Analyzing Image Structure by Multidimensional Frequency Modulation

Pattichis, Marios S.; Bovik, Alan C.

doi:10.1109/tpami.2007.1051

Cited by 55 publications

(41 citation statements)

References 42 publications

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“…The HT of a B-spline (respectively, dual-spline) wavelet is a B-spline (respectively, dual-spline) wavelet of same order, but with a different shift: (14) The importance of this result is that it allows us to identify the analytic B-spline wavelet of degree and shift…”

Section: Proposition 61 (Ht Pair Of B-spline Wavelets)mentioning

confidence: 99%

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Chaudhury

Unser

2009

IEEE Trans. Signal Process.

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Abstract-We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of , we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT-the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.

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Section: Proposition 61 (Ht Pair Of B-spline Wavelets)mentioning

confidence: 99%

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Chaudhury

Unser

2009

IEEE Trans. Signal Process.

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“…AM-FM models [5,8,13] provide a modulation domain image representation in terms of localized amplitude and frequency modulations. Recently, we demonstrated that such models are effective for representing infrared targets and backgrounds and can substantially enhance target-clutter class separability [7,11,12].…”

Section: Modulation Domain Frame Modelmentioning

confidence: 99%

Infrared Target Tracking with AM-FM Consistency Checks

Mould

Nguyen

Havlicek

2008

2008 IEEE Southwest Symposium on Image Analysis and Interpretation

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“…The eigen-harmonic decomposition (EHD) is based on planar and spherical functions that have been used for compact presentation of textured images as well as human facial images in some articles [31,32].…”

Section: Introductionmentioning

confidence: 99%

Approximation of bidirectional reflectance distribution function for highly efficient shading

Romanyuk¹,

Павлов²,

Romanyuk³

et al. 2017

Information Technology in Medical Diagnostics

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Abstract. Recognition of textured objects is a typical problem in computer vision and pattern recognition. Usually are meeting two variations of this problem. The first is the recognition of a signed texture. The second is objects of interest recognition in image with textured background. We offer an approach for solving of the both problems with using of the inverse resonant filtration. A textured object or background dynamic space can be approximated by a set of principal eigenvectors in the form of resonantharmonic functions called as eigen harmonics (EH). The Inverse ResonantFilter (IRF) which is resonant in respect to EH series eliminates textured background and forms indicator signal of certain species. The IRF is founded on the approximation and extrapolation of the texture template signal by series of EH. Two methods of 2-dimensional (2D) EH parameter estimation are considered. The methods give estimates robust tobreaks and noise peakspresentedin textured image signal. The first method is based on the linear symmetry model and can be presented as a double linear prediction model. Additionally the condition of the unitary symmetry is used to provide stationarity and periodicity of the model. The second method is based on 2D correlation matrix splitting with projection into the subspace of principal harmonic components. Implementation of the IRF is considered in spatial and spectral domains. Discrete Fourier transform with eigen kernel (DFTEK) was used for design and realization of the high order IRF. The DFTEK has fractionally fast transform algorithm. Aligning image fragment phases improved inverse resonant filtration in the spectral domain. It was shown that the optimal approach to image filtration consists of an initial fast filtration in the spectral domain, followed by postfiltration of the image zones containing anomalous background variations using IRF in the spatial domain. It was shown that the IRF is invariant to shift transform. It can be invariant to affine and scale transform if instead initial texture and image are using their invariant pattern in the form of image surface geometry characteristics.

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Analyzing Image Structure by Multidimensional Frequency Modulation

Cited by 55 publications

References 42 publications

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Infrared Target Tracking with AM-FM Consistency Checks

Approximation of bidirectional reflectance distribution function for highly efficient shading

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