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Table 4 Computational time complexity for VNN, PNN, DW, FMM, KR, BI and GPM algorithms

From: Global Patch Matching (GPM) for freehand 3D ultrasound reconstruction

Method

Computational time complexity

Bin-filling scheme

Hole-filling strategy

VNN

–

\(O(N \cdot N_{p} \cdot N_{u} \cdot N_{v} )\)

PNN

\(O(N_{p} \cdot N_{u} \cdot N_{v} )\)

\(O(N \cdot R)\)

DW

–

\(O(N \cdot N_{p} \cdot R \cdot N_{u} \cdot N_{v} )\)

FMM

\(O(N_{p} \cdot N_{u} \cdot N_{v} )\)

\(O(M \cdot \log (M) \cdot R^{3} )\)

KR

\(O(N_{p} \cdot N_{u} \cdot N_{v} )\)

\(O(M \cdot R^{6} )\)

BI

–

\(O(N \cdot N_{p} \cdot R \cdot N_{u} \cdot N_{v} \cdot T)\)

GPM

\(O(N_{p} \cdot N_{u} \cdot N_{v} )\)

\(O(N \cdot R \cdot N)\)

  1. \(N = N_{x} \cdot N_{y} \cdot N_{z}\), \(M = \hbox{max} (N_{x} ,N_{y} ,N_{z} )\)