The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form which is both concise and explicit. Since the conventional uncertainty principle is such a constraint on the first and second moments, our result constitutes a g...

The role of moments in image normalization and invariant pattern recognition is addressed. The classical idea of the principal axes is analyzed and extended to a more general definition. The relationship between moment-based normalization, moment invariants, and circular harmonics is established. Invariance properties of moments, as opposed to their recognition properties, are identified using ...

We derive the expectations of the matrices xx'" C3 xx' and xx'" C3 xx"' C3 xx.", where C3 denotes a Kronecker product. From this, second and third moments of quadratic forms are obtained. The moments are derived under the following assumption on the product moments of the elements X, of x: For any non-negative integers a,, . . . , ah with C a, 1 6 , E[XE1X2. . . X z ] is i) finite; ii) zero, if...

Moment of images provides efficient descriptors and has been used in different image analysis application. The main advantage is their ability to provide invariant characteristic. In this paper a novel methodology has been carried out to classify SAR images using the Moments. This paper also provides the overview of most commonly used of moments and then present a moment based approached for cl...

We perform a complete “Michel parameter” analysis of all possible helicity structures which can appear in the process B → Xc l ν̄l. We take into account the full set of operators parametrizing the effective Hamiltonian and include the complete one-loop QCD corrections as well as the non-perturbative contributions. The moments of the leptonic energy as well as the combined moments of the hadronic...

A new method of normalization is used for the construction of the affine moment invariants. The affine transform is decomposed into translation, scaling, stretching, two rotations and mirror reflection. The object is successively normalized to these elementary transforms by means of low order moments. After normalization, other moments of normalized object can be used as affine invariant featur...

In this paper, an effective procedure to determine the reduced order model of higher order linear time invariant discrete systems is discussed. A new procedure has been proposed for evaluating Time moments of the original high order system. Numerator and denominator polynomials of reduced order model are obtained by considering first few redefined time moments of the original high order system....

The role of moments in image normalization and invariant pattern recognition is addressed. The classical idea of the principal axes is analyzed and extended to a more general definition. The relationship between moment-based normalization, moment invariants, and circular harmonics is established. Invariance properties of moments, as opposed to their recognition properties, are identified using ...

Image descriptors based on the circular-Fourier-radial-Mellin transform are used for position-, rotation-, scale-, and intensity-invariant multiclass pattern recognition. The orders of the radial moments and of the circular harmonics are chosen to obtain an efficient image description. The first-order radial moments of three circular harmonics are sufficient to obtain a satisfactory recognition...

In image watermarking, the watermark’s vulnerability to geometric transformations has long been a difficult problem. Using invariant image features to carry the watermark is an effective approach to addressing this problem. In this paper, a multibit geometrically robust image watermarking algorithm using Zernike moments (ZMs) and pseudo-Zernike moments (PZMs) is proposed. Unlike its counterpart...