Combine and Simplify Equation

Hi Guys(Hi),

I'm newbie in this forum. Pardon me if this thread not in appropriate sub forum.

I have SSIM algorithm. I want to derive this algorithm.

$\displaystyle \mu_x$ for average x

$\displaystyle \sigma_x$ for variance x

$\displaystyle \sigma_{xy}$ for covariance x

$\displaystyle l(x,y) = \frac{2\mu_x\mu_y + c_1}{\mu_x^2 + \mu_y^2 + c_1}

$

$\displaystyle r(x,y) = \frac{2\sigma_x\sigma_y + c_2}{\sigma_x^2 + \sigma_y^2 + c_2}$

$\displaystyle r(x,y) = \frac{2\sigma_{xy} + c_2}{2\sigma_x\sigma_y + c_2}$

To be like this

$\displaystyle SSIM(x,y) = \frac{(2\mu_x\mu_y + c_1)(2\sigma_{xy} + c_2)}{(\mu_x^2 + \mu_y^2 + c_1)(\sigma_x^2 + \sigma_y^2 + c_2)}$

Please help me to solve step by step. (Nod)

Thank you.