ERROR ESTIMATION FOR MULTIPLE COMPARISON OF NOISY IMAGES
Abstract
The aim of this work is to study the effect of noise on the image on the quality of comparison of a
finite set of images of the same shape and size. This task inevitably arises when analyzing scenes, detecting
individual objects, detecting symmetry, etc. The noise factor must be taken into account, since the
difference between digital objects can be caused not only by the mismatch of the compared images of
real objects, but also by distortions due to noise, which is almost always takes place. This differenceturns out to be proportional to the level of the noise component. The main result of this article is an
analytical estimate for the probability of a given level of error, which may arise in the multiple comparison
of a finite set of commensurate digital images. This estimate is based on a low-level comparison,
which is a pixel-by-pixel calculation of image differences using the Euclidean metric. In this case, a
standard assumption is made about the independent normal noise of image intensities with zero mathematical
expectation and a priori established standard deviation in each pixel. The evidence presented in
the article allows us to assert that the obtained estimate should be regarded as sufficiently "cautious"
and it can be expected that in reality the scatter of the measure caused by noise in the image will be
significantly less than the theoretically found boundary. The estimates obtained in this work are also
useful for detecting various types of symmetry in images, which, as a rule, lead to the need to calculate
the difference of an arbitrary number of commensurate digital areas. In addition, they can be used as
theoretically grounded threshold values in tasks requiring a decision on the coincidence or difference of
images. Such threshold values inevitably appear at various stages of processing noisy images, and the
question of their specific values, as a rule, remains open; at best, heuristic considerations are proposed
for their selection.
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