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Title: On testing randomness of binary images Authors:  Bruno Ebner - Karlsruhe Institute of Technology (Germany) [presenting]
Abstract: New methods are presented for testing the randomness of binary image data. The tests are based on so-called Minkowski functionals such as the area, the perimeter or the Euler-Poincar characteristic. We derive the limit null distribution of the test statistics by means of Stein's method in the Kolmogorov distance using dependency graphs. A Monte Carlo simulation study shows that the tests are able to detect alternatives and we apply it to data related to some irrational numbers and mathematical constants such as pi, e, square root of 2, Euler-Mascheroni constant and the Catalan constant.