I am trying to add a new feature to our existing implementation of the bundle adjustment in code.
The algorithm uses the Gauss-Newton method and has been working for well over a decade. The least squares "A" matrix is populated using initial approximations of the image exterior orientations, as well as the object points. The book from Kraus - "Photogrammetry: Fundamental and Standard Processes" - was used for this.
A while ago, self calibration was added to this algorithm, however, only the formulae by Ebner and Gruen were added (formula for Ebner here). I am now trying to add the "Brown-Conrady" formula which is well documented in this paper (final algorithm under "concluding remarks"). It uses 10 parameters to determine deltaX and deltaY.
When I include all the parameters except for deltaC (the correction to the focal length/camera constant), our algorithm works and the adjustment converges and produces the desired residuals. However, as soon as I introduce deltaC (which mathematically I see as "allowing" the image points to scale by some amount in X and Y) the adjustment diverges.
The input to the algorithm is a large set of already undistorted aerial images, along with their control points and a large number of image points. We are therefore expecting the distortion/correction parameters to be close to zero, since the images are already undistorted. This is indeed the case for Ebner and Grun.
For Brown, however, some of the parameters (and therefore the delta corrections) grow uncontrollably. I have tried scaling these parameters (the principle points and focal length correction deltaC) so that they are closer in magnitude to the other parameters (K1,K2,K3,P1,P2) however this did not help - the adjustment diverges all the same.
Is there any reason for this? Could it perhaps be because the images are already undistorted? Or something to do with this aerial job in particular?
I have not provided code as it is simply too complex, however I feel it is maybe an understanding of the implementation as opposed to specific code where I am going wrong.
Thanks!
