Image Vignetting Correction Using a Deformable Radial Polynomial Model

Image vignetting is one of the major radiometric errors that occur in lens-camera systems. In many applications, vignetting is an undesirable effect; therefore, when it is impossible to fully prevent its occurrence, it is necessary to use computational methods for its correction. In probably the most frequently used approach to the vignetting correction, that is, the flat-field correction, the use of appropriate vignetting models plays a pivotal role. The radial polynomial (RP) model is commonly used, but for its proper use, the actual vignetting of the analyzed lens-camera system has to be a radial function. However, this condition is not fulfilled by many systems. There exist more universal models of vignetting; however, these models are much more sophisticated than the RP model. In this article, we propose a new model of vignetting named the Deformable Radial Polynomial (DRP) model, which joins the simplicity of the RP model with the universality of more sophisticated models. The DRP model uses a simple distance transformation and minimization method to match the radial vignetting model to the non-radial vignetting of the analyzed lens-camera system. The real-data experiment confirms that the DRP model, in general, gives better (up 35% or 50%, depending on the measure used) results than the RP model.