Orientation-dependent distribution of the length of a random segment and covariogram
Tóm tắt
The paper considers a random segment L(ω) in R
n
with fixed direction and length that intersects a given bounded convex body D ⊂ R
n
. We obtain a relationship between the covariogram of D and the distribution of the random variable |L| — the length of L ∩ D. A relationship between the distribution of |L| and the orientation-dependent chord length distribution is also obtained. As a consequence, we obtain a relationship between the chord length distribution function and the distribution of the random variable |L|.
Tài liệu tham khảo
L. A. Santalo, Integral Geometry and Geometric Probability (Addision-Wesley, Reading, MA, 2004).
R. De-Lin, Topics in Integral Geometry (Utopia press, Singapore, 1994).
G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975).
G. Bianchi and G. Averkov, “Confirmation of Matheron’s Conjecture on the covariogram of a planar convex body”, Journal of the European Mathematical Society 11, 1187–1202, 2009.
A. Gasparyan and V. K. Ohanyan, “Recognition of triangles by covariogram”, Journal of Contemporary Mathematical Analysis (Armenian Academy of sciences), 48(3), 110–122, 2013.
H. S. Harutyunyan and V. K. Ohanyan, “Orientation-dependent section distributions for convex bodies”, Journal of Contemporary Mathematical Analysis (Armenian Academy of sciences), 49(3), 139–156, 2014.
A. Gasparyan and V. K. Ohanyan, “Covariogram of a parallelogram”, Journal of Contemporary Mathematical Analysis (Armenian Academy of sciences), 49(4), 194–206, 2014.
N. G. Aharonyan, H. S. Harutyunyan and V. K. Ohanyan, “Random copy of a segment within a convex domain”, Journal of Contemporary Mathematical Analysis (Armenian Academy of sciences), 45(5), 348–356, 2010.