Metaheuristic Optimized Edge Detection for Recognition of Concrete Wall Cracks : A Comparative Study on the Performances of Roberts , Prewitt , Canny , and Sobel Algorithms

Crack detection is a crucial task in the periodic survey of high-rise buildings and infrastructure. Manual survey is notorious for low productivity. )is study is aimed at establishing an image processing-based method for detecting cracks on concrete wall surfaces in an automatic manner. )e Roberts, Prewitt, Canny, and Sobel algorithms are employed as the edge detection methods for revealing the crack textures appearing in concrete walls. )e median filtering and object cleaning operations are used to enhance the image and facilitate the crack recognition outcome. Since the edge detectors, the median filter, and the object cleaning operation all require the appropriate selection of tuning parameters, this study relies on the differential flower pollination algorithm as a metaheuristic to optimize the image processing-based crack detection model. Experimental results point out that the newly constructed approach that employs the Prewitt algorithm can achieve a good prediction outcome with classification accuracy rate � 89.95% and area under the curve � 0.90. )erefore, the proposed metaheuristic optimized image processing approach can be a promising alternative for automatic recognition of cracks on the concrete wall surface.


Introduction
Large vertical concrete structures are widely observed in highrise buildings, retaining structures, and infrastructure.Due to the combined effects of aging, inclement climate conditions, thermal expansion/contraction, and human activities, the health of concrete structures is reducing over time [1].us, ensuring the acceptable level of integrity of these structures is a crucial part in maintenance tasks.Notably, the periodic condition survey by means of visual inspection is the commonly used method to obtain valuable information on the current state of the structure.It is because visual changes in structures directly indicate structural health conditions [2].
A large number of previous works have particularly focused on detecting cracks in concrete structures [3][4][5].e reason is that cracks are a major concern when considering the safety, durability, and serviceability of structures [1,6].Identification of cracks is an important step in structure maintenance, which facilitates the effort in reducing their harmful effect.Moreover, timely information about cracks is crucial to prevent potential catastrophic events due to structural failures.
Despite the critical roles of reinforced concrete walls in various structures (e.g., high-rise buildings, retaining walls, dams, and tunnels), human-based visual inspection is still a common method especially in developing countries.is fact is due to the limited access to sophisticated but costly equipment used for machine-based periodic surveys of structure conditions.Needless to say, manual inspection is not only slow in progress but also has low consistency due to quantitative evaluation [1].
e assessment outcomes of human inspectors are largely determined by their level of training and experience.Notably, the observation of inspectors is also hindered by irregular lighting conditions and elevations [7].ese facts significantly reduce the accuracy of the manual crack detection.Moreover, the phase of data processing and compiling is also very time-consuming especially for structures with a large surface area of concrete walls such as skyscrapers and dams.Kim et al. [8] summarized that manual visual inspection is ineffective in terms of cost, safety, and evaluation accuracy.
Due to those reasons, developing automatic methods for detecting concrete wall cracks has drawn attentions of many scholars [9][10][11].Recently, various image processing techniques have been employed to boost the performance of concrete surface crack detection in both aspects of accuracy and productivity.In these methods, these techniques are aimed at recognizing cracks presented on a two-dimensional image, followed by further analysis of crack properties [12,13].
Abdel-Qader et al. [14] employed edge-detection approaches including Sobel, Canny, and fast Haar transform for detecting cracks appearing in bridges.A crack-measuring system relying on multitemporal images with the application of the first derivative of a Gaussian filter was proposed by Chen et al. [15].Chen and Hutchinson [16] utilized the level set method and morphological image processing techniques to recognize and analyze cracks in the laboratory environment.An image processing technique that uses various morphological operations including background brightness adjustment, binarisation, and shape analysis has been put forward by Lee et al. [6] to improve the crack detection performance.Adhikari et al. [17] established an edge detection-based method for measuring crack width of the bridge concrete structure.Dorafshan [18] relied on three commonly employed edge detectors including the Sobel, Roberts, and Gaussian high-pass filter methods for detecting cracks on surfaces of bridge decks; this study points out that the Sobel edge detector has achieved the most accurate crack detection outcome with an accuracy rate of 92%.
Recently, Yang et al. [5] investigated the performance of a novel approach that employs image matching based on the optical flow and subpixel to analyze slight concrete surface displacements; this approach has shown good performance in detecting thin cracks.An image processing-based model for detection of surface cracks in building structures using an improved Otsu method for image thresholding has been proposed by Hoang [12].Nguyen et al. [3] proposed a multiphase technique for analyzing images that use a B-spline level set model and a Savitzky-Golay filter.
Besides edge detection and image filtering approaches, machine learning has also been successfully employed in concrete surface crack detection [8][9][10].Particularly, convolutional neural network (CNN) models have drawn attention of many scholars in constructing automatic crack recognition models [2,4,19,20].
Recently, Dorafshan et al. [21] have compared the capability of six edge detectors (the Roberts, Prewitt, Sobel, Laplacian of Gaussian, Butterworth, and Gaussian algorithms) and CNN for crack detection in concrete structures.
e research finding is that CNN has outperformed those edge detectors by a large margin.e main advantage of CNN is that the feature extraction and pattern classification can be performed in an integrated and autonomous manner.However, CNNs often require a large number of training data samples and a considerable computational expense.Moreover, the performance of the edge detectors can be potentially optimized and improved with the use of metaheuristic algorithms.
Since automatic concrete wall crack detection is a challenging task due to arbitrary forms of cracks, inconsistent lighting condition, and disturbing noise patterns (e.g., spallings, stains, and holes) [8], investigating other alternative tools can be useful in both academic and practicing aspects.Moreover, despite the fact that edge detection algorithms have been employed for concrete surface crack detection, few studies have been dedicated in investigating the performance of these algorithms integrated with metaheuristics.It is noted that the implementation of edge recognition models demands a proper setting of tuning parameters.
e fine tuning of these parameters potentially leads to improvements in crack detection accuracy.erefore, there is a need to supplement the body of knowledge by conducting studies with the focus on the hybridization of edge detection and metaheuristic algorithms.
is study is aimed at filling the aforementioned gap in the literature by constructing novel edge detection-based methods for concrete wall crack recognition.
e new method relies on a median filter for noise removal, four edge detection algorithms (Roberts, Prewitt, Sobel, and Canny), and a morphological operation for filtering out unwanted background objects in digital images.e median filter, the four edge detection algorithms, and the employed morphological operation all necessitate appropriate settings of their tuning parameters.As being observed in the literature, the selection of parameters of image processing models can be formulated as optimization problems [22][23][24].Hence, our study relies on the differential flower pollination, as a metaheuristic algorithm, to optimize the crack detection model by means of identifying an appropriate set of model hyperparameters.Furthermore, a dataset including 1080 image samples has been collected to validate the new construction approach.
e rest of the paper is organized as follows: the second part briefly reviews the research methodology, followed by the third part that describes the image acquisition process; the proposed metaheuristic optimized edge detection model is presented in the fourth section; the experimental results will be reported in the fifth section, followed by several concluding remarks of the study being stated in the final section.

Median Filter (MF).
MF is an effective approach to smooth the digital image.is filter helps to remove the unwanted noise existing in the concrete wall background such as small stains or spallings.In image processing, MF is highly preferable since this image smoothing method can preserve edges which are potentially cracks.For a fixed window size and in the aspect of edge preservation, Arias-2 Advances in Civil Engineering Castro and Donoho [25] experimentally showed that the result of MF can be better than that of Gaussian blur.
For each pixel in an image under analysis for crack detection, MF replaces each pixel with the median of its neighboring pixels [26].e number of the neighboring pixels depends on the window size which is a parameter of MF. e common choice of the window size is definitely context dependent and usually requires a trial-and-error process to determine the appropriate setting.MF can help suppress unwanted details on the image background.However, a too large value of window size can lead to a significant loss of information regarding the cracking objects.In this study, the window size is considered to be a hyperparameter of the integrated crack detection model, and it is optimized by the employed metaheuristic algorithm.

2.2.
e Employed Edge Detection Algorithms.Generally, edge detectors are mathematical methods that are able to recognize points in an image at which the gray-level intensity expresses discontinuities [27].e point locations at which the gray-level intensity varies sharply can be grouped into segments called edges.Edge detection algorithms are highly suitable for identifying cracks in concrete walls.It is because crack pixels are highly associated with pixel locations having discontinued gray-level intensity.erefore, this study employs four edge detection approaches (the Roberts, Prewitt, Sobel, and Canny algorithms) for automatic crack recognition.e descriptions of these edge detection approaches are briefly presented in this section of the study.

Roberts Edge Detection Method.
e Roberts method, first described by Roberts [28], is a simple and fast algorithm for calculating the spatial gradient measurement on a digital image.
is algorithm quickly reveals locations featuring high spatial frequency which often correspond to crack objects.To implement the Roberts method, the image is first converted from the RGB format into the grayscale format.After being processed by this algorithm, pixel values at each location of the output image are the approximated absolute magnitude of the spatial gradient of the original grayscale image at the location [29].
e following filters R x and R y are applied to the whole image separately: Subsequently, these two filters are combined to calculate the absolute magnitude of the gradient as follows: where R G is the absolute magnitude of the gradient, the symbol • denotes a dot product of two matrices, and N IR denotes an image neighborhood with the size of 2 × 2 pixels [29].e Roberts edge detector requires a hyperparameter T R which is a threshold parameter.If the gradient values of pixels in the image are smaller than the threshold value, they are replaced by these threshold values.us, an image with detected edges can be obtained from the gradient with the use of a threshold value T R .
Figure 1 illustrates edge detection results using the Roberts method for an image without cracks and an image with cracks.It is clearly seen that the quality of the crack detection outcome strongly depends on the selection of the parameter T R .

Prewitt Edge Detection Method.
e Prewitt edge detection [30] also relies on two filters to estimate the derivatives of each location within an image.Similar to the Roberts algorithm, the Prewitt algorithm also requires a parameter T P which serves as a threshold value for determining edges.Figure 2 provides examples of edge detection results using the Prewitt method for an image without cracks and an image with cracks.
e following filters to compute the approximation to the derivatives are used to highlight edge pixels: e two aforementioned filters are combined to compute the total gradient as follows: where N IP denotes an image neighborhood with the size of 3 × 3 pixels [29].

Sobel Edge Detection Method.
As proposed in the previous work in [31], the Sobel edge detection is a widely employed method in image processing [32].Notably, this edge detector highlights edges by first smoothing the image before calculating the derivatives.e filter h x is employed for smoothing the image before computing the partial derivative in the x direction:

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Because the filters used for derivative approximation and image smoothing are both linear, they can be integrated into the following form for the x direction [29]: where h Sobel,x is the filter employed for approximating the derivative for the x direction.
In the same manner, the filter that computes the partial derivative in the y direction is shown as follows [29]: where h Sobel,y is the filter used for approximating the derivative for the y direction.Accordingly, the final outcome of the gradient approximations can be combined to give the gradient magnitude via the following formula: where h Sobel is the combined result of the gradient approximations and N IS denotes an image neighborhood with the size of 3 × 3 pixels [29].Notably, a threshold value T S determines the presentation of the output image with all edges being displayed (Figure 3).If the Sobel gradient values of pixels are lesser than the threshold value T S , they are substituted by the threshold value [33].[34] introduced a multistep algorithm for edge recognition.A Gaussian convolution is first applied to the image.Accordingly, a 2D first-derivative operator is computed to reveal locations of the image featuring intensity discontinuities.At the first step, the employed Gaussian filter is presented as follows:

Canny Edge Detection Method. Canny
where Moreover, G σ is a Gaussian function with the variance of σ 2 .Herein, the value of σ is chosen to be the default value � 2 √ as suggested by the MATLAB Image Processing Toolbox [35].e symbol * denotes the convolution operator; m and n are the indices used to specify the location of a pixel within an image.f(m, n) represents an image neighborhood at the pixel coordinate of (m, n).
Accordingly, the gradient of g(m, n) using a certain gradient operator (e.g., Sobel) is calculated using the following equation: where N IC represents an image neighborhood and g m,n (m, n) denotes the combined result of the estimated gradients.
In the next step, nonmaximum suppression is performed to thin out the edges [34].Moreover, it is noted that the Canny method relies on two parameters of T 1 and T 2 to carry out a double thresholding strategy (Figure 4).Edge pixels that are stronger than the upper threshold T 2 are determined as strong edges.ose that are weaker than the lower threshold T 1 are suppressed.Moreover, edge pixels that range between T 1 and T 2 are determined to be weak edges.Finally, all the edge pixels not connected to strong edge pixels and belonging to the weak edge group are all suppressed.

e Differential Flower Pollination (DFP) Algorithm for Model Parameter Optimization.
e determination of the hyperparameters of image processing approaches can be a challenging problem [36].e first reason is the landscape feature of the cost function to be minimized can be complicated and may contain a large number of local minima.Another reason is that the search space of the parameters is continuous; thus, there is an infinite number of possible solutions.Accordingly, metaheuristic algorithms are highly suitable for dealing with such a circumstance.
DFP [37] is a global optimizer that inherits the advantages from the two popular metaheuristic algorithms of the differential evolution (DE) and the flower pollination algorithm (FPA).DFP employs the Lévy-flight-based global explorative search of FPA [38] and the explorative local search based on mutation-crossover operators of DE.As experimentally demonstrated in the previous work [37], DFP can help optimize the model parameters with satisfactory outcomes.
e general picture of the DFP optimization algorithm is demonstrated in Figure 5.In the first iteration (g DFP � 1), all population members with PopSize individuals are randomly initiated within the feasible search domain.During the evolutionary process, each member's position is altered through either the FPA-based global pollination operator or the DE-based local pollination operator.Moreover, based on suggestions of previous works [37,39], a selection probability P � 0.8 is used to determine the frequencies of the global and local pollination phases.
e process of Lévy-flight-based global pollination can be expressed in the following equation: where g is the index of the current generation and X trial  Advances in Civil Engineering generate a mutated flower: where r 1 , r 2 , and r 3 represent three random indices and F denotes a mutation scale factor: generate a crossed flower : , if rand j ≤ Cr or j rnb(i), X j,i,g DFP , if rand j > Cr and j ≠ rnb(i), where Cr represents the crossover probability which is often chosen to be 0.8 [40].Moreover, as recommend by Hoang et al. [37], F is drawn from a Gaussian distribution with mean 0.5 and standard deviation 0.15.

Acquisition of Concrete Wall Images
To construct the image processing-based model for detecting cracks appearing on concrete wall surfaces, this study has collected images from several buildings in the Da Nang city (Vietnam).e camera is positioned at a distance of about 1 meter from the concrete walls.It is noted that image samples with their ground truth status of crack or noncrack have been categorized by inspectors.To alleviate the computation cost, image size is xed to be 50 × 50 pixels.us, image cropping operation is performed to create image samples.In addition, since one pixel represents an area of roughly 3.0 × 3.0 mm 2 , the surface area covered by one image sample is approximately 150 × 150 mm 2 .For each class label of concrete wall condition, 540 image samples have been collected.Hence, the image dataset includes 1080 samples.e collected dataset is demonstrated in Figure 6.It is noted that all the images have been captured by the camera of Asus ZenFone 4 Max Pro (16 MP resolution and F2.0 aperture lens).

The Proposed Metaheuristic Optimized Image Processing Model for Concrete Wall Crack Detection
is section describes the proposed method for automatic detection of cracks on the concrete wall surface.Since the model is a combination of metaheuristic and edge detection algorithms used for concrete wall crack recognition, it is named the "Metaheuristic Optimized Edge Detection model for concrete wall Crack Recognition" (MO-EDCR).
e MO-EDCR model (Figure 7) consists of three basic steps: (1) Noise suppression by means of MF (2) Edge identi cation using the algorithms of the Roberts, Prewitt, Sobel, and Canny detectors (3) Morphological operations for removing unwanted small objects As can be seen from Figure 7, to construct the automatic crack recognition model, there are three groups of hyperparameters needed to be determined: the window size parameter (W) used in the step of median ltering, the edge detectors' thresholds (T E ), and a threshold parameter (Th m ) used in the morphological operation for removing small objects.It is noted that the tuning parameters of the edge detection algorithms are T R for the Roberts method, T P for the Prewitt method, T S for the Sobel method, and T 1 and T 2 for the Canny method.e ranges of the window size parameter (W), the edge detectors' thresholds (T E ), and a threshold parameter (Th m ) are [2 10], [0 1], and [0, 0.1], respectively.
It is noted that the size of an image sample is 50 × 50 pixels.us, if elements of W are greater than 10 which surpasses 20% of the image size, the processed image sample is too blurred, and this leads to a signi cant loss in the image detail.us, the maximum value of elements of W is selected to be 10.
e range of T E is chosen to comply with the feasible range of thresholding parameters used in edge detectors which are speci ed by the MATLAB Image Processing Toolbox [35].In the case of Th m , since the removed objects are often dirts or noisy points, their sizes are comparatively smaller than those of crack objects.Based on several trial-and-error experiments, the range of Th m of [0, 0.1] is found to be appropriate for the collected image samples.erefore, this range of Th m is selected to ease the optimization process of DFP.
When the images with recognized edges are obtained, the objects, demonstrated by pixels having the intensity 1, are identi ed and isolated with the use of the MATLAB

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Image Processing Toolbox [35].Objects that have the size smaller than a certain threshold are removed from the digital image because they are often unwanted noncrack ones.e minimum size (MS) of an object is computed as follows: where PN is the total number of pixels of an image.Herein, PN 50 × 50 2500.As mentioned earlier, Th m is a threshold parameter employed for removing small objects; this parameter is also automatically determined by DFP.
Moreover, the following cost function (CF) is used to evaluate the quality of a set of model parameters: where FPR and FNR are the false-positive rate and the falsenegative rate, respectively.e equations used to compute FPR and FNR will be presented in the next section.us, if the aforementioned CF is minimized, then it is possible to obtain a model that features low values of both FPR and FNR.

Performance Evaluation.
Since the detection of cracks in concrete walls is formulated as a two-class categorization problem, the measurement indices used for quantifying the classification model can be employed.e first commonly used index is the classification accuracy rate (CAR).e higher the CAR value, the better the model performance.As mentioned earlier, ground truth labels of crack or noncrack for each image sample are assigned by human inspectors.Since this study serves as a preliminary survey to collect the current state of buildings, the ground truth labels are determined at an image level.
In addition, the true-positive rate TPR (the percentage of positive instances correctly classified), the false-positive rate FPR (the percentage of negative instances misclassified), the false-negative rate FNR (the percentage of positive instances misclassified), and the true-negative rate TNR (the percentage of negative instances correctly classified) are also widely employed.
ese four rates are computed as follows: where TP, TN, FP, and FN denote the true-positive, truenegative, false-positive, and false-negative values, respectively.Furthermore, based on the outcomes of TP, FP, and FN, the precision or positive predictive value (PPV), negative predictive value (NPV), recall, and F1 score can be computed for measuring predictive capability.ese indices are calculated as follows [41,42]:

Model Prediction Result and Performance Comparison.
Before the model construction phase, the dataset consisting of 1080 image samples has been divided into two sets: the training set which accounts for 70% of the data and the testing set which consists of 30% of the data.e first set is used for model construction, and the second set is employed for demonstrating predictive performance of the proposed model.During the model construction phase, DFP, as a metaheuristic algorithm, optimizes the tuning parameters of the image processing model.e most appropriate values of tuning parameters are then employed to establish the proposed MO-EDCR.Optimization results of MO-EDCR which employed the Roberts, Prewitt, Sobel, and Canny algorithms are illustrated in Figure 8. e maximum number of iterations (G MAX ) of the DFP-based search engine is set to be 100 iterations.As observed from this figure, the DFP metaheuristic algorithm can help the image processing-based crack detection model to quickly converge to a good solution of model parameters.
e optimized parameters of the proposed MO-EDCR for each edge detector are reported in Table 1.As can be seen from this table, the window sizes used in MF are 5 × 5 for the Roberts, Prewitt, and Sobel algorithms.However, the most appropriate window size in the case of the Canny algorithm is 3 × 3.In addition, the best threshold values of the Robert, Prewitt, and Sobel edge detectors are 0.0160, 0.0213, and 0.0220, respectively.Since the Canny algorithm requires two threshold values, these two values are found to be 0.3144 and 0.9058 by DFP.
e most suitable values of Th m used in the morphological operation phase of the Roberts, Prewitt, Sobel, and Canny algorithms are 0.0137, 0.0081, 0.0082, and 0.0196, respectively.It is interesting to see that the employment of the Prewitt and Sobel methods has resulted in a quite similar value of Th m .Meanwhile, the Roberts and Canny approaches require a comparatively higher value of Th m .us, it can be seen that the values of Th m for different edge detectors may not be similar.
is phenomenon can be explained by the fact that the edges obtained from different algorithms have different thicknesses.Moreover, the window size parameter employed by the Canny algorithm (W � [3,3]), which is automatically identified by DFP, is lower than those of other algorithms (W � [5,5]) because the Gaussian filter has been used in the Canny algorithm to partially smooth the image sample.
To reliably assess the model performance, the model construction and verification phases have been repeated 20 times to obtain the measurement indices of CAR, AUC, TPR, FPR, FNR, TNR, precision, and recall.It is noted that the training and testing datasets in an individual run are different and randomly sampled from the original dataset.
Table 2 provides the detailed outcomes of the predictive performances of the MO-EDCR that employs the Roberts algorithm, the Prewitt algorithm, the Sobel algorithm, and the Canny algorithm.In this table, the mean, standard deviation (Std), and coefficient of variation (COV) of the prediction performance of each crack detection model are reported.It is noted that COV is the ratio of the standard deviation to the mean of prediction performance.
e MO-EDCR model using these four edge detectors is denoted as DFP- Although the Roberts algorithm alone may not be as e ective in edge detection as other algorithms, the DFP-Roberts has obtained the prediction performance which surpasses other models in several performance measurement  is result can be due to the integration of the Roberts algorithm with the DFP metaheuristic approach, median lter, and morphological operations used for image cleaning.
e latter three methods of computational intelligence and image processing techniques have assisted the Roberts algorithm by alleviating its weakness.erefore, the integrated model of DFP-Roberts has obtained comparatively good crack classi cation performance for the currently collected image dataset.
e recall and TPR values of DFP-Canny (0.880) are close to those of DFP-Roberts (0.890); however, other indices of DFP-Canny are inferior to those of the other three edge detectors.e results of MO-EDCR using the four edge detectors are graphically shown in Figures 9 and 10. Figure 10 presents the statistical characteristics of classi cation performance of the four crack detection models obtained from the repeated subsampling process with 20 runs.e model performances are graphically described by the four box plots.It is noted that the bottom and top of each box plot are the rst and third quartiles of data, respectively; the red band within the box denotes the median [43].
Based on the result comparison and with the consideration that AUC is the main measurement index, it can be concluded that the MO-EDCR model that employs the Prewitt algorithm is best suited for the image dataset collected at hand. Figure 11 provides examples of crack detection results performed by MO-EDCR using the Prewitt edge detector.Moreover, the processing time of the MO-EDCR model employing the four edge detection algorithms, which is obtained through 20 repeated model runs, is reported in Table 3.

Conclusion
is study has constructed an automatic approach for the periodic survey of concrete wall structures.
e new approach is aimed at quickly and accurately identifying cracks on the concrete wall surface by analyzing the images captured by digital cameras.
e model, named MO-EDCR, consists of three main steps: MF-based noise suppression, edge detection, and cleaning of small objects.Each of these three steps requires hyperparameters to be appropriately set.e free parameter of the second step is the thresholding values of the four edge detection methods (the Roberts, Prewitt, Sobel, and Canny algorithms).erefore, DFP is used in this research to automatically identify the proper setting for those hyperparameters of MO-EDCR.Experimental results point out that MO-EDCR with the employment of the Prewitt method can help attain the most desired prediction outcome with CAR 89.954% and AUC 0.900.With CAR close to 90% and AUC of 0.9, the newly constructed MO-EDCR is a promising alternative to assist maintenance agencies in the tasks of periodic surveys of buildings and infrastructure.
Future developments of the current work may include the investigation of other advanced edge detectors and metaheuristic algorithms to meliorate the prediction accuracy.Moreover, comparative works that benchmark the performances of metaheuristic optimized edge detectors and deep neural networks can also be promising research directions in the eld of image-based crack recognition.
As mentioned earlier, at this current stage of the study, the ground truth labels of samples are considered at an image level.Accordingly, the classi cation result is considered to be a true positive if the edge detection model can detect a part of a crack object.is is a limitation of the current model since it is bene cial for building maintenance agencies to be capable of detecting the whole crack object.erefore, in a future work, a more sophisticated image processing model with the capability of recognizing cracks at a pixel level can be constructed to perform deeper analyses on the properties of cracks on the building surface.

Figure 1 :Figure 2 :
Figure 1: Edge detection result using the Roberts method: (a) an image without cracks and (b) an image with cracks.

Figure 3 :Figure 4 :
Figure 3: Edge detection outcome employing the Sobel method: (a) an image without cracks and (b) an image with cracks.

Figure 5 :
Figure5: e DFP optimization algorithm.Note: G MAX denotes the maximum number of generations.U(0, 1) is a uniform number generator.r denotes a random number generated from U(0,1).g DFP is the index of the current generation.

Figure 8 :
Figure 8: Optimizing result of MO-EDCR that employs (a) the Roberts algorithm, (b) the Prewitt algorithm, (c) the Sobel algorithm, and (d) the Canny algorithm.

Figure 11 :
Figure 11: Illustrations of crack detection results of MO-EDCR.

Table 1 :
e optimized model parameters.

Table 3 :
Processing time of the models.