On the Metric on Images Invariant with Respect to the Monotonic Brightness Transformation
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On the Metric on Images Invariant with Respect to the Monotonic Brightness Transformation A. N. Karkishchenkoa,*, and V. B. Mnukhina,** a
Southern Federal University, Taganrog, 347928 Russia * e-mail: [email protected] ** e-mail: [email protected]
Abstract—It is described how to construct a distance on analog and quantized images, which is invariant with respect to strictly monotonic increasing transformations of the brightness function. The distance function takes into account possible normal noise on the image. The maximal value of such a distance for any number of quantizing levels and noise parameters is calculated. The experimental results, which make it possible to compare the invariant distance measure with classical measures, are presented. Keywords: image, monotonic transformation, invariant distance, analog and quantized images, quasi-order relation, normal noise, structure matrix, sign representation DOI: 10.1134/S1054661820030104
INTRODUCTION When solving the problem on interpreting and recognizing video information, it is important to measure the distance or similarity between digital images, since as a rule at this stage, the final decision is formed. The quality of recognizing system operation depends on the procedure for estimating the proximity of images. There are different approaches for formalizing a concept for the proximity of images and methods for its measuring. But very often they share a common disadvantage: insufficient agreement with the human visual system. The human system for image perception is very complicated and due to this fact, it is very unlikely to construct a procedure for measuring proximity, which properly meets this requirement. Difficulties intrinsic to this problem can be separated to two categories. On one hand, the images are subject to variations: these are movements of the observed scene, rotation, zooming, deformation, etc. On the other hand, image brightness can change greatly due to lighting variations, shadows, and overlap from other objects. In addition, there are noises of different nature. But human easily find similar images even if one of them is subjected to mentioned transformations and distortions. The standard metrics do not consider the features of human perception. When a person analyzes images, he pays less attention to brightness distortion in the image, to shadows and specks, but he analyzes the character of brightness variation and pays more attention to qualitative differences, not quantitative one. In
Received July 4, 2019; revised December 15, 2019; accepted February 14, 2020
[1], properties of absolute and mean square error are examined in the case of power, logarithmic, gradient and Laplace transformations. As a result, it is revealed that the mentioned measures do not produce results being in good agreement with a subjective estimate. In [2] a model example is presented of two artificially generated test images on the base of the same initial image, which have nearly the same mismatching with initial image according to the Mink
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