Fast Reconstruction of 3D Images Using Charlier Discrete Orthogonal Moments

Partial 3D Image Reconstruction by Cuboids Using Stable Computation of Hahn Polynomials

“…This section presents the findings of experiments to test the theoretical structure of the previous sections. In order to achieve the objective of this section, a process is envisaged for track screening: the Mean Square Error (MSE) used to measure the error of reconstruction between the original image and the restoration image, MSE given by this equation [25] in the case of 3D image:…”

“…In theory, an original 3D image function f (x, y, z) of size [N × M × K ] can be represented from infinite series of 3D moments [25].…”

“…However, it has been noted that the computation of moments is a complex and costly task in terms of time. Therefore, several algorithms are implemented into the literature to reduce the cost of moment calculation; Most of the algorithms are either centered on the use of the image new representations [23][24][25][26], or the acceleration of time calculating values of polynomials [16][17][18][19]22].…”

Optimal reconstruction and compression of signals and images by Hahn moments and artificial bee Colony (ABC) algorithm

“…Moment descriptors are widely used for the analysis, storage and transmission of signals and images. They are successfully used in different applications such as pattern recognition [ 3 , 13 ], classification [ 16 , 28 ], reconstruction [ 7 , 21 ], compression [ 14 , 34 ] and watermarking [ 12 ]. The moments are defined as the coefficients of projection of signals or images on often orthogonal basis.…”

Watermarking Applications of Krawtchouk–Sobolev Type Orthogonal Moments

“…The key point of the application we present here relies on their novel properties related to their norm, and on the construction of the so-called weighted Krawtchouk-Sobolev type orthogonal polynomials. The use of orthogonal polynomials (and orthogonal moments) in a watermarking scheme is widely spread in the scientific community (see, for example [2][3][4][5][6][7][8][9] among many other references). Nevertheless, and to the best of our knowledge, it is the first time that any Sobolev-type orthogonal polynomial family has been considered in such an application, achieving reasonably different, and in some cases, positive results.…”