Using the variational principle of leveling illumination in images

Abstract

This work describes and practically implements the method of leveling illumination in images of various origins. Insufficient or uneven lighting can result in loss of detail, low contrast, or incorrect color reproduction. Lighting that is too bright can result in areas where detail is lost due to excessive brightness. Also, during the formation and analysis of various medical images, the problem of insufficient illumination of the image arises, that is, the image looks dark, details are difficult to see, especially in the shadows. The practical part of the work contains a description of the mathematical model of the transition from the variational problem (in the optimization form) to the differential form. A comparative analysis of existing computational methods of mathematical physics was also conducted. The working time and the number of iterations for obtaining results that form images with uniform illumination for various images were experimentally determined.