An Efficient Reversible Watermarking Method and Its Application in Public Key Fragile Watermarking

In this paper a reversible watermarking method based on generalized integer transform of a vector with n pixels is presented. This method was firstly introduced by Alattar (called Alattar’s method) has been concerned and expanded because it can achieve high embedding capacity without losing the implication of the cover. According to Alattar’s method, n-1 bits could be embedded into a vector with n pixels if this vector is expandable. The evaluation of vector expandability has exponential complexity in the length of the vector, so computing time is inversely proportional complexity of the embedding capacity. This is why this method can only use the vector with 3 or 4 pixels in practical. The larger the vector size is, the higher the embedding capacity is, thus, the embedding ability is not gained as mentioned in theoretical analysis. This paper proposes the expandable and changeable criteria for a vector with linear complexity in the length of a vector. Therefore, the embedding capacity of Alattar’s method is really obtained as theory indicated. Experimental results show that schemes which use the proposed algorithms to check if a vector is expandable and changeable, are much faster and outperform several widely different (used) schemes in terms of computational complexity. The public key watermarking based on the proposed reversible algorithm is faster and more efficient as well as detecting any modifications of the watermarked image.