Abstract: For some zero color image watermarking methods are insufficient for several attacks of
information loss, a zero color image watermarking algorithm based on nonnegative matrix
factorization and real matrix of quaternion is proposed. Firstly, three components (R, G, B) are
extracted from color image and each component is decomposed. Secondly, the coefficient matrix
decomposed is registered in the copyright center and the real matrix of quaternion is used to represent
the original color image, also the krawtchouk invariant moments of the real matrix is calculated.
Finally, some krawtchouk invariant moments are used to design and construct zero watermarking
information. The experimental results show that original color image under strong shear can be
recovered by residual shear part. When the area of shearing color image exceed 80%, watermark
information can still be extracted correctly. This performance in image clustering and watermark
error detection rate by using the quaternion to represent the whole color image is better than using each of three channels of color image processing or gray image directly.

Key words: quaternion, zero watermarking, color image, invariant moments, nonnegative matrix
factorization