Iterative illumination correction with implicit regularization

This paper presents a retrospective algorithm for correcting the uneven illumination field in microscopy images. The illumination field is iteratively made uniform using an increasing sequence of bivariate polynomials. At each iteration, the least squares problem of fitting a 2-D polynomial to a sampled image is solved by using QR decomposition with column pivoting, where image samples are obtained by dynamic programming or watershed transform. This incremental scheme allows the smoothness constraint of the estimated bias field to be implicitly satisfied. The proper number of iterations is determined by an automatic stopping criterion. The experimental results show the effectiveness of the proposed approach when compared to a set of different well-established methods.