# Real-Time Traffic Sign Detection and Recognition Method Based on Simplified Gabor Wavelets and CNNs
## 4 Traffic Sign Detection
### Simplified Gabor Wavelet Model  
The human visual system is composed of filter banks. The Gabor functions, with different orientations and scales, can model the responses of the respective filters of human beings. Gabor features have been found to be particularly effective for texture identification and representation [23; 24]. This characteristic of the Gabor filter has been applied to object detection [25], fingerprint recognition, facial expression recognition [26], image segmentation [27], etc. In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by a sinusoidal plane wave, where the function is shown by Equation (1):  
\[G(x,y)=\exp\left[-\frac{\left(x^{2}+y^{2}\right)}{2\sigma^{2}}\right]\cdot\exp [j\omega(x\cos\theta+y\sin\theta)] \tag{1}\]  
where \(\sigma\) is the standard deviation of the Gauss function in the x- and y-orientations; and \(\omega\) denotes the spatial frequency. To convolute the traffic scene with the Gabor filter with an input image, \(\mathrm{I}(x,y)\), the output of the Gabor filtered map, \(\phi(x,y)\), is given as Equation (2). Operator \(\otimes\) in the function denotes the 2D convolution operation. \[\phi(x,y)=G(x,y)\otimes\mathrm{I}(x,y) \tag{2}\]  
[PERSON] et al. [28] proposed that the imaginary part of the Gabor filter was an effective and robust edge detection method. The imaginary part of GW is shown in Equation (3), and \(\sigma\) and \(\omega\) satisfy the condition \(\sigma\cdot\omega\leq 1\):  
\[G(x,y)=\exp\left[-\frac{\left(x^{2}+y^{2}\right)}{2\sigma^{2}}\right]\cdot\sin [\omega(x\cos\theta+y\sin\theta)] \tag{3}\]  
The Traditional Gabor wavelet (TGW) was introduced to enhance the edge of the object of scenes for many years [29; 30], as it produces a better segmentation effect for this area. However, the edges of objects in images such as traffic signs, always had random orientations. To get the direction of the Gabor filter close to the edge, it would need filters of many different TGW orientations. The more filters with different orientations and scales, the more completely the information is expressed. From another point of view, the more the filters present, the more computational time required. One of the most serious problems in multi-orientations and multi-scale Gabor filter applications is time consumption. This is the main reason that TGW might be impractical for real-time application of traffic sign detection and recognition. Therefore, the reduction of processing time is one of the key problems in this area. To reduce time consumption in filtering and improve computational efficiency, we used a set of simplified Gabor filters to extract the features for edge detection, as proposed in Reference [31]. The SGWs were in the form of simple patterns for different scales and orientations, which could be computed efficiently. As proposed in Reference [31], these SGW features could be computed for each pixel position without requiring the use of Fast Fourier Transform (FFT), which greatly saved time. The selected quantization levels for an SGW, were the same as those in Reference [30]. We set one quantization level of the SGW to zero. As the image part of the Gabor function is antisymmetric, the positive and negative quantization level values were the same and we denoted them as \(n_{l}\), so that there were \(2n_{l}+1\) quantization levels in our approach. To discretize the Gabor amplitude, supposing that the largest magnitude of the TGW was \(A\) and \(k=1\),..., \(n_{l}\), the quantization levels \(q_{positive}\) and \(q_{negative}\) were defined by Equations (4) and (5), respectively. Then, the traffic sign scene was convolved with the SGW kernels with different scales and orientations:  
\[q_{positive}=\frac{A}{2n_{l}+1}\cdot 2k \tag{4}\]  
\[q_{negative}=-\frac{A}{2n_{l}+1}\cdot 2k \tag{5}\]  
As a trade-off between speed and efficiency, we chose four orientations and two scale filters. The output of convoluting image \(\mathrm{I}(x,y)\) with a SGW was denoted as \(\phi^{\prime}_{\omega_{i},\theta_{j}}(x,y)\).