2.1.1. Speeded up Robust Feature (SURF)

To overcome the issues related to SIFT, Bay et al. [27] introduced the SURF method to tackle the robustness issues of the SIFT approach. The SURF approach is based on Gaussian scale-space image analysis, similar to the SIFT method. Unlike the SIFT detector, the SURF approach depends on the Hessian Matrix determinant. It employs integrated images to enhance the speed of feature detection. SURF's 64-bin descriptor characterizes each detected feature using a dispersion of Haar wavelet responses within a specific area. Unlike SIFT, the SURF features show limited affine invariance. However, to deal with more considerable viewpoint shifts, the descriptor can be expanded to 128-bin values. The Hessian Matrix is generated at the point "*m* = (*m*, *n*)" at scale "*σ*".

$$H(m,\sigma) = \begin{bmatrix} L\_{mm}(m,\sigma) & L\_{mn}(m,\sigma) \\ L\_{mn}(m,\sigma) & L\_{nn}(m,\sigma) \end{bmatrix} \tag{1}$$

where *Lmm*(*m*, *<sup>σ</sup>*) is the Gaussian second-order derivate convolution *<sup>∂</sup>*<sup>2</sup> *<sup>∂</sup>x*<sup>2</sup> *<sup>g</sup>*(*σ*) with the image *I* at a point *m*, similar to *Lmn*(*m*, *σ*) and *Lnn*(*m*, *σ*).
