Table 7.

The correlation coefficients $\gamma$ of the testing images.

Image	$\mathit{\gamma }$	Input	Cipher Images
			DFDLC	FHDNA [2]	HCDNA [61]	CDCP [60]	IC-BSIF [51]	DFBC [6]
Lena	${\gamma }_h$	0.9691	0.0023	0.0000	−0.0015	−0.0004	−0.0032	0.0002
	${\gamma }_v$	0.9841	0.0009	−0.0022	−0.0020	0.0028	0.0013	0.0010
	${\gamma }_d$	0.9639	0.0008	0.0004	0.0024	0.0016	−0.0009	0.0006
Cameraman	${\gamma }_h$	0.9830	0.0011	0.0013	0.0004	−0.0001	−0.0015	−0.0008
	${\gamma }_v$	0.9887	0.0009	0.0033	0.0003	0.0019	0.0010	−0.0013
	${\gamma }_d$	0.9746	−0.0002	−0.0000	−0.0013	0.0010	−0.0012	−0.0002
Barbara	${\gamma }_h$	0.8940	−0.0003	−0.0022	0.0010	−0.0026	−0.0002	0.0027
	${\gamma }_v$	0.9572	0.0030	−0.0002	0.0004	0.0006	−0.0004	−0.0029
	${\gamma }_d$	0.8942	−0.0029	−0.0000	−0.0009	0.0005	0.0010	−0.0005
Mandril	${\gamma }_h$	0.9322	0.0022	0.0016	−0.0007	0.0012	0.0026	−0.0006
	${\gamma }_v$	0.9100	0.0005	0.0035	−0.0001	0.0009	−0.0001	−0.0018
	${\gamma }_d$	0.8647	−0.0023	−0.0025	−0.0017	−0.0004	0.0001	0.0016
Bw	${\gamma }_h$	1.0000	0.0019	0.0006	0.0004	−0.0004	0.0003	0.0000
	${\gamma }_v$	0.9922	−0.0006	0.0009	0.0013	0.0001	−0.0005	−0.0002
	${\gamma }_d$	0.9961	−0.0012	−0.0012	−0.0002	0.0005	0.0002	−0.0016
Pirate	${\gamma }_h$	0.9593	−0.0000	0.0015	−0.0023	−0.0012	−0.0026	−0.0012
	${\gamma }_v$	0.9675	0.0009	0.0057	−0.0000	−0.0008	−0.0006	0.0013
	${\gamma }_d$	0.9432	0.0015	0.0001	0.0011	0.0006	0.0005	0.0005
Couple	${\gamma }_h$	0.9451	0.0012	0.0013	0.0014	−0.0001	−0.0006	−0.0009
	${\gamma }_v$	0.9514	0.0025	−0.0026	0.0008	0.0001	0.0023	0.0022
	${\gamma }_d$	0.9116	0.0017	−0.0011	−0.0007	0.0005	−0.0008	−0.0024
Finger	${\gamma }_h$	0.9343	−0.0001	0.0002	0.0007	−0.0023	0.0004	−0.0025
	${\gamma }_v$	0.9168	0.0002	−0.0025	0.0029	−0.0032	−0.0009	0.0004
	${\gamma }_d$	0.8664	0.0017	0.0005	−0.0022	−0.0010	0.0030	−0.0006
Peppers	${\gamma }_h$	0.9733	0.0003	−0.0045	0.0000	−0.0003	−0.0031	0.0008
	${\gamma }_v$	0.9763	−0.0010	−0.0049	−0.0005	0.0003	−0.0010	−0.0003
	${\gamma }_d$	0.9650	0.0011	−0.0012	−0.0005	−0.0025	0.0017	−0.0010
Houses	${\gamma }_h$	0.9077	0.0020	0.0006	0.0004	0.0026	0.0001	−0.0002
	${\gamma }_v$	0.9173	0.0015	0.0004	−0.0032	0.0002	0.0017	0.0006
	${\gamma }_d$	0.8439	0.0020	0.0021	0.0038	−0.0011	0.0034	0.0002
Range		[0.8439,1.000]	[−0.0023,0.0030]	[−0.0049, 0.0057]	[−0.0032, 0.0038]	[−0.0032, 0.0028]	[−0.0032, 0.0034]	[−0.0029, 0.0027]
Interval Width		0.1561	0.0053	0.0106	0.0070	0.0060	0.0066	0.0056