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• ERROR ESTIMATION FOR MULTIPLE COMPARISON OF NOISY IMAGES

  A.N. Karkishchenko, V. B. Mnukhin

  2021-07-18

  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.