Fast Algorithm of 3D Discrete Image Orthogonal Moments Computation Based on 3D Cuboid

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

“…Theoretically, for the 3D image f (x, y, z) with a size of N × M × K samples and order (n + m + k)th, the 3D Hahn moments nmk can be defined as [26]:…”

“…In theory, to reconstruct the 3D image, the inverse transformations of the 3D Hahn moments can be applied as follows [26]:…”

“…However, it should be emphasized that the intensity is between 0 and 255 in gray images, whereas zero intensity cuboids are neglected. With this methodology, we will have few elements to treat [26]. We assume the volume can be expressed by a discreet function f (x, y, z), in which the intensity f i represents each voxel of coordinates (x, y, z) as shown in Fig.…”

“…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].…”

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].…”