In digital image watermarking and image encryption

researchers often require a pseudo random sequence which is statistically orthogonal to an image. The white noise sequences

such as m sequence

are often used in these situations. But our study shows they are not optimum on orthogonal property. To get a better orthogonality

we studied the cross correlation of unartificial images and pseudo random sequences by means of statistical mathematics method. The second order expectation of the cross correlation value was determined in both space and frequency domains. The expression suggests that sequences which are high pass in frequency domain

like Run Length Limited (RLL) sequences

have better orthogonal character with unartificial images than white noise sequences which are widely used at present. The conclusion and the validity of our mathematical model were also proved by the result of statistical experiments. In order to generate 2D RLL sequences rapidly

we developed a simple and convenient algorithm. The experiments that confirmed 2D RLL sequences have better orthogonality with natural images than m sequences.