Applied Science, Faculty of
Non UBC
Civil Engineering, Department of
DSpace
Gharehbaghi, Vahidreza
Farsangi, Ehsan Noroozinejad
Yang, Tony T. Y.
Noori, Mohammad
Kontoni, Denise-Penelope N.
This study proposes FastCrackNet, a computationally efficient crack-detection approach. Instead of a computationally costly convolutional neural network (CNN), this technique uses an effective, fully connected network, which is coupled with a 2D-wavelet image transform for analyzing and a locality sensitive discriminant analysis (LSDA) for reducing the number of features. The algorithm described here is used to detect tiny concrete cracks in two noisy adverse conditions and image shadows. By combining wavelet-based feature extraction, feature reduction, and a rapid classifier based on deep learning, this technique surpasses other image classifiers in terms of speed, performance, and resilience. In order to evaluate the accuracy and speed of FastCrackNet, two prominent pre-trained CNN architectures, namely GoogleNet and Xception, are employed. Findings reveal that FastCrackNet has better speed and accuracy than the other models. This study establishes performance and computational thresholds for classifying photos in difficult conditions. In terms of classification efficiency, FastCrackNet outperformed GoogleNet and the Xception model by more than 60 and 80 times, respectively. Furthermore, FastCrackNet’s dependability was proved by its robustness and stability in the presence of uncertainties produced by network characteristics and input images, such as input image size, batch size, and input image dimensions.
Citation: Gharehbaghi, V.;Noroozinejad Farsangi, E.; Yang, T.Y.;Noori, M.; Kontoni, D.-P.N. A NovelComputer-Vision Approach Assistedby 2D-Wavelet Transform andLocality Sensitive DiscriminantAnalysis for Concrete CrackDetection. Sensors 2022, 22, 8986.https://doi.org/10.3390/s22228986Academic Editors: Farzin Piltan andJongmyon KimReceived: 18 October 2022Accepted: 16 November 2022Published: 20 November 2022Publisher’s Note: MDPI stays neutralwith regard to jurisdictional claims inpublished maps and institutional affil-iations.Copyright: © 2022 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).sensorsArticleA Novel Computer-Vision Approach Assisted by 2D-WaveletTransform and Locality Sensitive Discriminant Analysis forConcrete Crack DetectionVahidreza Gharehbaghi 1 , Ehsan Noroozinejad Farsangi 2,3,* , T. Y. Yang 3, Mohammad Noori 4,5and Denise-Penelope N. Kontoni 6,7,*1 School of Civil Engineering, University of Kansas, Lawrence, KS 66045, USA2 Faculty of Civil and Surveying Engineering, Graduate University of Advanced Technology,Kerman 7631818356, Iran3 Department of Civil Engineering, The University of British Columbia (UBC), Vancouver, BC V6T 1Z4, Canada4 Department of Mechanical Engineering, California Polytechnic State University,San Luis Obispo, CA 93407, USA5 School of Civil Engineering, University of Leeds, Leeds LS2 9JT, UK6 Department of Civil Engineering, School of Engineering, University of the Peloponnese,GR-26334 Patras, Greece7 School of Science and Technology, Hellenic Open University, GR-26335 Patras, Greece* Correspondence: noroozinejad@kgut.ac.ir (E.N.F.); kontoni@uop.gr (D.-P.N.K.)Abstract: This study proposes FastCrackNet, a computationally efficient crack-detection approach.Instead of a computationally costly convolutional neural network (CNN), this technique uses aneffective, fully connected network, which is coupled with a 2D-wavelet image transform for analyzingand a locality sensitive discriminant analysis (LSDA) for reducing the number of features. Thealgorithm described here is used to detect tiny concrete cracks in two noisy adverse conditions andimage shadows. By combining wavelet-based feature extraction, feature reduction, and a rapidclassifier based on deep learning, this technique surpasses other image classifiers in terms of speed,performance, and resilience. In order to evaluate the accuracy and speed of FastCrackNet, twoprominent pre-trained CNN architectures, namely GoogleNet and Xception, are employed. Findingsreveal that FastCrackNet has better speed and accuracy than the other models. This study establishesperformance and computational thresholds for classifying photos in difficult conditions. In terms ofclassification efficiency, FastCrackNet outperformed GoogleNet and the Xception model by morethan 60 and 80 times, respectively. Furthermore, FastCrackNet’s dependability was proved by itsrobustness and stability in the presence of uncertainties produced by network characteristics andinput images, such as input image size, batch size, and input image dimensions.Keywords: deep learning; FastCrackNet; crack classification; noisy data; wavelet; locality sensitivediscriminant analysis1. IntroductionThe majority of civil engineering facilities were built decades ago and have structuralflaws owing to deteriorating materials, fire, chemical attacks, impacts, and seismic loads.According to the American Society of Civil Engineers (ASCE), 56,000 bridges are structurallydefective and require 123 billion dollars for repair [1]. The collapse of the Minnesota I-35Wbridge [2] and the 16-story Plasco building in Tehran are examples of disasters caused byignoring structural conditions [3].Structural health monitoring (SHM) provides innovative solutions for the monitoringand identification of various damages in engineering infrastructure, from large dams andlong roads to small residential buildings. Here, damage is defined as any changes in thematerial and/or geometric properties, which can be reflected as concrete cracks, spalling ofSensors 2022, 22, 8986. https://doi.org/10.3390/s22228986 https://www.mdpi.com/journal/sensorsSensors 2022, 22, 8986 2 of 16concrete cover, steel corrosion, fatigue cracks, or buckling of reinforced rods. Routine visualinspection by a trained specialist, along with conducting nondestructive tests (NDTs), suchas penetrant testing, eddy-current, magnetic particle testing, ultrasonic and X-rays, and CTscans, are common and initial approaches for condition assessment [4]. However, SHMprovides different contact or non-contact solutions that are automated, economical, andwith higher accuracy and the least amount of human intervention.For decades, a wide number of contact-based condition assessment approaches havebeen established by researchers. For instance, vibration-based damage detection (VBDD)methods use natural frequency, mode shapes, and frequency response functions. A largenumber of these methods require the attachment of various types of sensors for recordingdisplacement, strain, or acceleration. While VBDD techniques can be useful to evaluateboth the global behavior of structure and conditions of components locally, embeddingnumerous sensors and interrupting the servicing of structure puts a limit on them inpractical engineering applications when time and money are critical manners.Recent advancements in sensors, optics, computer capabilities, and memory capacityhave made it easier to do a huge number of computations, which has led to a quickrevolution in image processing algorithms. In both traditional vision-based systems foredge detection, which need manual feature extraction and human vision to evaluatethe results, or in advanced computer vision techniques employing deep learning, theseaccomplishments are evident.Civil engineers have performed extensive research to create and modify computer-vision methods for monitoring and investigative purposes. Additionally, vision-basedtechniques, when coupled with cameras and drones, provide the potential for quick andautomated infrastructure inspection and condition monitoring. Deep learning has rein-forced and enhanced traditional vision-based damage diagnosis for a wide scope of visualdefects, including cracks, spalling, and corrosion [5].Modern deep learning-based computer vision techniques are used for damage detec-tion in three categories: object detection, image classification, and semantic segmentation.Deep learning models encompass long short-term memory (LSTM) [6], convolutionalneural networks (CNNs) [7], deep belief networks (DBNs) [8], denoising auto-encoders(DAEs) [9] and recurrent neural networks (RNNs) [10]. Among the methods described,CNNs play an important role in all triple groups of computer vision.Training a deep learning architecture from scratch demands a vast quantity of dataand, as a result, increased processing resources. Transfer learning provides a solution forscientists. This means that the model may be used to solve a new problem by transferringexisting knowledge, and the approach can be employed to tackle a new problem by utilizinga pre-trained model. Transfer learning is divided into two key stages: a pre-trained phasefor gathering information from multiple activities and a fine-tuning step for applying theacquired knowledge to the target tasks. Transfer learning addresses the gap left by therequirement for large amounts of data, and as a result, it has been applied in a varietyof computer vision application fields. Accordingly, a set of CNNs is trained using theImageNet dataset [11]. As a result, the ImageNet dataset has been used to train a set ofCNNs [12]. Several computer vision tasks, including image segmentation [13–15], objectdetection [16–18], image classification [11,19], and captioning [20,21], have been studiedusing pre-trained deep learning models.Multiple pre-trained networks, including GoogleNet, AlexNet, VGG16, Xception,InceptionV3, and Resnet50, have reached state-of-the-art accuracy in various image identifi-cation problems. In this regard, CNN architectures have been extensively utilized for crackclassification [22,23], pavement crack recognition [24,25], and crack segmentation [14,26].In order to precisely evaluate surface imperfections on bridges made of cement con-crete, Zhu and Song [19] upgraded VGG-16’s framework. Before being preprocessed withmorphology-based weight adaptive denoising, the photos were segregated into a trainingand test set. To validate its performance, the enhanced VGG-16 was compared to con-ventional shallow neural networks (NNs) such as the backpropagation neural networkSensors 2022, 22, 8986 3 of 16(BPNN), support vector machine (SVM), and deep CNNs such as AlexNet, GoogleNet, andResNet using the same dataset of surface defects on cement concrete bridges. The findingsdemonstrate that the suggested technique can extract multi-layer features from surfacedefect data while emphasizing edges and textures.Wu et al. [27] presented GoogleNet and Inception V3 as a crack-detecting methodbased on a convolutional neural network. They demonstrated that the crack datasetretrained the pre-trained GoogleNet and Inception V3 model to better detect crack images.Islam et al. [23] developed a transfer learning approach based on CNNs to recognizeconcrete surface cracks from images. The transfer learning technique used in this studyemploys four existing deep learning models named ResNet18, DenseNet161, VGG16, andAlexNet, with pre-trained weights.Deep learning has previously been used to classify images. Few researchers havefocused on the negative effects of noise [28]. Numerous papers have created algorithmsto improve image quality rather than classify images. Another disadvantage of utilizingpre-trained models is the time-consuming training process, which is especially difficultfor larger architectures that require a considerable amount of memory. As a result, thereis a research gap where approaches to correctly classify concrete cracking data with thepresence of image noise in a quicker fashion are required.To fill the previous gaps, the present authors propose a computationally efficientapproach for classifying concrete cracks under unfavorable operational and environmentalsituations, such as noise and network uncertainties. To that end, this work investigates thepotential of signal transformations and feature conditioning methods in order to design anovel technique capable of achieving the following objectives:• Enhancing the performance of crack classification compared to pre-trained CNNs.• Stable in terms of model parameter uncertainty.• Keeping a high level of robustness in unfavorable imaging situations.• Potential to adapt adjustments in the quantity of training images and image size.• Benefit from high speed to lower the time of computation.As a result, the standard classification strategy based on deep learning networksis established as the reference method, and the new approach outlined in this paper iscompared to this reference.Consequently, the remainder of the paper is structured as follows. First, the three majorcalculation steps of FastCrackNet are described along with an overview of the theoriesunderpinning the proposed technique. Next is a description of the reference pre-trainedCNN models. The image dataset used for comparing the efficiency of the methods isprovided in the following section. The next part compares the classification results ofcracks under various iterations to those obtained by typical CNNs. The subsequent sectionsevaluate the algorithm’s robustness and stability under various types of uncertainty. Theconclusion section concludes with a discussion of the research findings.2. Materials and MethodsComputer vision-based SHMs are becoming more prevalent as a result of their quickand easy installation in many engineering projects. However, in real-world applications, sta-bility and robustness must be addressed. The other argument is about deep learning models,which are vital in computer vision. However, the processing capabilities and complexityof deep learning networks may impose constraints when using embedded single-boardGPUs with inferior performance and power supplies. As a result, the emphasis in thisnovel methodology is on demonstrating an efficient computer-vision algorithm that canwithstand adverse environmental conditions via a swift and non-complex network design.To that purpose, three primary FastCrackNet components are given initially: imagetransformation, feature reduction, and classification network. The FastCrackNet architec-ture is depicted in the diagram of Figure 1. The suggested method is compared to commonpre-trained CNN models in terms of performance and speed in the next sessions.Sensors 2022, 22, 8986 4 of 16Sensors 2022, 22, x FOR PEER REVIEW 4 of 16 that can withstand adverse environmental conditions via a swift and non-complex net-work design. To that purpose, three primary FastCrackNet components are given initially: image transformation, feature reduction, and classification network. The FastCrackNet architec-ture is depicted in the diagram of Figure 1. The suggested method is compared to common pre-trained CNN models in terms of performance and speed in the next sessions. Figure 1. FastCrackNet Architecture. 2.1. Step One: Image Transformation Using Wavelet Herein, a new feature space is generated with the aid of time–frequency transfor-mation. There are numbers of transformations in frequency and time–frequency domains, such as Fourier transformation and fast Fourier transformation [29], short-time Fourier transform [30], Hilbert transform [31], and Stockwell transform [32]. One of the most com-mon approaches is wavelet transformation, used by several researchers in the realm of computer vision and image processing [5]. Wavelet methods are particularly well-suited to situations where scalability and tol-erable deterioration are critical concerns. The wavelet transform breaks down a signal into a series of basic functions. Wavelets are created by scaling and translating a single proto-type wavelet φ known as the mother wavelet [33]. 𝜑ሺ𝑠, 𝜏ሻ = 1√𝑠 𝜑ሺ𝑡 − 𝜏𝑠 ሻ𝑑𝑡 (1)where 𝑠 and 𝜏 are scale and transition factors, respectively, and √𝑠 is for energy normali-zation at different scales. While continuous wavelet is highly redundant, discrete wavelets have solved this issue by scaling and transitioning in discrete intervals. The discrete wave-let for 'I' level is presented in the equation below: 𝜑ሺ2௝𝑡ሻ = ෍ 𝛾ூାଵሺ𝑘ሻ𝜃௞ሺ2ூାଵ𝑡 − 𝑘ሻ𝑡 (2) where 𝜃 is the scaling function and 𝛾 shows the wavelet filter. The wavelets are sampled at distinct intervals in the discrete wavelet transform. The normal image space, expressed as a pixel matrix, is referred to as the spatial domain. Transformation algorithms in this area operate directly on image pixel values. The fre-quency domain is concerned with the rate at which these spatial domain pixel values change. Frequency refers to the rate at which an image's color components change. DWT Figure 1. FastCrackNet Architecture.2.1. Step One: Image Transformation Using WaveletHerein, a new feature space is generated with the aid of time–frequency transforma-tion. There are numbers of transformations in frequency and ti e–frequency domains,such as Fourier transformatio a fast Fo rier tra sfor ation [29], short-time Fouriertransform [30], il ert transform [31], and Stockwell transform [32]. One of the ostco mon approaches is wavelet transformation, used by s veral r searchers in the realm ofcomputer vision and image processin [ ].Wavel t methods are particularly wel -suited to situati s ler-able deterioration are critical concerns. The wavel t ransform breaks down a i aseries of basic functions. Wavelets are creat d by scaling and translating a single prot ypewavelet ϕ known as the mother wavelet [33].ϕ(s, τ) =1√sϕ(t− τs)dt (1)where s and τ are scale and transition factors, respectively, and√s is for energy normaliza-tion at different scales. While continuous wavelet is highly redundant, discrete waveletshave solved this issue by scaling and transitioning in discrete intervals. The discrete waveletfor ’I’ level is presented in the equation below:ϕ(2jt)=∑kγI+1(k)θ(2I+1t− k)t (2)where θ is the scaling function and γ shows the wavelet filter.The wavelets are sampled at distinct intervals in the discrete wavelet transform. Thenormal image space, expressed as a pixel matrix, is referred to as the spatial domain. Trans-formation algorithms in this area operate directly on image pixel values. The frequencydomain is concerned with the rate at which these spatial domain pixel values change.Frequency refers to the rate at which an image’s color components change. DWT providessimultaneous spatial and frequency resolutions. Combining an analytical filter bank witha decimation method, DWT is utilized to break down a picture into discrete sub-bands.Two major frequency components exist: high-frequency components that relate to imageedges and low-frequency components that correspond to smooth areas [34]. Combiningtwo separate 1D transformations yields the 2D transform.In 1D-DWT, approximation coefficients include low-frequency data, whereas detailcoefficients include high-frequency information. The approximation illustrates the generaltrend of pixel values as well as the specifics, such as the horizontal, vertical, and diagonalcomponents. Two-dimensional DWT divides the input picture into four distinct sub-bands,as seen below [35] (See Figure 2):Sensors 2022, 22, 8986 5 of 16• LL: low-frequency components oriented horizontally and vertically.• LH: low-frequency components oriented horizontally and vertically.• HL: both the horizontal and vertical directions include components with a highfrequency.• HH: both the horizontal and vertical directions include components with a highfrequency.Sensors 2022, 22, x FOR PEER REVIEW 5 of 16 provides simultaneous spatial and frequency resolutions. Combining an analytical filter bank with a decimation method, DWT is utilized to break down a picture into discrete sub-bands. Two major frequency components exist: high-frequency components that re-late to image edges and low-frequency components that correspond to smooth areas [34]. Combining two separate 1D transformations yields the 2D transform. In 1D-DWT, approximation coefficients include low-frequency data, whereas detail coefficients include high-frequency information. The approximation illustrates the gen-eral trend of pixel values as well as the specifics, such as the horizontal, vertical, and di-agonal components. Two-dimensional DWT divides the input picture into four distinct sub-bands, as seen below [35] (See Figure 2): • LL: low-frequency components oriented horizontally and vertically. • LH: low-frequency components oriented horizontally and vertically. • HL: both the horizontal and vertical directions include components with a high fre-quency. • HH: both the horizontal and vertical directions include components with a high fre-quency. Figure 2. Image decomposition using 2D-DWT. Daubechies [35] proposed a new mother wavelet (Daub). It is an orthogonal wavelet with scaling and wavelet function coefficients that show vanishing moment numbers. De-pending on the sequence of the filter coefficients, other kinds of transformations using Daubechies families have been defined, such as Daub1 and Daub2. In this area, Daub4 consists of four scaling and wavelet coefficients. The Daub4 wavelet is popular due to its smoother behavior and the small number of coefficients [36]. Accordingly, Daub4 is used as the mother wavelet in the current method to extract features from concrete images. 2.2. Step two: Feature Reduction When presented with various characteristics that are not essential for predicting the intended output, supervised machine learning practical approaches lack efficacy (predic-tion accuracy). The extraction of a limited number of essential features is a high priority in computer vision, machine learning, knowledge identification, and pattern recognition. Figure 2. Image decomposition using 2D-DWT.Daubechies [35] proposed a new mother wavelet (Daub). It is an orthogonal waveletwith scaling and wavelet function coefficients that show vanishing moment numb rs.Depending on the sequ nce of the filter coefficients, other kinds of transformations usingDaubechies families have b en defined, such as Daub1 and Daub2. In this area, Daub4consists of four scaling and wavelet coefficients. The Daub4 wavelet is popular due to itssm other behavior and the small number of coefficients [36]. Accordingly, Daub4 is usedas the mother wavelet in the current method to extract features fro concrete i ages.2.2. Step Two: Feature ReductionWhen presented with various characteristics that are not essential for predicting the in-tended output, supervised machine learning practical approaches lack efficacy (predictionaccuracy). The extraction of a limited number of essential features is a high priority in com-puter vision, machine learning, knowledge identification, and pattern recognition. Usingdimensionality reduction methods is a common strategy for overcoming this difficulty.In this study, we employed a method of linear discriminant analysis termed LocalitySensitive Discriminant Analysis (LSDA). When there is a shortage of training data, the localstructure is often more important than the global configuration for discriminant analysis.LSDA finds a projector that optimizes the gap between data points from different classes ineach local region by identifying the local manifold structure. The data points are preciselymapped into a subspace, where neighbors with the same label are clustered together, andthose with different labels are widely spaced [37].When N training samples x1 to xN are taken from the underlying sub-manifold M.The between-class graph in LSDA is thus created by a vertex set X that is not specified asSensors 2022, 22, 8986 6 of 16well as the weight matrix Ww. The subscription w displays the within-class subscription.The weight matrix elements Ww, ij are shown below [38]:Ww, ij ={1 i f xi ∈ Nw(xj)or xj ∈ Nw(xi)0 otherwise}(3)where the set Nw(xi) consists of the k closest neighbors of xi which have the same labelas xi. Within-class compactness in LSDA may be learned via Laplacian embedding, asshown below:miny J(y) =∑i,j(yi − yj)2Ww, ij (4)where yi = αTxi is a scale and shows the one-dimensional map of xi.α is the projectiondirection. To characterize the similarity of local data, the objective function (2) is oftenutilized. In this research, we employed LSDA to optimize class margins and improveclassification performance. To that purpose, LDSA is used to decrease the retrieved charac-teristics of each sub-band [37]. In the following sections, the combination of four sets ofextracted features from each sub-bands creates the feature vector.2.3. Step Three: ClassificationFinally, a deep neural network (DNN)-based classifier was trained with the reducedfeatures. DNNs have demonstrated higher performance when compared to traditionalANNs and have found a variety of applications in image recognition. A complex network,on the other hand, necessitates high-performance computing capacity as well as a significantamount of time. To avoid using a computationally expensive and slow classifier, wedeveloped a simple, rapid, fully connected-based classifier by decreasing features andimproving discrimination with LDSA.According to LDSA-modified input features, the images were subsequently catego-rized using a simple DNN. After that, a fully connected (FC) network was utilized forclassy crack and non-crack images. Batch normalization layers sped up the training process,while rectified linear unit (ReLU) and dropout were employed to reduce overfitting issuesand generalization. Finally, a SoftMax layer composed of two nodes linked to the final FCdivided images into two groups. The architecture of this DNN is depicted in Figure 3.Sensors 2022, 22, x FOR PEER REVIEW 7 of 16 Figure 3. DNN Architecture. 2.4. Reference Image Classification Models LeCun et al. [39] were the first ones who applied CNN in computer vision applica-tions. After years, CNNs became popular in other fields such as video analysis and face recognition object detection. CNNs are a sort of neural network that provides higher-res-olution automatic feature extraction. The images are presented in three scales, from lowest to highest order. The first neural network extracts local characteristics and microscopic details such as edges, lines, and curves. The retrieved features are assembled at the sub-sequent deeper levels, and the final layers reconstruct the entire image. Convolution, pool-ing, fully connected layers, and activation functions are the primary processes in this pro-cedure. CNNs adopt two distinct training methodologies. The first is training the network from scratch, which requires massive amounts of data. The second is transfer learning using pre-trained models and parameter tuning. This method is more efficient and uses significantly fewer data for network training. Transfer learning involves training a net-work on a large dataset and then transferring the bias of the learned weights to another network with a new task. The vast majority of pre-trained networks were trained using the ImageNet dataset of one million pictures with one thousand categories [11]. Based on research by Nguyen et al. [40], eight of the popular networks for image classification were adapted, trained on concrete crack images, and compared in terms of performance and stability under adverse conditions. The networks were studied in two classes: smaller models (AlexNet, SqueezeNet, Goog-leNet, and ResNet-18) and larger models (ResNet-50, ResNet-101, InceptionV3, and Xception). The results demonstrated that GoogleNet (Small model) and Xception (Large model) were challenged and verified as highly reliable networks on average, particularly when utilized with reasonable batch sizes. In this paper, the performance of the established method is compared with the pairs of small and large models GoogleNet and Xception, respectively. Other experiments have demonstrated their capacity to detect fractures and damage. Table 1 outlines the key at-tributes of these two models [40]. Table 1. Characteristics of the two networks used for comparison. Network Layers Size (MB) Parameters Input Image Size GoogleNet 22 27 7.0 224×224 Xception 71 85 22.9 229×229 Figure 3. DNN Architecture.2.4. Reference Image Classification ModelsLeCun et al. [39] were the first ones who applied CNN in computer vision applications.After y ars, CNNs became popular in other fields such as video analysis and face recogni-tion object det ction. CNNs are a s rt of neural network that provides higher-resolutionautomatic feature extraction. The images are presented in three scales, from lowest tohighest order. The first neural network extracts local characteristics and microscopic detailsSensors 2022, 22, 8986 7 of 16such as edges, lines, and curves. The retrieved features are assembled at the subsequentdeeper levels, and the final layers reconstruct the entire image. Convolution, pooling, fullyconnected layers, and activation functions are the primary processes in this procedure.CNNs adopt two distinct training methodologies. The first is training the networkfrom scratch, which requires massive amounts of data. The second is transfer learningusing pre-trained models and parameter tuning. This method is more efficient and usessignificantly fewer data for network training. Transfer learning involves training a networkon a large dataset and then transferring the bias of the learned weights to another networkwith a new task. The vast majority of pre-trained networks were trained using the ImageNetdataset of one million pictures with one thousand categories [11].Based on research by Nguyen et al. [40], eight of the popular networks for imageclassification were adapted, trained on concrete crack images, and compared in terms ofperformance and stability under adverse conditions. The networks were studied in twoclasses: smaller models (AlexNet, SqueezeNet, Goog-leNet, and ResNet-18) and largermodels (ResNet-50, ResNet-101, InceptionV3, and Xception). The results demonstratedthat GoogleNet (Small model) and Xception (Large model) were challenged and verified ashighly reliable networks on average, particularly when utilized with reasonable batch sizes.In this paper, the performance of the established method is compared with the pairsof small and large models GoogleNet and Xception, respectively. Other experiments havedemonstrated their capacity to detect fractures and damage. Table 1 outlines the keyattributes of these two models [40].Table 1. Characteristics of the two networks used for comparison.Network Layers Size (MB) Parameters Input Image SizeGoogleNet 22 27 7.0 224 × 224Xception 71 85 22.9 229 × 229Using a non-adaptive learning rate approach called stochastic gradient descent withmomentum (SGDM), the authors were able to optimize network parameters and boostnetwork performance in terms of over-fitting, convergence, generalization, and runtime.L2 regularization was used across all layers to prevent over-fitting. The training wasconducted over the length of 2700 iterations and 300 epochs. As a result of trial and error,the appropriate values were determined to guarantee convergence of training progress inthe initial stages. To ensure that all the pre-trained models were being compared on a levelfield, we used the hyperparameters from Table 2. In order to achieve the best performancewith the least amount of over-fitting, these settings were determined by a grid search basedon prior study [40].Table 2. Hyper-parameters of networks.Parameter ValueOptimization method SGDMInitial learning rate 1e−4L2 Regularization 1e−3Epochs 300Iterations 27002.5. Indices of EvaluationThe classification efficiency of neural networks can be measured using several distinctindices. We employed three of the most commonly used metrics for image classification. Inthis context, precision refers to the accuracy with which a given result is identified, whereasrecall measures the extent to which all relevant results are correctly predicted. One mayalso refer to the recall rate of a validation, which is another terminology for accuracy. WhenSensors 2022, 22, 8986 8 of 16evaluating the efficacy of different CNNs, the F1-score is beneficial, since it integrates theaccuracy and recall variables into a single, straightforward measure.Precision =True PositiveActual Classes(5)Recall =True PositivePredicted Classes(6)F1− score = 2 × Precision × RecallPrecision + Recall(7)In order to have a better comparison in a view, we combined the indices into a newindex named Overall F1Score, as below:Overall F1− score = 2×Overall Precision × Overall RecallOverall Precision + Overal Recall(8)where the overall term indicates the average values for each index.2.6. Concrete Image DatasetIn several ways, the integrity of image data can be compromised after pictures aretaken in practice. The appearance of salt and pepper owing to improper digital ISO settings,Gaussian noise due to image sensor temperature increase in voltage and illumination set-backs, and motion blur due to relative movement between the image-capturing equipmentand focus sites are among the most typical reasons [28].Thus, to construct two versions of the original 3000 image dataset, salt and peppernoise and motion blur are applied to the original data. These images were taken from thesurfaces of concrete walls and have been cropped to 256 × 256 pixels. The variant sets arereferred to as 3000 SP and 3000 MB image datasets in the rest of this investigation. A noisedensity of 6% is used for salt and pepper noise and motion blur, the motion duration is setto 20 pixels, and the motion angle is set to 11 degrees. Readers are invited to obtain thedataset and related details in these references [40,41].Shadows and ambient lighting are the other adverse situations that occur in theactual world. So, different shadows, such as black rectangles, leaves, and gradient shad-ows, are applied on the original images to simulate real-world settings named SH data.Figure 4 depicts four types of image variation utilized to imitate adverse conditions in thecurrent study.Sensors 2022, 22, x FOR PEER REVIEW 9 of 16 set to 20 pixels, and the motion angle is set to 11 degrees. Readers are invited to obtain the dataset and related details in these references [40,41]. Shadows and ambient lighting are the other adverse situations that occur in the ac-tual world. So, different shadows, such as black rectangles, leaves, and gradient shadows, are applied on the original images to simulate real-world settings named SH data. Figure 4 depicts four types of image variation utilized to imitate adverse conditions in the current study. In this study, each model is evaluated with the same 3000 image dataset in an ap-proximate 70/15/15 ratio for training/validation/testing. The mentioned performance in-dices employ the test data that the networks have not previously seen. (a) Nrm Data (b) MB Data (c) SP Data (d) SH Data Figure 4. Normal Image data versus compromised variants. 3. Related Studies Although wavelets and deep learning have been utilized in several studies for dam-age identification [4,42–44], few researchers have employed the combination of them to detect cracks in image datasets. In this section, a brief literature review is provided on the application of deep learning and wavelets to the detection of concrete crack image. To overcome the issues of manual inspection, Dixit and Wagatsuma [45] proposed a novel method to detect micro-cracks in parts of concrete bridges using a drone with a high-resolution proximity camera. To study the texture features of the images of bridge deck, we used morphological component analysis (MCA) based on sparse coding. Dual tree complex wavelet transform (DTCWT) and anisotropic diffusion (AD) were used in MCA to find the coarse components of the images acquired by camera. AlexNet, GoogleNet, SqueezNet, ResNet-18, ResNet-50, ResNet-101, DenseNet-201, and Inception-v3 were among the models used by Ranjbar [46] et al. to evaluate the per-formance of retrained deep learning models in the detection and classification of pave-ment cracking. In addition, a more efficient crack segmentation technique is provided, one that employs a modified wavelet transform module and extra regularization parameters. The results of the confusion matrix performance ranged from 0.94 to 0.99, indicating that retrained classifier models generate reliable results. After conducting non-destructive ultrasonic testing on a structure, Arbaoui et al. [47,48] developed an effective way to track the development of cracks in the concrete. This technique relies on wavelet-based multi-resolution analysis of ultrasonic signals collected from samples or specimens of the examined material that have been subjected to a variety of different solicitation. Finally, the authors proposed a deep leaning-based method for crack detection using CNNs. To address the challenge of accurately predicting the location of surface cracks in concrete, Yang et al. [49] offer a unique discrete wavelet transform and attention (DWTA) module built on top of the popular skeleton network U-net. Both the mean intersection and mean union over the mean F1-score are 0.848 and 0.824, respectively. Based on the preceding discussion, this study attempts to not only boost classification speed by employing feature reduction, feature fusion, and a fully connected deep learning classifier, but also to improve accuracy, particularly in environmental adverse conditions, using wavelet transformation. According to the authors' knowledge, this is the first method for concrete crack classification based on wavelet transformation and deep Figure 4. Normal Image data versus compromised variants.In this study, each model is evaluated with the same 3000 image dataset in an approxi-mate 70/15/15 ratio for training/validation/testing. The mentioned performance indicesemploy the test data that the networks have not previously seen.3. Related StudiesAlthough wavelets and deep learning have been utilized in several studies for damageidentification [4,42–44], few researchers have employed the combination of them to detectSensors 2022, 22, 8986 9 of 16cracks in image datasets. In this section, a brief literature review is provided on theapplication of deep learning and wavelets to the detection of concrete crack image.To overcome the issues of manual inspection, Dixit and Wagatsuma [45] proposeda novel method to detect micro-cracks in parts of concrete bridges using a drone with ahigh-resolution proximity camera. To study the texture features of the images of bridgedeck, we used morphological component analysis (MCA) based on sparse coding. Dualtree complex wavelet transform (DTCWT) and anisotropic diffusion (AD) were used inMCA to find the coarse components of the images acquired by camera.AlexNet, GoogleNet, SqueezNet, ResNet-18, ResNet-50, ResNet-101, DenseNet-201,and Inception-v3 were among the models used by Ranjbar [46] et al. to evaluate the perfor-mance of retrained deep learning models in the detection and classification of pavementcracking. In addition, a more efficient crack segmentation technique is provided, onethat employs a modified wavelet transform module and extra regularization parameters.The results of the confusion matrix performance ranged from 0.94 to 0.99, indicating thatretrained classifier models generate reliable results.After conducting non-destructive ultrasonic testing on a structure, Arbaoui et al. [47,48]developed an effective way to track the development of cracks in the concrete. Thistechnique relies on wavelet-based multi-resolution analysis of ultrasonic signals collectedfrom samples or specimens of the examined material that have been subjected to a varietyof different solicitation. Finally, the authors proposed a deep leaning-based method forcrack detection using CNNs.To address the challenge of accurately predicting the location of surface cracks inconcrete, Yang et al. [49] offer a unique discrete wavelet transform and attention (DWTA)module built on top of the popular skeleton network U-net. Both the mean intersectionand mean union over the mean F1-score are 0.848 and 0.824, respectively.Based on the preceding discussion, this study attempts to not only boost classificationspeed by employing feature reduction, feature fusion, and a fully connected deep learningclassifier, but also to improve accuracy, particularly in environmental adverse conditions,using wavelet transformation. According to the authors’ knowledge, this is the first methodfor concrete crack classification based on wavelet transformation and deep learning thatsurpasses typical pre-trained CNN models in terms of speed and accuracy and consideringdifferent adverse conditions.4. Results and DiscussionFastCrackNet’s performance is compared to that of the reference techniques in thissection under a variety of conditions. Following that, the purpose and impact of its compo-nents, including transformation and feature reduction, are studied. Finally, the robustnessis evaluated in the presence of different network designs, input data uncertainties andoverfitting issues.4.1. Efficiency EvaluationInitially, FastCrackNet’s performance is assessed in a variety of adverse scenarios,employing the same number of epochs and total iterations (i.e., 2700 and 300) as GoogleNetand Xception. The comparison of efficiency begins with a comparison of classificationperformance and processing time. The proposed strategies are devised and implementedin MATLAB 2020b with the help of a deep learning package. This study used a ASUSVivoBook (ASUS, Fort Riley, KS, USA) with the following specifications, for all methods tohave a fair comparison.• AMD Ryzen 5 3500U Processor (4M Cache, 2.1 GHz up to 3.7 GHz);• 24 GB DDR4 RAM & 512 GB SSD;• Nvidia GTX 1050 4 GB Graphics.The suggested technique exceeds the previous reference methods in terms of classifi-cation accuracy for all variations, as indicated in Table 3. Furthermore, adverse conditionshave nearly no effect on FastCrackNet’s efficiency. In terms of classification performance,Sensors 2022, 22, 8986 10 of 16our technique is almost 60 and 80 times quicker than GoogleNet and Xeption, respectively,and it was shown that our proposed method greatly improved the computing time.Table 3. Comparison of Methods.Model Image Type Overall F1-Score Time (s)GoogleNetNrm 0.95 8635SP 0.93 8203MB 0.92 8191SH 0.86 8251XceptionNrm 0.97 11,235SP 0.93 10,662MB 0.92 10,591SH 0.84 11,657FastCrackNetNrm 0.98 127SP 0.98 130MB 0.97 132SH 0.92 1414.2. Finding Time-Saving ApproachThis section specifies a criterion for determining the most competent way to classifyimages in noisy circumstances, taking performance and calculation cost into account. Theefficiency index (EI) is calculated using the following formula:EI =PmCT× 100 (9)where Pm is each method’s average performance as measured by its F1-score across allcases, and CT is the duration of time spent on the computations, presented in Table 3. Thisindex provides an overall perspective of each methodology by averaging its performanceand calculation time over three image types in both standard and noisy settings. Thus,better efficiency with less computing time corresponds to a higher EI value.5. Stability AssessmentHerein, some of the typical uncertainties in the training of models are discussed. Tothis end, the stability and efficiency of the proposed method are being evaluated withinfour situations, namely change of bath size, input image size, the number of samples andgeneralization.5.1. Batch Size ImpactMany hyperparameters must be modified in order to train deep learning architecturesto classify images correctly. These parameters will have an influence on the network’sperformance as it converges. Herein, the tuning size of batches, or the number of inputimages employed in each training epoch, is an important hyperparameter. If this factor isset too high, the network may take too long to converge. On the other hand, if it is set toolow, the network may oscillate excessively, yielding undesirable results. Another variablethat may influence batch size is the dataset’s complexity, which is especially considerablein medical data [50].The overall F1Score and computation time are shown in Figure 5. It is clear that whenbatch size declines, analysis time increases. For example, the necessary time for the originalimage is nearly seven times greater for a batch size of 32 than 256. Additionally, except forthe SP data, the batch size of 64 gives better accuracy in all image variants.Sensors 2022, 22, 8986 11 of 16Sensors 2022, 22, x FOR PEER REVIEW 11 of 16 where Pm is each method's average performance as measured by its F1-score across all cases, and CT is the duration of time spent on the computations, presented in Table 3. This index provides an overall perspective of each methodology by averaging its perfor-mance and calculation time over three image types in both standard and noisy settings. Thus, better efficiency with less computing time corresponds to a higher EI value. 5. Stability Assessment Herein, some of the typical uncertainties in the training of models are discussed. To this end, the stability and efficiency of the proposed method are being evaluated within four situations, namely change of bath size, input image size, the number of samples and generalization. 5.1. Batch Size Impact Many hyperparameters must be modified in order to train deep learning architec-tures to classify images correctly. These parameters will have an influence on the net-work's performance as it converges. Herein, the tuning size of batches, or the number of input images employed in each training epoch, is an important hyperparameter. If this factor is set too high, the network may take too long to converge. On the other hand, if it is set too low, the network may oscillate excessively, yielding undesirable results. Another variable that may influence batch size is the dataset's complexity, which is especially con-siderable in medical data [50]. The overall F1Score and computation time are shown in Figure 5. It is clear that when batch size declines, analysis time increases. For example, the necessary time for the origi-nal image is nearly seven times greater for a batch size of 32 than 256. Additionally, except for the SP data, the batch size of 64 gives better accuracy in all image variants. Figure 5. Comparison of overall F1Score and computation time. Figure 6 shows the average of the overall F1Score (AveF1) and EI for each batch size. As shown, while the AveF1 is nearly constant for all batches, the EI increases significantly from lower batch sizes to higher ones. Accordingly, we conclude that using higher batch sizes is more efficient as the computation time drops dramatically for higher batch sizes, but at the same time, the accuracy does not change. Figure 5. Comparison of overall F1Score and computation ti e.Figure 6 shows the average of the overall F1Score ( veF1) a I for eac batch size.As shown, while the AveF1 is nearly constant for all batc es, t e I i creases sig ifica tlyfrom lower batch sizes to higher ones. Accordingly, e concl e t at si g ig er batcsizes is more efficient as the computation ti e drops ra atically for ig er batc sizes,but at the same time, the accuracy does not change.Sensors 2022, 22, x FOR PEER REVIEW 12 of 16 Figure 6. AveF1 and EI index for different batch sizes. 5.2. Image Size Impact The size of images can have an impact on training performance. As a result, in this section, we challenge the stability of the proposed approach. In the previous investigation of this paper, the input image was 64X64 pixels. In order to see the impact of input image size, in this section, the image data sets are resized into two different sets, including 48X48 and 56X56 pixels. Likewise, before, the classification was conducted via FastCrackNet, and the results are compared. As seen in Figure 7, the normal data experienced the least variance owing to sample changes and achieved almost the same level of accuracy. FastCracknet's accuracy does not fall below 0.90 in either of the reduced scenarios. Figure 7. Comparison of Impact of Image Sizes. 5.3. Impact of Number of Samples To see the impact of samples in the performance of the network, herein, two condi-tions with different numbers of images for training are defined: one with 90% of the orig-inal data and the other with 80%. This includes 2700 and 2400 images, respectively, for the new dataset. Once again, the FastCrackNet classifies images but with a new number of images. The results for the two scenarios are denoted in Figure 8. It is apparent that a reduc-tion of 20% of tainting data could degrade the performance higher in all cases. Overall, the variations in all conditions fluctuate between nearly 0.90 to less than 0.97, which shows the stability of the model in terms of training samples. Figure 6. AveF1 and EI index for different batch sizes.5.2. Image Size ImpactThe size of images can have an impact on training performance. As a result, in thissection, we challenge the stability of the proposed approach. In the previous investigationof this paper, the input image was 64 × 64 pixels. In order to see the impact of input imagesize, in this section, the image data sets are resized into two different sets, including 48 × 48and 56 × 56 pixels. Likewise, before, the classification was conducted via FastCrackNet,and the results are compared.As seen in Figure 7, the normal data experienced the least variance owing to samplechanges and achieved almost the same level of accuracy. FastCracknet’s accuracy does notfall below 0.90 in either of the reduced scenarios.Sensors 2022, 22, 8986 12 of 16Sensors 2022, 22, x FOR PEER REVIEW 12 of 16 Figure 6. AveF1 and EI index for different batch sizes. 5.2. Image Size Impact The size of images can have an impact on training performance. As a result, in this section, we challenge the stability of the proposed approach. In the previous investigation of this paper, the input image was 64X64 pixels. In order to see the impact of input image size, in this section, the image data sets are resized into two different sets, including 48X48 and 56X56 pixels. Likewise, before, the classification was conducted via FastCrackNet, and the results are compared. As seen in Figure 7, the normal data experienced the least variance owing to sample changes and achieved almost the same level of accuracy. FastCracknet's accuracy does not fall below 0.90 in either of the reduced scenarios. Figure 7. Comparison of Impact of Image Sizes. 5.3. Impact of Number of Samples To see the impact of samples in the performance of the network, herein, two condi-tions with different numbers of images for training are defined: one with 90% of the orig-inal data and the other with 80%. This includes 2700 and 2400 images, respectively, for the new dataset. Once again, the FastCrackNet classifies images but with a new number of images. The results for the two scenarios are denoted in Figure 8. It is apparent that a reduc-tion of 20% of tainting data could degrade the performance higher in all cases. Overall, the variations in all conditions fluctuate between nearly 0.90 to less than 0.97, which shows the stability of the model in terms of training samples. Figure 7. Comparison of Impact of Image Sizes.5.3. Impact of Number of SamplesTo see the impact of samples in the performance of the network, herein, two conditionswith different numbers of images for training are defined: one with 90% of the originaldata and the other with 80%. This includes 2700 and 2400 images, respectively, for the newdataset. Once again, the FastCrackNet classifies images but with a new number of images.The results for the two scenarios are denoted in Figure 8. It is apparent that a reductionof 20% of tainting data could degrade the performance higher in all cases. Overall, thevariations in all conditions fluctuate between nearly 0.90 to less than 0.97, which shows thestability of the model in terms of training samples.Sensors 2022, 22, x FOR PEER REVIEW 13 of 16 Figure 8. Impact of Data Reduction. 5.4. Generalization One of the main issues in the training of models is the problem of over-fitting, which occurs when a model learns too specifically from its input data. This could degrade the performance of the model by changing the input data. One way for evaluating the effec-tiveness of a machine learning model is to employ cross-validation, which is a resampling strategy used to evaluate a model when insufficient data is available. Cross-validation necessitates preserving some data that were not used to train the model so that it may be tested and validated later. The input dataset is divided into K equal-sized subsets for the k-fold cross-validation method. The prediction function uses k-1 folds for each training set, keeping the rest folds for the test set. K-fold cross-validation separates the dataset into K distinct subsets ( See Figure 9). The size of the data set deter-mines the value of K, and one part of the dataset (out of k total) is utilized for testing, while the rest is used for training. Figure 9. K-fold cross validation procedure. In this research, k-fold cross-validation is conducted for K=10 folds, and the results are shown for test data in Table 4. The lack of noticeable changes in the accuracy reveals that the proposed technique is well-fitted for training data. Figure 8. Impact of Data Reduction.5.4. GeneralizationOne of the main issues in the training of models is the problem of over-fitting, whichoccurs when a model learns too specifically from its input data. This could degrade theperformance of the model by changing the input data. One way for evaluating the effec-tiveness of a machine learning model is to employ cross-validation, which is a resamplingstrategy used to evaluate a model when insufficient data is available.Cross-validation necessit tes preserving some data that were not use to train themodel so that it may be tested and validated later. The input dataset is divided into K equal-sized subsets for the k-fold cross-validation method. The prediction function uses k-1 foldsfor each training set, keeping the rest folds for the test set. K-fold cross-validation separatesthe dataset into K distinct subse s (S e Figure 9). The size of the data set determines theSensors 2022, 22, 8986 13 of 16value of K, and one part of the dataset (out of k total) is utilized for testing, while the rest isused for training.Sensors 2022, 22, x FOR PEER REVIEW 13 of 16 Figure 8. Impact of Data Reduction. 5.4. Generalization One of the main issues in the training of models is the problem of over-fitting, which occurs when a model learns too specifically from its input data. This could degrade the performance of the model by changing the input data. One way for evaluating the effec-tiveness of a machine learning model is to employ cross-validation, which is a resampling strategy used to evaluate a model when insufficient data is available. Cross-validation necessitates preserving some data that were not used to train the model so that it may be tested and validated later. The input dataset is divided into K equal-sized subsets for the k-fold cross-validation method. The prediction function uses k-1 folds for each training set, keeping the rest folds for the test set. K-fold cross-validation separates the dataset into K distinct subsets ( See Figure 9). The size of the data set deter-mines the value of K, and one part of the dataset (out of k total) is utilized for testing, while the rest is used for training. Figure 9. K-fold cross validation procedure. In this research, k-fold cross-validation is conducted for K=10 folds, and the results are shown for test data in Table 4. The lack of noticeable changes in the accuracy reveals that the proposed technique is well-fitted for training data. Figure 9. K-fold cross validation procedure.In this research, k-fold cross-validation is conducted for K=10 folds, and the resultsare shown for test data in Table 4. The lack of noticeable changes in the accuracy revealsthat the proposed technique is well-fitted for training data.Table 4. K-fold cross-validation results.Model Image Type Average of Overall F1-ScoreFastCrackNetNrm 0.95SP 0.94MB 0.95SH 0.906. ConclusionsThe major purpose of this research was to create a reliable and computationallyefficient crack identification method for identifying pictures of concrete fractures obtainedunder varied unfavorable situations. Two types of digital filters were utilized to imitateunfavorable conditions in the images: motion blur, and salt and pepper noise. Because ofthe small cracks, these noise types were introduced to a complex concrete crack dataset,and the noise challenge was effectively handled using a unique deep learning-based imageclassification system named FastCrackNet.The three computational steps of FastCrackNet are the wavelet image processing, theLSDA feature conditioner, and a basic 12-layer deep network for classification. In orderto evaluate and compare FastCrackNet’s performance, two of the most renowned CNNmodels, Xception and GoogleNet, were employed to identify concrete cracks under variousadverse conditions. It was revealed through a comparison of two methods and the useoverall of F1-score data that:1. FastCrackNet outperforms the traditional CNNs in terms of the accuracy of concretecrack classifications.2. FastCrackNet does not degrade due to adverse environmental conditions.3. FastCrackNet is significantly faster than the pre-trained CNNs.4. The batch size and uncertainties do not affect the performance of FastCrackNetsignificantly.5. The proposed approach encounters no over-fitting issues.Sensors 2022, 22, 8986 14 of 16Author Contributions: Conceptualization, V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; methodology,V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; software, V.G., E.N.F. and D.-P.N.K.; validation, V.G., E.N.F.,T.Y.Y., M.N. and D.-P.N.K.; formal analysis, V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; investigation, V.G.,E.N.F., T.Y.Y., M.N. and D.-P.N.K.; resources, V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; data curation,V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; writing—original draft preparation, V.G., E.N.F., T.Y.Y., M.N.and D.-P.N.K.; writing—review and editing, V.G., E.N.F., T.Y.Y., M.N. and D.-P.N.K.; visualization,V.G., E.N.F., and D.-P.N.K.; supervision, T.Y.Y., M.N. and D.-P.N.K.; project administration, E.N.F. andD.-P.N.K. All authors have read and agreed to the published version of the manuscript.Funding: This research received no external funding.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: The data presented in this article are available upon request to thecorresponding authors.Conflicts of Interest: The authors declare no conflict of interest.References1. Affonso, C.; Rossi, A.L.D.; Vieira, F.H.A.; de Leon Ferreira, A.C.P. Deep learning for biological image classification. Expert Syst.Appl. 2017, 85, 114–122. [CrossRef]2. Hao, S. I-35W bridge collapse. J. Bridge Eng. 2010, 15, 608–614. [CrossRef]3. Behnam, B. Fire structural response of the plasco building: A preliminary investigation report. Int. J. Civ. Eng. 2019, 17, 563–580.[CrossRef]4. Gharehbaghi, V.R.; Noroozinejad Farsangi, E.; Noori, M.; Yang, T.; Li, S.; Nguyen, A.; Málaga-Chuquitaype, C.; Gardoni, P.;Mirjalili, S. 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Article
eng
Reviewed
Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
CC BY 4.0
Faculty
deep learning
FastCrackNet
crack classification
noisy data
wavelet
locality sensitive discriminant analysis
A Novel Computer-Vision Approach Assisted by 2D-Wavelet Transform and Locality Sensitive Discriminant Analysis for Concrete Crack Detection
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