A Smooth Non-Iterative Local Polynomial (SNILP) Model of Image Vignetting

Abstract

Image vignetting is one of the major radiometric errors, which occurs in lens-camera systems. In many applications, vignetting is an undesirable phenomenon; therefore, when it is impossible to fully prevent its occurrence, it is necessary to use computational methods for its correction in the acquired image. In the most frequently used approach to the vignetting correction, i.e., the flat-field correction, the usage of appropriate vignetting models plays a crucial role. In the article, the new model of vignetting, i.e., Smooth Non-Iterative Local Polynomial (SNILP) model, is proposed. The SNILP model was compared with the models known from the literature, e.g., the polynomial 2D and radial polynomial models, in a series of numerical tests and in the real-data experiment. The obtained results prove that the SNILP model usually gives better vignetting correction results than the other aforementioned tested models. For images larger than UXGA format (1600×1200), the proposed model is also faster than other tested models. Moreover, among the tested models, the SNILP model requires the least hardware resources for its application. This means that the SNILP model is suitable for its usage in devices with limited computing power.

Research on Quality Detection of Jujube (Ziziphus jujuba Mill.) Fruit Based on UAV Multi-Spectrum

“…Afterward, the ROI tool was used again to obtain jujube fruit information. The sampling window was set to 3 × 3 pixels and the unpolarized and polarized reflectances of 100 jujube fruits were calculated [30,31].…”

Image Vignetting Correction Using a Deformable Radial Polynomial Model

“…The method for a simple realization of non-radial to radial vignetting transformation is taken from the method of modeling non-radial vignetting presented in [ 37 ]. According to the solution presented there, to accomplish such transformation it is sufficient to slightly modify Equation ( 4 ) by a parameter , as follows The can be treated as the measure of non-radiality of the vignetting, where, for ideal radial vignetting , and for non-radial vignetting , e.g., for , the vignetting in the vertical ( y ) direction is stronger than in the horizontal ( x ) direction.…”

“…The entire experiment, that is, from the image acquisition, through all calculations, to data presentation, was carried out using the MATLAB R2021b software package with the Image Acquisition Toolbox and the Optimization Toolbox. In the experiment, four vignetting models have been compared, that is, the novel deformable radial polynomial (DRP) model; known from the literature the radial polynomial (RP) [ 38 ] and polynomial 2D (P2D) [ 25 ] models; and the model which in terms of the quality of the vignetting correction can be treated as a state-of-the-art solution, that is, the smooth non-iterative local polynomial (SNILP) model [ 37 ].…”

“…For the others parameters of the function their default values have been used. The other two models, that is, the P2D and SNILP models, have been implemented according to the information given in [ 37 ].…”

“…Adjusting the flat-field method to the analyzed system is a matter of using the vignetting model, which is appropriate for the actual vignetting occurring in this system. In the literature, different parametric vignetting models have been presented, for example, the polynomial 2D (P2D) model [ 25 , 35 , 36 ], the exponential 2D polynomial model [ 35 ], the smooth non-iterative local polynomial (SNILP) model [ 37 ], the radial polynomial (RP) model [ 38 ], the hyperbolic cosine model [ 39 ], and the Gaussian function [ 40 ]. The last three mentioned vignetting models belong to a widely used approach, which assumes that the actual vignetting V of the lens-camera system has a cylindrical symmetry.…”