A Multiscale Wavelet-Based Test for Isotropy of Random Fields on a Regular Lattice

A test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed. The test is based on the wavelet theory, and can operate on the horizontal and vertical scale of choice, or on any combination of scales. Scale is introduced through the wavelet v...

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Bibliographic Details
Published in:IEEE transactions on image processing 2015-02, Vol.24 (2), p.694-708
Main Authors: Thon, Kevin, Geilhufe, Marc, Percival, Donald B.
Format: Article
Language:English
Subjects:
Algorithms
Anisotropic magnetoresistance
Anisotropy
Covariance matrices
Density
Discrete wavelet transforms
Equations
Fields (mathematics)
Handles
Horizontal
Humans
Image Processing, Computer-Assisted - methods
Isotropy
Lattices
Mammography
Maximal overlap discrete wavelet transform
Methods
random fields
Transaction processing
VDP
Vectors
Wavelet
Wavelet Analysis
Wavelet transforms
wavelet variance
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Summary:A test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed. The test is based on the wavelet theory, and can operate on the horizontal and vertical scale of choice, or on any combination of scales. Scale is introduced through the wavelet variances (sometimes called as the wavelet power spectrum), which decompose the variance over different horizontal and vertical spatial scales. The method is more general than existing tests for isotropy, since it handles intrinsically stationary random fields as well as second-order stationary fields. The performance of the method is demonstrated on samples from different random fields, and compared with three existing methods. It is competitive with or outperforms existing methods since it consistently rejects close to the nominal level for isotropic fields while having a rejection rate for anisotropic fields comparable with the existing methods in the stationary case, and superior in the intrinsic case. As practical examples, paper density images of handsheets and mammogram images are analyzed.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2014.2387016