Fixing distortion in photographic reproductions

Question

I am currently building a photographic setup which I intend to use to make reproductions of a large amount of transparencies(positive and negative film strips). As I will be using a fairly small (1") sensor and writing custom software for my rig, I intend to stitch together multiple images per frame. The way I intend to do this is by fitting the short (24mm) edge of the frame with the long(12mm) edge of my sensor and taking 3-4 overlapping images per frame. As all of this will be automated, the time consumption isn't really an issue.

The camera I am using has a ccd sensor of approximately 12x10mm and I will be using a lens from a film scanner (Minolta Dimage Scan 5400) as it is known to have high resolution and a very flat field.

never the less, in an effort to obtain the best possible results, I am currently looking into buying a distortion target to characterize the lens and minute errors in optical alignment at accquisition time and eventually undistort the images. This is because I would like to stitch the shots together and there for it is paramount to remove any distortion whatsoever.

While I have taken a course in Photogrammetric Computer Vision and am generally familiar with camera calibration, the fact that I am trying to characterize a static system with a perfectly planar image, is confusing me somewhat and I am uncertain what size/resolution distortion target would best suit my requirements.

I am tempted to think, that a couple frames 1-3(even one if the target is large enough) with a high resolution dot grid(such as this one ) would be enough and that I don't need 20+ images as one does in conventional camera calibration.

My question is: How many frames does one need to asses and correct distortion in a numerically stable way? Should the distortion target fill the entire frame or are multiple shots with shifts prefereable? Is there a specific term more suited to what I am trying to do than camera calibration, as I am trying to characterize the error in the whole system?

I will be using OpenCV.

Answer 1

In a general setting, multiple observations of a calibration target are needed because otherwise the focal length parameter(s) and principle point parameters are coupled so you would not be able to determine the correct value of both from a single image. Zhang's closed form solution would yield an under-determined system of equations.

Focal length estimation also require that at least one of your images presents some foreshortening. Otherwise you cannot discern between a long focal length and a target far away and a short focal length with a close target.

However if you do fix the linear pin-hole parameters and only want to estimate the non-linear Brown-Conrady parameters (for radial and tangential distortion), a single fronto-parallel image would be enough. Depending on the feature count, multiple images might be beneficial. Note that circles are imaged as distorted ellipses in general, so for high accuracy you might want to use an advanced detection algorithm, small circles, or saddle points instead.

Since many factors contribute to the stability of your solution, I recommend to study the unbiased covariance estimate of the parameters at your solution to judge if enough data was collected. More information: https://calib.io/blogs/knowledge-base/understanding-parameter-uncertainty

I believe camera calibration is the correct term, albeit "distortion correction" could be your search term. There is more direct solutions when only calibrating for lens distortion and specific instruments for that purpose, e.g. calibration harp.

Answer 2

I answered a related question in SO some time ago. Briefly, you can work your setup through a standard camera calibration procedure, and you have the option of "freezing" the focal length to a nominal value (which you can compute from the lens's focal length in mm and the sensor's dot pitch), since you are only interested in the nonlinear distortion. In fact, it is likely preferable to do so, since you can't show any perspective foreshortening to the calibration procedure, which makes the calibration of the focal length and principal point ill-conditioned.

As a practical matter, I'd still take multiple images, e.g. shifting your dot target half-spacing up and down, left and right, just to increase the size of the data set, and/or to have a separate data set for verification of the results.