Could you possibly have misread the paper. I doubt if the statement you quoted is true. Perhaps you could cite the paper. Best wishes, David Booth

OR PERHAPS I misunderstood. If you wish to compare the 2 curves with a chi-square goodness of fit test simply google chi-square goodness of fit test along with your favorite stat package. Best, David Booth

Hello Priyansi,

The formula appears to yield a value proportional to the average squared difference in pixel values over the interval 0-255. It's not, strictly speaking, a variance as usually defined. Whether the "z", as in z(5), represents a count, a proportion, a percent, or an actual z-score would change the scale for the final value (and the maximum possible upper limit), but otherwise shouldn't change the relative difference between a plain and ciphered version of an image.

So, be sure that:

1. You're using the correct values for "z";

2. You index the calculation over the full range of possible pixel gradients, from 0-255 (note that when i = j, the value is always zero); and

3. Remember that indexing starts at "1" in some software/programming languages, and "0" in others (like Python).

Good luck with your work.

David Eugene Booth Sir,

this is a similar paper with the calculations and formula I found

Article Secure Image Transmission Using Chaotic-Enhanced Elliptic Cu...

The computed variance cannot equal 630730 for the simple reason that (Zi-Zj)²/2 cannot exceed 32512.5. Anyway, it could be that the author is confusing pixel value and value frequency.