Table 4 Correlation coefficients in all directions of Goldhill, Baboon, and Peppers.

From: A novel 4D chaotic system coupling with dual-memristors and application in image encryption

Images

Direction

Plain images

Ciphered image

4D-DMCS

Ref.44

Ref.60

Ref.63

Goldhill

Horizontal

0.9791

0.0389

− 0.0231

− 0.0115

− 0.0171

Vertical

0.9765

− 0.0151

0.0138

− 0.1290

− 0.0009

Diagonal

0.9624

0.0380

− 0.0002

− 0.0031

− 0.0094

Reverse diagonal

0.9623

− 0.0108

–

0.0505

–

Baboon

Horizontal

0.7533

0.0080

0.006

0.174

0.0101

Vertical

0.8686

0.0426

− 0.0324

− 0.0319

− 0.0091

Diagonal

0.7301

0.0129

− 0.0064

0.0236

− 0.0046

Reverse diagonal

0.7019

− 0.0092

–

0.0080

–

Peppers

Horizontal

0.9797

− 0.0014

0.0081

− 0.0112

0.0192

Vertical

0.9764

0.0342

− 0.0126

0.0017

− 0.0025

Diagonal

0.9605

0.0047

− 0.0097

0.0366

0.0294

Reverse diagonal

0.9699

− 0.0085

–

0.0080

–