Moments are expectation values of products powers position and momentum, taken over quantum states (or averages a set classical particles). For free particles, the evolution in case is closely related to that particles. Here we consider symmetrized moments for particles one dimension, first examining geometric properties up fourth order, as determined by their extrema inflections. These specifi...

An algorithm is given for the computation of moments of f 2 S, where S is either a principal h-shift invariant space or S is a nitely generated h-shift invariant space. An error estimate for the rate of convergence of our scheme is also presented. In so doing, we obtain a result for computing inner products in these spaces. As corollaries, we derive Marsden-type identities for principal h-shift...

A new set, to our knowledge, of orthogonal moment functions for describing images is proposed. It is based on the generalized pseudo-Zernike polynomials that are orthogonal on the unit circle. The generalized pseudo-Zernike polynomials are scaled to ensure numerical stability, and some properties are discussed. The performance of the proposed moments is analyzed in terms of image reconstruction...

Tchebichef moments are successfully used in the field of image analysis because of their polynomial properties of discrete and orthogonal. In this paper, two new affine invariant sets are introduced for object recognition using discrete orthogonal Tchebichef moments. The current study constructs affine Tchebichef invariants by normalization method. Firstly, image is normalized to a standard for...

The presence of unique quantum correlations is the core of quantum-information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using correlation functions defined for quasiprobability distributions. In particular, we discuss the possibility of probing the negativity of a quasiprobability by comparin...

Feature extraction is the key process in any pattern recognition issues. There is no exception in object recognition. In this paper, several feature extraction approaches in the field of object recognition are summed up. Zernike and Hu are two invariant moments and geodesic descriptors are applied directly to binary images and so we can have more information about the general shape of the objec...

We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of them, with possible discontinuities at the endpoints. Even more surprising is the fact that functions preserving moments of three point masses must preserve...

In this paper we proposed a method to design and numerically calculate high-order rotation invariants from Gaussian–Hermite moments. We employed the invariant properties of the Gaussian–Hermite moments discovered earlier in [1] and we showed how to construct rotation Gaussian–Hermite invariants even in the cases when no explicit invariants from geometric moments are available. We verify by expe...

A novel moment, called 3D polar-radius-invariant-moment, is proposed for the 3D object recognition and classification. Some properties of these new moments including the invariance on translation, scale and rotation transforms are studied and proved. Then structure moment invariants are given to distinguish complicated similar shapes. Examples are presented to illustrate the performance and inv...