DocumentCode :
2507406
Title :
Statistical assessment of image symmetries
Author :
Pawlak, Miroslaw ; Holzmann, Hajo
Author_Institution :
Electr. & Comput. Eng., Univ. of Manitoba, Winnipeg, MB, Canada
fYear :
2011
fDate :
28-30 June 2011
Firstpage :
805
Lastpage :
808
Abstract :
This paper formulates the problem of assessing reflection and rotations symmetries of an image function observed in the presence of noise. Rigorous statistical tests are developed for testing image invariance under reflections or under rotations through rational angles, as well as joint invariance under both reflections and rotations. The symmetry relations are expressed as restrictions for Fourier coefficients with respect to a class of radial orthogonal functions. Therefore, our test statistics are based on checking whether the estimated radial coefficients approximately satisfy those restrictions. We derive the asymptotic distribution of the test statistics under both the hypothesis of symmetry and under fixed alternatives. The tests require novel statistical analysis based on the theory of quadratic forms of random variables. Furthermore, the problem of estimating the parameters defining a given class of symmetry is also tackled. This is resolved by using the theory of semiparametric inference.
Keywords :
Fourier analysis; image processing; statistical distributions; statistical testing; Fourier coefficients; asymptotic distribution; image function; image invariance testing; image symmetries; radial orthogonal functions; reflection symmetry assessment; rigorous statistical tests; rotation symmetry; semiparametric inference theory; statistical analysis; statistical assessment; Joints; Noise; Noise measurement; Polynomials; Smoothing methods; Statistical analysis; Testing; limit distributions; noisy images; radial polynomials; semi-parametric; symmetry detection; testing hypothesis;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Statistical Signal Processing Workshop (SSP), 2011 IEEE
Conference_Location :
Nice
ISSN :
pending
Print_ISBN :
978-1-4577-0569-4
Type :
conf
DOI :
10.1109/SSP.2011.5967827
Filename :
5967827
Link To Document :
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