Results 1 to 2 of 2

Math Help - Combine and Simplify Equation

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    1

    Combine and Simplify Equation

    Hi Guys,

    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.
    \mu_x for average x
    \sigma_x for variance x
    \sigma_{xy} for covariance x

    l(x,y) = \frac{2\mu_x\mu_y + c_1}{\mu_x^2 + \mu_y^2 + c_1}<br />

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

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

    To be like this

    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.
    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Sep 2009
    Posts
    502
    Quote Originally Posted by dhany19 View Post
    Hi Guys,

    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.
    \mu_x for average x
    \sigma_x for variance x
    \sigma_{xy} for covariance x

    l(x,y) = \frac{2\mu_x\mu_y + c_1}{\mu_x^2 + \mu_y^2 + c_1}<br />

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

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

    To be like this

    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.
    Thank you.
    I am not an optic engineer, but I found the definition of SSIM.

    Definition says SSIM(x,y) = L(x,y)C(x,y)S(x,y) where

    L(x,y) = \frac{2\mu_x\mu_y + c_1}{\mu_x^2 + \mu_y^2 + c_1}<br />

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

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

    where the <> canceled out. Only you would know how the Stabilizer Constant and Dynamic Range come about.

    You can post your question at the physics forum. There are people there who can help you.
    Last edited by novice; January 10th 2010 at 09:39 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combine the equation into a single logarithm
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 10th 2010, 11:05 PM
  2. Can I combine like terms?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 23rd 2009, 03:52 PM
  3. Replies: 1
    Last Post: April 1st 2009, 07:32 AM
  4. Combine the fractions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 22nd 2009, 05:50 AM
  5. A combine terms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 6th 2007, 05:49 PM

Search Tags


/mathhelpforum @mathhelpforum