# 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}∑^{m}_{i=1 }∑^{n}_{i=1}I[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(MAX^{2}/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=(2μ_{x}μ_{y}+ c_{1})(2σ_{xy}+c_{2})/((μ_{x})^{2}+(μ_{y})^{2 }+c_{1})((σ_{x})^{2}+(σ_{y})^{2}+ c_{2})

**Description –**

c_{1 }= (k_{1}l)^{2}c_{2 }= (k_{2}l)^{2}μ_{x}and μ_{y }are the mean intensity values of images x and y. (σ_{x})^{2}_{ }is the variance of x, (σ_{y})^{2}is the variance of y (σ_{xy})^{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 k_{1}=0.01 and k_{2}=0.03. SSIM value close to 1 indicates good quality.