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Table 3 Image quality measures

From: A novel edge based embedding in medical images based on unique key generated using sudoku puzzle design

Measures

Formula

PSNR

10log10 \(\left( {\frac{256*256}{MSE}} \right)\)

MSE

\(\frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{m}} \mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} ({\text{A}}\left( {{\text{i}},{\text{j}}} \right) - {\text{B}}({\text{i}},{\text{j}}))^{2} }}{m*n}\)

SSIM

\(\frac{{(2 * {{\upmu }}_{\text{A}} * {{\upmu }}_{\text{B}} + {\text{c}}_{1} ) (2 * {{\upsigma }}_{\text{AB}} + {\text{c}}_{2} ) }}{{ ({{\upmu }}_{\text{A}}^{2} + {{\upmu }}_{\text{B}}^{2} + {\text{c}}_{1} )({{\upsigma }}_{\text{A}}^{2} + {{\upsigma }}_{\text{B}}^{2} + {\text{c}}_{2} )}}\)

UIQI

\(\frac{{4 * {{\upsigma }}_{\text{AB}} * {{\upmu }}_{\text{A}} * {{\upmu }}_{\text{B}} }}{{({{\upsigma }}_{\text{A}}^{2} + {{\upsigma }}_{\text{B}}^{2} )({{\upmu }}_{\text{A}}^{2} + {{\upmu }}_{\text{B}}^{2} ) }}\)

R

\(\frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{N}} \left( {\frac{{{\text{A}}_{\text{i}} - {{\upmu }}_{\text{A}} }}{{{{\upsigma }}_{\text{A}} }}} \right)\left( { \frac{{{\text{B}}_{\text{i}} - {{\upmu }}_{\text{B}} }}{{{{\upsigma }}_{\text{B}} }}} \right)}}{{{\text{N}} - 1}}\)