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Table 3 Computational time complexity for VNN, PNN, Spline, PT, FMM and KR algorithms

From: Reconstruction of freehand 3D ultrasound based on kernel regression

VNN

PNN

Spline

PT

FMM

KR

O(N · N p )

O(N · R3)

O(N)

O N · N p 2

O(N m  · log(N m ) · R3)

O(N · R6 · D)

  1. N x , N y , N z are the dimensions of the volume grid in x, y and z direction, N = N x ·N y ·N z , N p is the number of B-scans. N m = max(N x ,N y ,N z ), R is the size of cubic region, d is the number of dimsentions of the volume, D = d + 1.