According to the traffic sign image processing in Section 2.1, the SURF method is used to quickly identify the static traffic sign information of highway by feature matching. SURF feature is an efficient variant of SIFT algorithm. SURF inherits the advantages of SIFT. It is several times faster than SIFT and has better stability in multiple images. This is needed in the process of traffic sign recognition [14, 15, 16, 17, 18, 19, 20, 21].

In order to further improve the efficiency and accuracy of traffic sign recognition, the icon image is normalized. In the dimension normalization of the icon image, assuming the size of the original traffic sign image is *m* × *n* and the target image is *m*^{'} × *n*^{'}, then the ratio of edge lengths of the two images is *m*/*m*^{'} and *n*/*n*^{'}. The (*i*, *j*)th pixel 5 (line *i* and line *j*) of the target image can be obtained by using the ratio of the length of a side to the original image, and its corresponding coordinate is *(i* × *m*/*m*^{'}, *j* × *n*/*n*^{'}). Obviously, the coordinate value is not an integer, but only an integer can be used as the pixel value of the image. Bilinear interpolation algorithm role is to find the nearest four points to the corresponding coordinates, and calculate the value of the point. Its principle is shown in Figure 4.

Figure 4 The principle of bilinear interpolation algorithm

In Figure 4, *E*_{11}, *E*_{12}, *E*_{21} and *E*_{22} denote four pixels. Linear interpolation is performed in the transverse direction, blue dot *T*_{1} is inserted between *E*_{11} and *E*_{12}, and blue dot *T*_{2} is inserted between *E*_{21} and *E*_{22}. Point *P* is obtained by interpolating in the longitudinal axis by *T*_{1} and *T*_{2}.

Assuming that the values of function *f* at *E*_{11} = *(x*^{'}_{1}, *y*^{'}_{1} ), *E*_{12} = *(x*^{'}_{1}, *y*^{'}_{2}), *E*_{21} = *(x*^{'}_{2}, *y*^{'}_{1}), and *E*_{22} = *x*^{'}_{2}, *y*^{'}_{2}) are known, linear interpolation is performed in the transverse direction as shown in Eq. (6) and Eq. (7). The difference in the longitudinal direction is shown in Eq. (8), and the value of *f* at *P* = *(x*^{'}, *y*^{'}) can be calculated, as shown in Eq. (9).

$$f\left({T}_{1}\right)\approx \frac{{{x}^{\prime}}_{2}-{x}^{\prime}}{{{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}}\cdot f\left({E}_{11}\right)+\frac{{x}^{\prime}-{{x}^{\prime}}_{1}}{{{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}}f\left({E}_{21}\right)$$(6)$$f\left({T}_{2}\right)\approx \frac{{{x}^{\prime}}_{2}-{x}^{\prime}}{{{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}}f\left({E}_{12}\right)+\frac{{x}^{\prime}-{{x}^{\prime}}_{1}}{{{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}}f\left({E}_{22}\right)$$(7)$$f\left(P\right)\approx \frac{{{y}^{\prime}}_{2}-{y}^{\prime}}{{{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}}f\left({T}_{1}\right)+\frac{{y}^{\prime}-{{y}^{\prime}}_{1}}{{{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}}f\left({T}_{2}\right)$$(8)$$\begin{array}{l}f\left({x}^{\prime},{y}^{\prime}\right)\approx \frac{\left({{x}^{\prime}}_{2}-{x}^{\prime}\right)\left({{y}^{\prime}}_{2}-{y}^{\prime}\right)}{\left({{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}\right)\left({{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}\right)}f\left({E}_{11}\right)\\ +\frac{\left({{x}^{\prime}}_{2}-{x}^{\prime}\right)\left({{y}^{\prime}}_{2}-{y}^{\prime}\right)}{\left({{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}\right)\left({{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}\right)}f\left({E}_{21}\right)\\ +\frac{\left({{x}^{\prime}}_{2}-{x}^{\prime}\right)\left({y}^{\prime}-{{y}^{\prime}}_{1}\right)}{\left({{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}\right)\left({{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}\right)}f\left({E}_{12}\right)\\ +\frac{\left({{x}^{\prime}}_{2}-{x}^{\prime}\right)\left({y}^{\prime}-{{y}^{\prime}}_{1}\right)}{\left({{x}^{\prime}}_{2}-{{x}^{\prime}}_{1}\right)\left({{y}^{\prime}}_{2}-{{y}^{\prime}}_{1}\right)}f\left({E}_{22}\right)\end{array}$$(9)The result of Eq. (9) is the normalized result of icon size. Using the above results, the SURF feature points can be extracted. The core of SURF algorithm is to construct Hessian matrix. Hessian matrix is a square matrix composed of the second-order partial derivatives of multivariate functions in mathematics. Assuming that a pixel in the traffic sign image is represented by *f (x*^{'}, *y*^{'}), its Hessian matrix is shown in Eq. (10):

$${H}^{\prime}\left(f\left({x}^{\prime},{y}^{\prime}\right)\right)=\left[\begin{array}{cc}\frac{{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{{x}^{\prime}}^{2}}& \frac{{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{x}^{\prime}\mathrm{\partial}{y}^{\prime}}\\ \frac{{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{x}^{\prime}\mathrm{\partial}{y}^{\prime}}& \frac{{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{{y}^{\prime}}^{2}}\end{array}\right]$$(10)According to Eq. (10), the Hessian matrix of each pixel can be obtained, and then the positive and negative results of Hessian matrix discriminant Eq. (11) can be used as a basis to determine whether the point is an extremum, where *H* ^{0} is a Hessian matrix and det *(H*^{'}) is its eigenvalue.

$$det\left({H}^{\prime}\right)={\left(\frac{{\mathrm{\partial}}^{2}f{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{{x}^{\prime}}^{2}\mathrm{\partial}{{y}^{\prime}}^{2}}-\frac{{\mathrm{\partial}}^{2}f}{\mathrm{\partial}{x}^{\prime}\mathrm{\partial}{y}^{\prime}}\right)}^{2}{I}_{filled}$$(11)In order to obtain the features of acceleration robustness with size invariance, Gaussian filtering as shown in Eq. (12) is usually used before constructing Hessian matrix.

$${L}^{\prime}\left({x}^{\prime},t\right)=det\left({H}^{\prime}\right)\cdot I\left({x}^{\prime},t\right)\cdot {G}^{\prime}\left(t\right)$$(12)where *L*^{'} *(x*^{'}, *t)* represents the traffic sign image with different resolution, and can be convoluted by image function *I (x*^{'}, *t)* and Gaussian function *G*^{'} (*t*) at point *x*^{'}.

Among them, the expression of *G*^{'} (*t*) is:

$${G}^{\prime}\left(t\right)=\frac{{\mathrm{\partial}}^{2}g\left(t\right)}{\mathrm{\partial}{{x}^{\prime}}^{2}}$$(13)Where, *g* (*t*) represents the Gauss function, and *t* represents the Gauss variance.

By analyzing the pixels processed by Hessian algorithm, these pixels are compared with the size of the points in its three-dimensional domain, and the points with the maximum or minimum value are retained as the initial feature points. Then the sub-pixel feature points are obtained by three-dimensional linear interpolation method, the threshold is set to remove the weaker feature extreme points, and the strongest feature points retained are used as the traffic sign feature points. The representation of the final feature set is:

$$V={H}^{\prime}\left(f\left({x}^{\prime},{y}^{\prime}\right)\right){L}^{\prime}\left({x}^{\prime},t\right)\cdot {G}^{\prime}\left(t\right)\cdot \delta $$(14)In the above equation, *δ* represents the weaker extreme point after removing threshold, which is controlled in the range of [4.5, 4.6], and the best removal effect is obtained, that is, the traffic sign image recognition effect is the best.

After extracting the SURF features, the FLANN algorithm is used to realize the feature point matching, and the static traffic sign information is recognized.

Eq. (15) is used to calculate the Euclidean distance between the matching feature points of two traffic sign images, and the minimum Euclidean distance of min (*dist*) is obtained. The threshold *S* is set, so that when *S* ≤ *N*1 × min (*dist*), it is determined as the best matching point.

$${D}^{\u2033}=\sqrt{{\left({{x}^{\prime}}_{1}-{{x}^{\u2033}}_{1}\right)}^{2}+{\left({{x}^{\prime}}_{2}-{{x}^{\u2033}}_{2}\right)}^{2}+\cdots +{\left({{x}^{\prime}}_{r}-{{x}^{\u2033}}_{r}\right)}^{2}}$$(15)where *(x*^{'}_{1}, *x*^{'}_{2}, · · · , *x*^{'}_{r}) and *(x*^{''}_{1}, *x*^{''}_{2}, · · · , *x*^{''}_{r}) represent two matching SURF feature vectors in the feature set, respectively. The number of the best matching points in the two images is *N* 2, and the threshold value is *S*^{'}. When *N* 2 ≥ *S*^{'}, the matching is successful, the traffic signs are judged to be the successful matching classes, so as to complete the information recognition of the static sign of the highway.

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