Performance metrics for image steganography

Overview :
Various methods are used to evaluate the quality of image steganography. Each of these methods assesses a different aspect of the result obtained after steganography. Some of the well-known methods are Mean Square Error(MSE), Peak Signal to Noise Ratio(PSNR), Structured Similarity Index Measure(SSIM), Payload Capacity.

Payload capacity :
Payload capacity refers to the measure of the volume of information present within the cover image. This measure is important in a steganographic system as the communication overhead depends on the maximum payload capacity. It is measured in Bits Per Pixel(BPP).

BPP = NUMBER OF SECRET BITS EMBEDDED/ TOTAL NUMBER OF PIXELS

Mean Square Error(MSE): 
Mean Square Error is the averaged value of the square of the pixel-by-pixel difference between the original image and stego-image. It gives us a measure of the error produced in the cover image due to the data embedding process.

MSE=(mxn)-1∑mi=1 ∑ni=1I[I(i,j)-k(I,j)]2

Description –
A lower value of MSE indicates a good quality embedding.

m,n = Dimensions of the image
I   = Original Image
K   = stego-image

Peak Signal to Noise Ratio(PSNR) : 
PSNR is another popular way to measure the degree of distortion in the cover image due to embedding.  It is the ratio between the maximum possible value of a signal and the power of distortion noise(MSE). It is measured in dB’s. A higher value of PSNR indicates a better quality embedding.

PSNR = 10xlog(MAX2/MSE)

Description –

MAX = 255 for a 8-bit grayscale image

Structured Similarity Index Measurement(SSIM): 
SSIM is a metric of comparison to check the similarity between the cover image and stego-image. It measures the perceptual difference between the two images. 

SSIM=(2μxμy + c1)(2σxy +c2)/((μx)2+(μy)2 +c1)((σx)2 +(σy)2 + c2)

Description –

c1 = (k1l)2
c2 = (k2l)2

μx  and μy  are the mean intensity values of images x and y. 

(σx)2  is the variance of x, 
(σy)2  is the variance of y 
(σxy)2 is the covariance of x and y. 

c₁ and c₂ are the two stabilizing parameters, 
L is the dynamic range of pixel values (2#bits per pixel - 1)  
the contents k1=0.01 and k2=0.03.
SSIM value close to 1 indicates good quality.