Fast 3D image reconstruction by cuboids and 3D Charlier’s moments

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

“…High-dimensional extension of image moments appeared very early [148] and attracted significant attention in the last decade [145,158,[185][186][187][188][189]. A possible explanation for its popularity might be the rapid development of devices and technologies related to 3D images such as medical imaging [183] and computer graphics [184].…”

Fast computation of 3D Tchebichef moments for higher orders

“…Mesbah et al [20,21], uses a fast and accurate algorithm based on matrix multiplication to extract local characteristics of 3D Krawtchouk moments. Karmouni et al presents the fast and stable computation of Mexnier [22] and Charlier [23] 3D moments by using digital filters the Z transformation and dividing it into a set of fixed-size blocks that are processed moments separately. Also, they propose a fast and efficient method for calculating 3D discrete orthogonal invariant moments [24].…”

“…Finally, Sayyouri et al [25] performs a way to compute generalized Laguerre orthogonal polynomials based on matrix multiplication. From the previous works, there are three strategies for moment computation; direct calculation, dividing the object into cubes [18,[22][23][24]26] and calculating using matrices [20,21,25,[27][28][29].…”

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

“…In theory, the moment approach is divided into three main categories: The non-orthogonal moments, such as geometric and complex moments [5,6], the continuous orthogonal moments [7][8][9][10][11][12][13], and the discrete orthogonal moments (DOMs). We are going to focus mainly on DOMs such as the moments of Tchebichef [14,15], Krawtchouk [14][15][16][17], Hahn [18], Charlier [19][20][21], and last but not least Meixner [21,22], as these have concrete advantages over 3D image analysis. However, it has been noted that the computation of moments is a complex and costly task in terms of time.…”

“…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].…”