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Estimation of non-radial vignetting using minimization procedures (CROSBI ID 726593)

Prilog sa skupa u zborniku | prošireni sažetak izlaganja sa skupa | međunarodna recenzija

Potoč, Dorotea ; Petrinović, Davor Estimation of non-radial vignetting using minimization procedures // Abstract Book 7th International Workshop on Data Science. 2022. str. 17-19

Podaci o odgovornosti

Potoč, Dorotea ; Petrinović, Davor

engleski

Estimation of non-radial vignetting using minimization procedures

Vignetting is a drop in pixel intensity from the center to the edges of an image and is caused by camera settings or lens limitations. It is mostly conceived and presented as a radially symmetrical model that can be easily observed and estimated from the image. The assumption is that there can be even a model that has an arbitrary non-radial shape. Often in the case of camera lens systems with non-radial vignetting, an incomplete correction occurs. For many applications, the compensation of this damping is very significant, which is difficult to achieve. There are also methods that can give good correction results with parabolic vignetting model [1]. The aim of this paper is to improve and extend the function for vignetting estimation of the radially symmetric model, for which the synthetic image creation was presented in the earlier paper [2]. The general form of vignetting is conceived as a function of the radius V = f(R’), where R’ is the normalized radius multiplied by the angle- dependent factor k(θ), R0 = R/maxR·k(θ), which realizes the desired non-radial model of vignetting. For a non-radially symmetric model, the factor changes depending on the angle. To try to find such a non-radial form of damping from scratch, first, a synthetic image was created following the described model, whose parameters are estimated using optimization procedures and compared with the given ones. Due to the non- linearity of the damping model estimation process itself, the problem of finding the optimal solution cannot be carried out analytically. The model will be well estimated if, by applying the reciprocal model to the image, a uniform brightness of the entire frame is obtained with as few deviations as possible. The minimization of ž these deviations, considering the parameters of the model, was carried out by numerical optimization with Matlab functions. The radius function is determined by the sum of the given harmonics. k(θ)= 1+sum (from n=1, to n = N-1) of (mai·cos(arctan((y − y0)/(x − x0))·i+ani), where mai is magnitude, ani is angle of harmonics. In our experiment, we used a function that contains 2 basic harmonics of given amplitudes and phases, which determined a non-circular curve of the same image intensities. Then we tried to find its form using minimization procedures, and we investigated how the initialization of the optimization procedure affects the possibility of finding the right solution. Testing was done to insert modified parameters of the damping model compared to the defaults used for image synthesis into the minimum search function as initialization of the vector of free optimization variables, for example, the shifted origin of the model, or changed magnitudes and phases of the radial factor angular dependence model. The first test was with a noise-free image, where good results are obtained, because the function founds a true parameters which truly minimize the objective function if it initializes with default values. Then, during the initialization of the optimization procedure, the negated default parameters of the model were applied, so the function does not find good solutions for these cases. The hypersurface of the objective function itself contains a lot of local minima, so we get closest possible local minimum it encounters, and that is not our desired solution. In the case of an initialization equal to the scaled value of the default parameter vector, for example, if all parameters are scaled to 40% of the default values, the minimization of the objective function is very successful in finding the desired results. If the scaling is carried out by <40%, good solutions are no longer obtained, but they are still better than in the case of negation because we are in the same hyper-quadrant of the parameters space, and the optimization moves in good directions. When noise is added to the image (SNR =29 dB), if just the default parameters are chosen for initialization, good results are also obtained, and the function finds a proper center very quickly. We get little bit worse results than with image without noise , but still pretty good center is found for scaled initial conditions used for initialization as long as the parameters are scaled by at most 40%. Similarly, as with noise- free images, if the initial parameters are negated, suboptimal solutions are obtained. When the noise is increased (SNR = 15 dB), for slightly scaled initial parameters (e.g. 70% of given value) , a well-flattened surface is also obtained, but now the center is shifted a little more, but they are in the same hyper-quadrant. Noise in the image can make it harder to find the center, but regardless of that, the function can still find and align the vignetting. This work has shown that for different initial conditions, excellent alignments of the surface can be obtained, but for certain cases, we cannot obtain the specified origin of the vignetting model that we assigned to it. In further work, we will further investigate this initialization problem to get the desired alignment of the surface through optimization.

image processing, vignetting, non-radial model

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Podaci o prilogu

17-19.

2022.

objavljeno

Podaci o matičnoj publikaciji

Abstract Book 7th International Workshop on Data Science

Podaci o skupu

7th International Workshop on Data Science (IWDS 2022)

poster

26.10.2022-26.10.2022

Zagreb, Hrvatska

Povezanost rada

Elektrotehnika, Računarstvo