**4. Related work**

The most commonly used detection method is the Harris-cornered method [24], which was proposed in 1988. It is based on the intrinsic values of the secondary-momentary matrix. However, Harris angles are not fixed. The Lindberg detection method introduces the principle of automatic scaled selection [1], which allows the detection of a full point of interest in an image together with its scope. He experimented with the Hessian matrix operation identifier and Laplacian (corresponding to the Hessian matrix operation effect) to detect bulb structure. The detectors, which were developed by Harris-Laplace and Hessian-Laplace, are robust and stable with high reproducibility [25]. The Harris (Adaptive Scale) or the Hessian Matrix Locator and Laplacian have been applied to determine scale. Focusing on speed, [26] estimates Laplace Gaussians (LoG) on the basis of the candidate Gauss (DoG). Several fixed-interest rate detectors that increase the entropy in the area and the edged-based zone detection have been proposed [11]. Nevertheless, these detectors are inflexible. Several detection methods have been proposed for fixed properties that can adapt to long-term changes but are not discussed in this article. A review of the literature [9, 12] shows that (1) Harris-based detection methods are stable and replicable. The use of a specific Hessian matrix addition instead of its effect (the Laplacians) is useful because fires occur less on elongated and nonlocal structures. In addition, (2) an approximation, such as DoG, has low-cost computational speed and low loss of precision. A wider set of attribute descriptions has been suggested, such as the Gaussian-derived function [13], a fixed moment [27], complex feature [4, 28], guiding filters [29], and phaselocalized functions [30], to represent the distribution of small features in a region of interest. The latter [2] has been shown to surpass the others [8] because they capture a basic quantity of information on the special intensity of level models when large to small deformations or localization mistakes occur. In [2], SIFT has been applied as a general level gradient diagram around the indicator of interest and is stored in boxes in a 128-dimension vector (eight routing boxes for each 4 × 4 box). Various improvements have been proposed on this basic scheme [3]. PCA has been applied to slope images. These operations (PCA, SIFT) provide a 36-dimension characteristic that is rapidly harmonized but is less distinct from SIFT in terms of secondary comparison [9]. The slow calculation function reduces the impact of quick coping. In similar papers [9], the authors suggested a variation on SIFT, named GLOH, which proved to be more distinct with the same dimensional count. However, GLOH is computationally expensive. SIFT is the most attractive for practical application and is currently the most widely applied algorithm. It is distinct and relatively quick, which is crucial for online applications. Recently, [31] used a field-programmable area grid to improve its order of magnitude relation. However, the height dimensions of the descriptions in SIFT are defective when compared with those of corresponding methods. For online applications on an ordinary computer, each of the three steps (detection, description, and correspondence) must be fast. Alternatively, best-bin-first [2] accelerates computation but provides inaccurate solutions. A novel detection method based on SURF has been proposed by [1, 25]. However, basic approximation was applied because DoG [2] is a basic Laplacian-based detector. Given that it depends on the embedded image to reduce computing time, we designated this algorithm as the "Quick Hessian" detector. Description, on the other hand, describes the distribution of the Haar-wavelength reactions in the area of interest. We operate the built-in speed images repeatedly. In addition, only 64 dimensions are used, thus decreasing the calculation time of the corresponding characteristic and simultaneously increasing durability. We again propose a new index step based on the Laplacian marker. This step accelerates correspondence and increases the robustness of the description. To illustrate the self-sufficiency of the algorithm, we briefly discussed the conception of an integrated image, as defined in [32]. It allows the quick execution of filter to wrap a box type. The insertion of an integrated image IΣ (z) into *x* = (*z*, *y*) represents the amount of all

Rotation Invariant on Harris Interest Points for Exposing Image Region Duplication Forgery

http://dx.doi.org/10.5772/intechopen.76332

The calculated IΣ only requires four additions to calculate the total intensity on any vertical

We based our detection method on Hessian matrix addition because of its superior calculation time and accuracy. Therefore, instead of using an applied range to select position and scale (as in the Hessian-Laplace [25]), we used a Hessian identifier for both. Given the indicators *z* = (*z*,

where, similar to L,zy(z, σ) and L,yy(z, σ), L,zz(z, σ) is the rotation of the Gaussian secondorder differential ∂2 ∂,z2 g(σ) with the image I in indicator *z*. Gaussian analysis has been optimized for large-scale analysis, as shown in [33]. However, in practice, Gaussian analysis should be reduced (**Figure 1** of the allowed half) because filtering Gaussians with aliases will result in image subsamples. In addition, a property that cannot show new structures when resolutions are decreased has been proven in one-dimensional images and cannot be applied in two-dimensional images [34]. Thus, the importance of the Gaussian filter may have been exaggerated in this respect, and here we test a simple alternation. Given that the Gaussian filter is not idealistic in any event because of the success of the LoG with the approximations of the newspaper, we push the rounding with the filters of the box (**Figure 6** on the right). These approximate Gaussian second-class derivatives can be rapidly evaluated with an integrated image irrespective of size. It can be evaluated very quickly using embedded images regardless of size. The algorithm's performance is similar to that used for esterized crops and Gaussians. When applied to rectangular areas, SURF remains simple and arithmetically efficient. However, we need additional relative weight in equilibrium. This weight is specifically expressed with

*y*) in **Figure 1**, the matrix Hessian *H* (*z*, *σ*) in *x* is defined on the scale as follows.

(2)

37

(3)

(4)

the pixels of the income I of a rectangularity area formed by the *z* and the origin.

and rectangular surface, regardless of its shape.

**5. Quick-Hessian detection**

dimensions are used, thus decreasing the calculation time of the corresponding characteristic and simultaneously increasing durability. We again propose a new index step based on the Laplacian marker. This step accelerates correspondence and increases the robustness of the description. To illustrate the self-sufficiency of the algorithm, we briefly discussed the conception of an integrated image, as defined in [32]. It allows the quick execution of filter to wrap a box type. The insertion of an integrated image IΣ (z) into *x* = (*z*, *y*) represents the amount of all the pixels of the income I of a rectangularity area formed by the *z* and the origin.

$$I\_{\Sigma}(\mathbf{x}) = \sum\_{i=0}^{i \le x} \sum\_{j=0}^{j \le y} I(i, j) \tag{2}$$

The calculated IΣ only requires four additions to calculate the total intensity on any vertical and rectangular surface, regardless of its shape.
