BRIDGE PAVEMENT CRACK DETECTION UNDER UNEVEN ILLUMINATION USING IMPROVED PCNN ALGORITHM

For bridge pavement cracks under uneven illumination, the existing image segmentation algorithm does not remove this effect, and the segmentation effect is affected. In this paper, the image preprocessing consists of two parts: the process of removing uneven illumination and image noise, and the traditional bilateral filtering is improved based on the stationary wavelet algorithm (Cross-bilateral filtering). In the image segmentation part, the traditional PCNN (Pulse Coupled Neural Network) model parameters and the number of iterations are difficult to determine reasonably, and the use of a certain complexity makes it difficult to automate. This paper combined the synaptic integration characteristics of neurons, image gray and spatial features, to simplify PCNN model. The improved PCNN algorithm (SPCNN) based on the gray threshold of Markov network directly completes the segmentation without the need to manually set parameters and determine the optimal number of iterations. Through the analysis of the experimental results, the following three conclusions were drawn. (1) Compared with the histogram equalization, the enhancement algorithm of this paper removed the influence of illumination well and had advantages for the subsequent segmentation processing. (2) The cross-bilateral filtering algorithm could improve the image signal-to-noise ratio from 18.855 to 32.037, which was better than the original bilateral filtering algorithm. (3) The average segmentation accuracy rate of segmentation of SPCNN algorithm was more that 90%. Compared with the traditional PCNN method, this method is better in subjective visual effects and objective segmentation performance, less time consuming.


INTRODUCTION
The total number of highway bridges in China exceeds 830,000.
The occurrence of bridge collapse accidents will not only cause huge economic losses, but also hurt many innocent people. Therefore, our country pays more attention to road and bridge maintenance work. Relevant historical data showed that bridge safety accidents caused by cracks account for about 90% of the total disasters of bridges. And pavement crack detection has become a core part of maintenance work. The existing bridge crack detection methods can be roughly divided into three methods: manual detection, large-scale inspection vehicle detection and non-destructive testing technology. The first two detection methods are completely dependent on the operator, affecting traffic during operation, have safety hazards and low efficiency. With the development of computer vision noises. Yusuke et al.(2006) used image smoothing to remove the effects of uneven illumination and noise, then used threshold segmentation to extract crack information. The algorithm could successfully extract the crack information on a part of the concrete images, but the method of fixed threshold was poor in flexibility and the application surface was narrow. On the basis of fully analyzing the characteristics of concrete bridge pavement cracks, this paper firstly preprocessed the images under uneven illumination. The pre-processing process included removing the illumination effect and using the crossbilateral filtering to smooth images. Then used the global and local gradation characteristics of the crack distribution, a simplified PCNN model based on fixed threshold determined by the Markov network (SPCNN) is proposed to perform image segmentation. The experimental results not only showed that the proposed algorithm had better detection performance for the targets in the uneven illumination bridge crack images, but also had better robustness for various changes of images.

The Derivation Process
The image can be represented by a two-dimensional luminance function f(x, y) formed by reflected light on the object.
Assuming that reflected light is equal to incident light multiplied by the reflection coefficient, f(x, y) depends on the amount of incident light i(x, y) on the scene and reflectivity r(x, y) of the object. The equation of ( , ) can be expressed as: In theory, 0 < ( , ) < +∞, 0 < ( , ) < 1。According to equation (1), ( , ) = ( , )/ ( , ) could be obtained.
Through further analysis we found that the illumination function i(x, y) changed slowly in space, and the reflection function r(x, y) would abruptly change at the edge of the object.
It could be considered that the low frequency part of f(x, y) mainly affected by i(x, y), and r (x, y) was reflected in the high frequency part of f (x, y). Therefore, the spatial distribution of i(x, y) could be approximated by the low-frequency part of the image f(x, y) (Wu et al.,2010). In this paper, wavelet analysis was performed on f(x, y), and the low-frequency part was extracted as an estimate of i(x, y). An image that removed the influence of illumination (ie, a reflection function) could be obtained according to the above equation. However, in practical applications, some restrictions needed to be added. In order to avoiding the value of the above formula is too large, the value of denominator i(x, y) was greater than or equal to 1, and r(x, y) was relaxed from [0, 1] to [0,2]. Finally, the reflection function was linearly stretched to the [0,255] to achieve image enhancement.

Remove Uneven Illumination Algorithm
For the image of the crack on the surface of the bridge, the image is sometimes dark due to insufficient light or insufficient exposure, or the image is partially over-bright due to uneven illumination. The images in these two cases were selected to The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15-17 November 2019, Guilin, Guangxi, China perform histogram equalization(HE) and the de-lighting influence algorithm. After many experiments, the remove uneven illumination(RUI) algorithm selected the "coif3" wavelet, and the decomposition layer was 5 to perform wavelet decomposition to obtain the de-illuminated image results that was best. After the dark crack image (named test1) and the uneven light image (named test2) were respectively subjected to histogram equalization and remove uneven illumination algorithm, which could be found that the histogram equalized image became brighter, but the background gray level was uneven, would affect target extraction; the image of removing uneven illumination and it's background gray were even, at the same time the target of image was effectively highlighted, it was of great help to the subsequent segmentation process.
Therefore, the enhancement method of this paper is better than traditional histogram equalization, the results were shown in Figure 1:

Cross-Bilateral Filtering (Cross-BF)
The Gaussian filter weight uses the spatial distance measure factor: the farther the surrounding pixel is from the center point, the smaller the weight. The Yaroslavsky filter weight depends on the gray similarity: the closer the surrounding pixel points are to the center point gray value, the larger the weight. The bilateral filtering algorithm (BF) combines the spatial distance measure factor of Gaussian filtering with the grayscale measure factor of Yaroslavsky filtering, which preserves the edge details well when the image is smoothed. Bilateral filter grayscale measure factor calculates the gray difference between two independent pixels, when two adjacent pixels are polluted by noise, the stability of the grayscale measure factor calculation between the center pixel and the neighborhood pixel will be drop. Therefore, the key to improving the performance of the weighted average algorithm such as bilateral filtering is to improve the accuracy of the grayscale measurement weight. In this paper, a cross-bilateral filtering algorithm is proposed. The stationary wavelet algorithm is used as a pre-filter, the grayscale measurement matrix is obtained as the new grayscale similarity weight of the bilateral filtering, and the spatial neighboring weights remain unchanged. The algorithm flow is shown in Figure 2. In this paper, the stationary wavelet transform (SWT) algorithm was used as the pre-filter. Some parameters in the SWT algorithm were set as follows: the wavelet basis function selected "symlet" wavelet which was approximately symmetric, and the decomposition scale was 3. According to the characteristics of wavelet transform and noise normal distribution of road image, the threshold value in this paper was set to k= 3σ , wherein the noise standard deviation σ (σ 2 = (| |)/0.6745) was estimated by the first layer high frequency coefficient after wavelet decomposition. Soft threshold method was adopted for threshold processing.
Wavelet threshold denoising belongs to frequency domain denoising method, bilateral filtering belongs to spatial domain denoising method, and the cross-bilateral filtering algorithm combines them to achieve better denoising effect.

A Simplified PCNN Model Based on Markov Network
Threshold(SPCNN)

PCNN Model and Its Basic Principle
Eckhorn (  The traditional PCNN model has many parameters, the number of iterations is difficult to determine, and the segmentation result is closely related to parameter selection, so it is difficult to achieve the adaptive segmentation of PCNN. Where Sij ( )= a combination of neuronal excitatory link input Eij ( ) and neighborhood inhibitory link input Iij ( ) In order to realize the adaptive and real-time performance of the segmentation algorithm, this paper simplifies and improves the model (SPCNN) is shown in equation (3).
The exponential decay mechanism of the PCNN threshold function is independent of grayscale, which brings certain difficulties to image segmentation with low contrast (Xu et al.,2011), so the exponential decay mechanism is removed after simplification. The link input Sij ( ) can improve the information capacity acquired by neurons and improve the image segmentation effect. SPCNN model only needs to determine three parameters M, and , which will described in detail in the next section.
(2) Three Main Parameters 1) M takes the inverse of square of the distance between pixels.
2) The tightness of the connection between F and L channels of can be expressed as:  (6) can also be regarded as a composite representation of two systems, which are equivalent to the static system T 1 (t) = ln( ) and the dynamic system T 2 (t) = ln superposition. After the equivalent conversion, can be obtained: It can be found that equation (7) is actually the cross entropy composed of the image static system (P X = 1/ sum ) and the dynamic system (P = 1/ ). On the one hand, the static system probability distribution attempts to homogenize the image gray scale; on the other hand, the dynamic system probability distribution tries to preserve the change information of the original image gray level as much as possible. Image segmentation can be performed by the process of interaction between them to find local grayscale inconsistencies. The pixel gray value is regarded as the maximum entropy value of the corresponding DMN node and each network node is excited at the same time. In this way, all values of the node variable space are excited to maximum state, and the average deviation value between the maximum entropy value (grayscale value) of all nodes and their initial values at this time is calculated as the threshold for network neighbor connection search. θ (Markov network threshold) proposed in this paper can be expressed as: (

3) SPCNN Algorithm Steps
The specific steps of crack image segmentation as follows: 1) Input: link field F is the image pixel value, initializing the following values: 2) The EOL of each pixel is calculated according to equation (6) as the link strength value β of the corresponding neuron; 3) The Markov network grayscale threshold value θ m is calculated according to the equation (8)

Objective Evaluation
Commonly used evaluation indicators are Mean Square Error

Subjective Evaluation
The crack image was filtered by the three methods in this paper, and the result was shown in Figure 5:

Segmentation Experiment Results and Analysis
Two typical bridge crack images (

Subjective Visual Effects Comparison
Compared the segmentation results of the two uneven illumination bridge pavement images, in terms of subjective vision, OTSU was greatly affected by environmental factors and the segmentation effect was unstable. The optimal iteration times of PCNN segmentation was difficult to determine. It spent a lot of time, and there were still many false extracts and faults in the segmentation results. Compared with the previous two segmentation methods, the SPCNN model algorithm proposed in this paper had the best segmentation effect.
Although the crack target extracted in figure 4(f4) had slight fracture, the overall segmentation result was good.

Objective Segmentation Performance Comparison
In this paper, results of manual identification were taken as the standard to evaluate the performance of the above three algorithms by calculating the correct extraction rate and error rate . The larger the value of or the smaller the , the better the effect.
Where TN= the number of pixels correctly segmented for the crack target FN = the number of pixels mistakenly divided into cracks in the image of experimental results and = the number of crack pixels and non-crack pixels in the standard crack segmentation image The above three methods were used for segmentation of 100 images captured, and the accuracy and error rate of segmentation results were averaged. It could be found that SPCNN had higher (up to 91%) and lower (down to 10%).
As shown in Figure   (1) Compared with the histogram equalization, the enhancement algorithm of this paper removed the influence of illumination well and had advantages for the subsequent segmentation processing.
(2) The cross-bilateral filtering algorithm could improve the image signal-to-noise ratio from 18.855 to 32.037, which was better than the original bilateral filtering algorithm.
(3) The average segmentation accuracy rate of segmentation of SPCNN algorithm was more that 90%. Compared with the traditional PCNN method, this method is better in subjective visual effects and objective segmentation performance, less time consuming.