A fast and efficient reversible watermarking method using generalized integer transform

The earliest reversible watermarking using generalized integer transform proposed by Alattar [3] has been concerned and expanded because this technique can achieve high embedding capacity without losing the implication of the cover difference expansion (DE) method. According to Alattar's technique, n-1 bits will be embedded into a vector with n pixels if it is expandable. The larger the vector size is, the higher the embedding capacity is. Weng et el. [16] improved Alattar' scheme to achieve the higher capacity. The evaluation of vector expandability or a scheme changeability based on the idea of Alattar (called the Alattar's method) and Weng based method have exponential complexity in the length of the vector, so calculation time is inversely proportional complexity of the embedding capacity. Alattar or Weng based methods only considered the vector with 3 or 4 pixels for that drawback. For larger vectors, example a vector in size of 16, it is divided into 4 sub-vectors in size of 4 and 3 bits could be embedded in each subvector. Therefore, only 12 bits were embedded into a vector with 16 pixels. Thus, the embedding ability didn't gain as theoretical analysis. This paper proposes the expandable and changeable criteria for a vector with linear complexity according to the length of vector. Since, the embedding capacity of Alattar or Weng based methods is really obtained as theoretical analysis that means the embedding capacity of those schemes are better. Experimental results show that schemes applied to the proposed algorithms to check the expandable and changeable of vector is fast and it outperforms several widely used schemes in terms of computational complexity.