In these publications we have similarity measures for images..

http://web.imis.athena-innovation.gr/~azigomit/publications/2013MetadataMultimediaStreams.pdf

http://web.imis.athena-innovation.gr/~azigomit/publications/2011ImgQR.pdf

thank you brothers Hamza Kheddar and Athanasios Zigomitros for your response

I want  another measures for image quality after hiding process exception the MSE and PSNR measures

I think you are interested in performance evaluation measure of an image steganographic algorithm/model.From literature, image steganographic techniques could be evaluated for metrics such as imperceptibility,payload capacity and robustness.This can be achieved evaluating the image quality of the final stego image using image quality metrics such as SNR,MSE,PSNR and for full reference case such as Structural Similarity index metric.

Authors might need to check my contribution to secure e-voting in this link: https://www.academia.edu/6371423/Performance_Evaluation_of_modified_Stegano-Cryptographic_model_for_Secured_E-voting

I strongly disagree. Evaluation of a data hiding scheme for images cannot be reduced to image quality measurement. Either this data hiding scheme is meant for watermarking. Then robustness, payload, security must also be evaluated. Either this data hiding scheme is meant for steganography and then payload and detectability must be evaluated too. In any case, data hiding is matter of trade-off. Only looking at one criterion (such as image quality) is useless. 

Dear Olaniyi Olayemi Mikail thank you for your response.

hi Teddy Furon, thank for your comment.

now how can evaluated the robustness and the security for any steganography method

robustness of  a steganographic method is evaluated by the following method:

1. allow the watermarked image to undergo various attack like noise, compression, histogram equalization, scaling, cropping, rotation etc. (One attack to be studied at a time)

2. retrieving the watermark(hidden message) from these attacked copies of the watermarked image.

3. compare the retrieved information with the originally hidden information. (if the hidden message is binary, use Bit correct ratio)

4. if the original and retrieved information are same, the technique  (used for hiding) is robust against the specific attack.

The best result is given by PSNR value

"how can evaluated the robustness and the security for any steganography method".

No, no, no. Data hiding is divided into 2 sub-fields: watermarking and steganography.

Usually, in steganography, robustness and security do NOT matter. What matters is whether Eve, the eavesdropper, can detect the presence of hiding messages.

On the contrary, security and robustness are important for watermarking. 

 Don't confuse steganography and watermarking!

You may work on statistical steganalysis techniques for misusing the security of steganography techniques.

Structural Similarity Index Metric(SSIM) can be used for quantitative objective evaluation since PSNR and MSE lack ability to assess image similarity across distortion types and  are not very well matched to perceived visual quality.Our similar evaluation for secure e-voting in https://www.academia.edu/6371423/Performance_Evaluation_of_modified_Stegano-Cryptographic_model_for_Secured_E-voting could be consulted for further information.

The proposed algorithm has binary codes and pixels inside an image