Robust Watermarking Algorithm against the Geometric Attacks based on Non-Subsampled Shearlet Transform and Harris-Laplace Detector

Table 1

The analysis of some references.

References	Watermarking schemes	Advantages	Disadvantages
[6–10]	Based on the DWT	The DWT can approach the one-dimensional signal well	The DWT lacks of directional sensitivity
[11, 17]	Based on ridgelet	Ridgelet can capture the singularity of high dimensional signals effectively	The redundancy of analysis is very large
[12, 13, 18]	Based on curvelets	It is so efficient for natural images whose edge lines are dominated by curves	Curvelets have high redundancy
[14, 19]	Based on contourlets	Contourlets inherits the benefits from the ridgelet transform and the curvelet transform	Contourlets have no translation invariance
[15, 16, 20–23]	Based on shearlet	Shearlet possesses the characteristics of multi-scale and the ability to capture the geometry of multidimensional data	The discrete shearlet transform may produce the pseudo-Gibbs phenomenon
[24, 25]	Based on PHFMs	PHFMs are image rotation invariant	It would lead to higher numerical errors when processing smaller images
[26, 27]	Based on Harris detection	Harris feature points have good rotation invariance	Harris feature points are short of the scale invariance and affine invariance
[28]	Based on Harris-Laplace detection	Harris-Laplace feature points have scale invariance and affine invariance	It would lead to the overlapping of feature regions
[29]	Based on SIFT	The SIFT feature points are invariant to the geometric attacks	The SIFT feature points do not have affine invariance
[30, 34]	Based on ASIFT	The ASIFT feature points have affine invariance	It can not well resist rotation attack