How we can show that 2 correlated videos are similar?
The video is actually a sequence of images (frames, for a PAL standard that is 25 frames) and in such a sequence you can apply objective measures of quality to the certain number of frames. The most frequently used quality measures are PSNR (Peak Signal to Noise Ratio)1  and SSIM (Structural Similarity Index) 2.
In the matlab, there is a built-in fuction that calculate PSNR and SSIM:

psnr(image, ref_image) PSNR in Matlab
ssim(image, ref_image) SSIM in Matlab