**5. Quick-Hessian detection**

**4. Related work**

36 Evolving BCI Therapy - Engaging Brain State Dynamics

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

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

$$\mathcal{H}(\mathbf{x},\ \sigma) = \begin{bmatrix} L\_{xx}(\mathbf{x},\ \sigma) \ L\_{xy}(\mathbf{x},\ \sigma) \\ L\_{xy}(\mathbf{x},\ \sigma) \ L\_{yy}(\mathbf{x},\ \sigma) \end{bmatrix},\tag{3}$$

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

$$\frac{|L\_{xy}(1.2)|\_{F}|D\_{xx}(9)|\_{F}}{|L\_{xx}(1.2)|\_{F}|D\_{xy}(9)|\_{F}} = 0.912... \simeq 0.9,\tag{4}$$

**Figure 6.** Left to right: (intact and trimmed) Gaussian secondary arrangement partly derived in the *y*-direction and z*y*direction, and our approximation of the applied box filter. Gray areas are null.

where |z|F is the Frobenius norm.

$$\det(\mathcal{H}\_{\text{approx}}) = D\_{xx}D\_{yy} - (0.9D\_{xy})^2. \tag{5}$$

This view clearly shows the Hessian-detecting characteristics. Medium: Warp types applied in SURF. Right: Image of graffiti showing the size of the window descriptors on different

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

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

39

The first levels of each Octavian are relatively large. **Figure 7** (left) shows the points of interest

The superior performance of SIFT compared with that of other [9] benchmarks is remarkable. Their mixing with local informatics and the distribution of gradient-related characteristics provide fine characteristic resistance that mitigates the effect of settlement faults in terms of size or surface area. The application of relative resistance and gradient directions decreases the effect of illumination changes. The proposed SURF descriptor is based on similar properties, further complicating the process. The first step is to identify a direction that can be reproduced from data from a circular area surrounding the indicator of interest. Next, we

detected when quick-Hessian detection is applied.

**Figure 7.** Left: points of interest detected in an image of a sunflower field.

scales.

**6. SURF description**

In addition, the responses to the filters are normalized to mask size to ensure that the continuous Frobenius is standard for any filter size. In an image, space generally takes the form of a triangle. The image is repeated with a Gaussian filter and subsamples to reach the apex of the triangle. Given the application of box filter and plot image, we do not duplicate the filtering to output a previous filter layer. Nevertheless, filters of any size can be used at the same speeds when applied to the original image (even parallel to the latitude, if not used here). Therefore, size spacing is analyzed by increasing filter size rather than decreasing image size. The output of the 9 × 9 filters above is considered as the primary gauge level. Thus, scaling *s* = 1.20 (corresponding to the derivate Gaussian with *σ* = 1.20). The following levels are obtained by filtering the image with a progressively larger mask, taking into account the distinct nature of the integrated image and the specific structure of our filter. Specifically, this phenomenon leads to sizes 9 × 9, 15 × 15, 21 × 21, and 27 × 27. On a large scale, the increment in filter size must also vary accordingly. Thus, for each new Octavian, the volume of the filter doubles from 6 to 12 to 24. At the same time, sampling periods can be doubled to enable the extraction of points of interest. Given that our filter arrangement ratios remain constant after expansion, the bypass scale is approximately matched. For example, 27 × 27 filters correspond to *σ* = 3 × 1, 2 = 3, 6 = s. Moreover, given that the Frobenius base remains constant in our filtering, they soon normalize [35]. To locate points of interest in the image and the scaling, maximizing suppression is not applied on the 3 × 3 × 3 neighbor. The maximum limit for the Hessian matrix is then encountered in the range and proposed spacing of the image [36]. The spatial interpolation scale is particularly important in our case, and the difference in size among the first levels of each Octavian is relatively large.

Rotation Invariant on Harris Interest Points for Exposing Image Region Duplication Forgery http://dx.doi.org/10.5772/intechopen.76332 39

**Figure 7.** Left: points of interest detected in an image of a sunflower field.

This view clearly shows the Hessian-detecting characteristics. Medium: Warp types applied in SURF. Right: Image of graffiti showing the size of the window descriptors on different scales.

The first levels of each Octavian are relatively large. **Figure 7** (left) shows the points of interest detected when quick-Hessian detection is applied.
