally lower reprojection errors as well as a significant gain in accuracy in the peripheral parts of the image.

[schneith]

If you need to undistort images in ROS using a pinhole camera and an equidistant distortion model, the code in the repo below might be useful for you.

https://github.com/schneith/undistorter

[NikolausDemmel]

@schneith: this looks indeed very helpful. Thanks for the pointer! I will test this once I have augmented our data with current calibration in CameraInfo format.

[NikolausDemmel]

So while implementing the calibration model in our system an additional question came up about the undistort function:

@schneith uses a fixed number of 20 iterations to compute the undistorted radius. Why 20? Is this value just common wisdom for "large enough"? What could be an appropriate abort criteria?

P.S.: The undistorter ROS package works nicely with our calibration values to rectify recorded sequences, thanks @schneith.

[NikolausDemmel]

One more question actually about @schneith 's implementation: Is there a reason that there is no check for really small thetad in undistort, like there is for r in distort.

[rehderj]

There is little justification for the specific number of 20 iterations. Feels free to implement your favorite abort criterion, good candidates might either be the amount of change in the incidence angle theta in subsequent iterations or the absolute difference between the measured distorted theta and your modelled distorted theta when applying the distortion to the current estimate.
The check for small r is for numerical stability. We have not evaluated if it is necessary, nor whether there cannot arise numerical instabilities in the undistortion under all circumstances.

[NikolausDemmel]

That makes perfect sense, thank you!