Enhanced Scratch Detection for Textured Materials Based on Optimized Photometric Stereo Vision and Fast Fourier Transform–Gabor Filtering

Abstract

In the process of scratch defect detection in textured materials, there are often problems of low efficiency in traditional manual detection, large errors in machine vision, and difficulty in distinguishing defective scratches from the background texture. In order to solve these problems, we developed an enhanced scratch defect detection system for textured materials based on optimized photometric stereo vision and FFT-Gabor filtering. We designed and optimized a novel hemispherical image acquisition device that allows for selective lighting angles. This device integrates images captured under multiple light sources to obtain richer surface gradient information for textured materials, overcoming issues caused by high reflections or dark shadows under a single light source angle. At the same time, for the textured material, scratches and a textured background are difficult to distinguish; therefore, we introduced a Gabor filter-based convolution kernel, leveraging the fast Fourier transform (FFT), to perform convolution operations and spatial domain phase subtraction. This process effectively enhances the defect information while suppressing the textured background. The effectiveness and superiority of the proposed method were validated through material applicability experiments and comparative method evaluations using a variety of textured material samples. The results demonstrated a stable scratch capture success rate of 100% and a recognition detection success rate of 98.43% ± 1.0%.

1. Introduction

In tandem with the burgeoning digital transformation and escalating industrial automation, there is a concomitant surge in the demand for stringent product quality benchmarks. The advent of sophisticated machine vision systems has revolutionized traditional manufacturing paradigms, enabling unparalleled precision and efficiency in automated defect detection across production lines [1,2,3]. Scratches on textured surfaces, in particular, represent a critical challenge that significantly impairs product integrity. Consequently, the meticulous identification and analysis of such defects have emerged as a cornerstone in contemporary quality assurance protocols, underscoring the pivotal role of machine vision in maintaining high-quality standards.

Machine vision-based capture and image processing analysis are two of the most important methods to achieve high-quality and high-precision defect detection [4,5]. Analyzed according to the detection method, the commonly used machine vision-based surface defect detection methods can be divided into two-dimensional (2D) methods, three-dimensional (3D) methods, and deep learning techniques. While deep learning stands as a powerful defect detection technology capable of automatically learning defect features, its industrial application faces certain limitations. Although deep learning models can rapidly and accurately detect scratch defect locations after being trained on a large dataset, their industrial implementation is currently constrained by the high costs associated with collecting and training large volumes of sample data. Furthermore, extensive network parameter tuning is required for different material scenarios, which involves a trial-and-error process that is less acceptable in high-precision industrial applications. This is because high-precision industrial settings demand a level of accuracy and stability that cannot be easily achieved without significant investment in time and resources for fine-tuning the deep learning.

Two-dimensional detection methods are mainly based on image processing techniques to detect defects, and the specific methods include grayscale symbiotic matrix segmentation [6,7], the spectral method [8,9,10], and the template matching method [11]. Two-dimensional methods are widely used due to their simplicity of use and ease of maneuverability. Zhang J [12] proposed a method combining an adaptive threshold segmentation algorithm and a mathematical morphological reconstruction of the solution to solve the defect segmentation problem and for the detection of aluminum metal materials. CAO G [13] developed a hybrid surface defect detection method for complex and widely varying curved surfaces, which realizes defect detection for different regions through image region segmentation, gradient threshold, and image alignment. Abdel S [10] propose a vision-based fabric inspection method that is based on the fast Fourier transform and cross-correlation techniques followed by a filter transform, highlighting the defective portions to check the structural regularity features of the fabric image in the spatial domain. However, due to the lack of depth information, 2D methods do not have sufficient reliability and stable robustness.

Contrary to the image processing methods that hinge on 2D techniques, providing merely a planar perspective, the inspection methods based on three-dimensional visual measurement offer an all-encompassing perspective of flaws. This perspective encompasses the depth, volume, and spatial orientation of defects, rendering a rich, detailed analysis of surface anomalies paramount. It empowers us to evaluate the severity and position of defects with greater accuracy and nuance [14].

Notably, 3D defect detection techniques, inclusive of those employing structured light [15,16] and photometric stereo vision [17], demonstrate a reduced susceptibility to inaccuracies engendered by variable lighting conditions. Their inherent robustness against fluctuations in ambient light, shadows, and specular reflections is a testament to their superiority over conventional 2D methods. Moreover, the provision of multiple vantage points ensures an exhaustive coverage that is essential for identifying defects which may remain concealed or ambiguous in a single 2D image. This all-encompassing approach significantly amplifies the overall effectiveness of defect detection, underscoring the superior capabilities of 3D visual measurement in surface defect analysis. Wu K [18] introduced a multi-exposure structured light method for the three-dimensional reconstruction of battery surfaces. By utilizing height-gray transformation, the anomalous parts of the three-dimensional point cloud are converted into two-dimensional images, effectively addressing the challenge of classifying surface defects with two-dimensional detection. Gu J [19] utilized a depth camera to capture color images and depth maps of cabbages for point cloud reconstruction. Subsequently, the normal vector for each point in the point cloud was estimated using a least-squares plane fitting method, and the curvature feature of the point cloud was calculated. More specifically, the curvature estimation was performed by fitting a quadratic surface to the local region around each point. Mohsen N [20] employed a photometric stereo vision and established a device with four light sources to acquire multi-angle images of road surfaces, subsequently introducing optimal angles for different light sources to restore the three-dimensional morphology of road surface texture for defect detection. Huang S [21] introduced a new method which is based on photometric stereo vision with four light sources to recover the lost depth information in NPP images and improve the detection of surface defects on textured metal parts.

While machine vision has, to a significant extent, resolved the majority of defect detection challenges in manufacturing, thereby substantially boosting industrial productivity, it encounters notable hurdles when dealing with textured materials. Materials such as wood, leather, textiles, and specialty papers present unique difficulties due to the impact of lighting angles and subtle surface irregularities at the microscopic level. These factors can mask the distinct features of scratch defects, thereby significantly escalating the intricacy involved in their detection. This phenomenon is vividly illustrated in Figure 1.

To address the challenges posed by textured materials, we developed an enhanced scratch defect detection method for textured materials based on optimized photometric stereo vision and FFT-Gabor filtering. Initially, we developed an Enhanced Scratch Detection method for textured materials. This method is characterized as a composite-enhanced defect detection method that combines optimized photometric stereo vision hardware with an FFT-based image enhancement algorithm. The main contributions of this paper can be summarized as follows:

(1)

Optimized Hemispherical Photometric Stereo Vision Device: We designed and optimized a new type of hemispherical photometric stereo vision image acquisition device with selective light source angles. Based on the selectivity of the multi-angle light source, we can choose the light source angle by ourselves according to the irregularity and complexity of the texture of the material, so as to achieve a balance between the acquisition time and the quality of the input image.

(2)

Photometric Stereo Vision Algorithm with Eight Light Sources: Using images captured under eight distinct light source angles, we implemented a photometric stereo vision algorithm. This approach mitigates issues caused by specular reflections or shadows under single-light-source conditions, enabling the complete capture of both texture and defect information via Albedo and Curl Gradient images.

(3)

FFT-Gabor Filtering Image Enhancement Algorithm: To further enhance defect visibility, we combined the existing photometric stereo vision algorithm with the defect detection algorithm based on image enhancement, and developed an enhanced scratch defect detection method for textured materials based on optimized photometric stereo vision and FFT-Gabor filtering to realize the enhancement of the defect information of the textured material and to weaken or filter out the texture information of the texture itself.

(4)

This paper proves the effectiveness of the proposed method through a single-material experiment and designs the experimental effect comparison of materials with different textures, which verifies the effectiveness and superiority of the proposed enhanced scratch defect detection method for textured material defect detection. Through the experimental data, for the experiments on different textured materials, the detection rate of the enhanced scratch defect detection method for textured material defect detection can be stabilized at 98.43% ± 1.0%.

Our method offers a practical alternative to deep learning-based approaches by leveraging traditional machine vision techniques and advanced image processing to achieve high detection rates with minimal training data requirements. Our approach represents a significant advancement in traditional machine vision techniques, offering a robust alternative to deep learning methods, especially in scenarios where high precision and reliability are critical.

2. Methods

Addressing the prevalent challenge in traditional machine vision where defects on textured materials are often arduously difficult to capture and photograph, and where distinguishing anomalous defects from the inherent texture of the material itself poses significant difficulties, we have initiated the optimization from the image acquisition stage. This paper proposes an enhanced scratch defect detection for textured materials based on optimized photometric stereo vision and FFT-Gabor filtering. It is described as a cooperative approach between image capturing hardware-based photometric stereo vision and image enhancement algorithm-based fast Fourier transform.

The enhanced scratch detection method for textured materials, as illustrated in Figure 2, comprises a defect capturing process based on optimized photometric stereo vision and an image defect information enhancement process using the fast Fourier transform.

Firstly, in order to overcome the possibility of defects being obscured under traditional single-light-source conditions and to balance image acquisition quality with computation time, we designed and optimized a novel hemispherical photometric stereo vision image acquisition device with light source selectivity. This enabled the acquisition of image information under multiple light sources. On this foundation, we introduced a photometric stereo vision algorithm with 8 light sources. The optimized photometric stereo vision image acquisition device captures material images under multi-angle light sources, which are then processed through the photometric stereo vision algorithm to obtain Albedo and curvature gradient images. This approach mitigates the effects of high reflections or shadows that occur under single-angle light sources.

Subsequently, to address the difficulty in distinguishing between the material’s own texture and defects, we introduced an FFT-Gabor filtering-based image enhancement algorithm. This involves designing a Gabor filter, transforming the image into the frequency domain through the fast Fourier transform, convolving the frequency domain representation with the textured material surface image, and returning to the spatial domain to obtain a background image that emphasizes the material’s own texture. Subtracting this background image from the original image achieves the effect of weakening the texture and highlighting the defects. Finally, this paper introduces the threshold segmentation method (OTSU) [22,23] to realize the detection and localization of textured material defects.

2.1. Scratch Defect Capture on Textured Material Surface Based on Optimized Photometric Stereo Vision

Texture is an inherent property of a material’s surface, and the visual representation of the material texture, as perceived by the human eye or captured by camera sensors, is contingent upon the interplay between the light source’s reflection and incidence characteristics and the morphology of the object’s surface under distinct lighting angles [24,25,26]. Based on photometric stereo vision, the information captured regarding the textured material’s surface defects mainly includes a light-source-selective image acquisition device and an image processing module based on the photometric stereo vision algorithm.

Photometric stereo vision was first proposed by Prof. Robert J. Woodham in 1978 [27]. In recent years, photometric stereo vision technology has attracted much attention in the field of industrial production and quality inspection [28,29,30]. The principle is illustrated in Figure 3, where Figure 3A presents the principle of photometric stereo vision, and Figure 3B presents the principle of application based on photometric stereo vision. This technique relies on the nature of light reflected from the surface of an object, capturing multiple images under varying lighting conditions to recover the normal phase information and reconstruct the subtle three-dimensional shapes of the object’s surface.

Based on the photometric stereo vision principle, we have innovatively conceived and fabricated a novel light-source-selective image acquisition device, as graphically represented in Figure 3. Our design features a hemispherical dome support structure, where the industrial camera is fixed on the top of the hemispherical support structure. At the same time, to accommodate the diverse surface structures of various materials, we have predicated the complexity of the material’s own texture and, consequently, optimized the selection of three distinct light source angles. These angles, calibrated at 15°, 45°, and 75°, respectively, enable nuanced imaging across a wide spectrum of surface textures. We show more details of the designed photometric stereo vision algorithm-based light-source-selective image acquisition device, including the structure of the acquisition device’s housing, light, and camera.

High load-bearing stiffness ensures structural stability during operation, preventing deformation of the camera and lighting angles due to external pressures or the weight of internal components—a critical consideration for the photometric stereo vision algorithm [31]. In order to provide enough space for the sample to be collected, the radius of the shell structure was designed to be 30 cm with a thickness of 6 mm. The selection of these dimensions was not only aimed at providing ample room for samples of varying sizes but also at ensuring structural integrity and stability. To ensure that the hemispherical structure is as smooth as possible, with good lightweight properties and load-bearing stiffness, we selected a black 3D printing material for the 3D printing production. The black material minimizes the interference of external stray light and internal reflected light, while the 90% slicing density provides increased rigidity for the hemispherical shell. Both the industrial camera and the point light source are affixed to the surface of the hemispherical structure via pre-drilled holes and O-screw positioning. For the diverse surface structures encountered on various material surfaces, we have devised three distinct elevation angles for the light source, specifically 15°, 45°, and 75°, predicated on the complexity of the material’s native texture. This nuanced approach ensures comprehensive coverage and optimal imaging capabilities across a wide range of surface complexities.

Given that the photometric stereo algorithm adopted herein necessitates binarized grayscale processing for acquired images, we carried out preliminary investigations, leading us to conclude that the impact of light color temperature on image quality can be largely disregarded. According to the principles of photometric stereo algorithms, at least three images from different lighting angles need to be captured. Our analysis, as illustrated in Figure 4, elucidates the influence of varying numbers of light sources on image quality. We have presented the Albedo images synthesized using the photometric stereo algorithm under different numbers of light sources, along with the Computational Time and the Detection Area Rate of scratches that can be observed. To better illustrate the impact of varying numbers of light sources on image quality, we introduced 3D Illuminated Grayscale Images to evaluate the uniformity of surface illumination. A gradual shift towards bluer colors in the images indicates lower heights, aiding in distinguishing scratches from background textures. A reduced number of light sources markedly expedites computational processes; however, this comes at the cost of uneven illumination, which may obscure certain scratch areas, thereby compromising the quality of the synthesized images. Conversely, augmenting the number of light sources offers enhanced cues for accurate reconstruction, albeit at the expense of decreased computational efficiency. In pursuit of an equilibrium between image quality and computational time, while concurrently striving to mitigate the uneven illumination issues inherent to photometric stereo lighting, this paper has judiciously selected eight light sources positioned at angles of 0°, 45°, 90°, 135°, 180°, −135°, −90°, and −45°. These sources are sequentially activated in strict accordance with their angular arrangement via the computer interface, thereby ensuring consistent and uniform lighting across every image captured.

Owing to the stringent alignment of the design configuration, the locations of both the camera and the point light source remain stationary, enabling the acquisition of quantifiable angular data. An 8-light source, arranged in a circular pattern with a 45° angular spread, was selected for illumination. Drawing upon the principles of photometric stereo vision, for a pixel residing at any given point on the material’s surface, we can deduce the lighting conditions resulting from the eight distinct angles of incidence.

$$\left\{\begin{array}{c}{I}_1=\rho L_{1}N\\ I_2=\rho L_{2}N\\ I_3=\rho L_{3}N\\ ···\\ I_8=\rho L_{8}N\end{array}\right.$$

(1)

Each of these angles contributes unique information about the surface properties, facilitating the reconstruction of surface normal and, by extension, the topography of the material under scrutiny. This composite-enhanced method allows for the precise determination of surface characteristics, essential for the detection and analysis of subtle defects or variations in texture. $I$ represents the intensity of the measured pixel; $N$ denotes the unit normal vector of the measured pixel point; $\rho$ denotes the diffuse reflectance value of the material surface; and $L_I$ denotes the unit direction vector of the point light source in the 3D direction, which can be expressed as ${L_1=L}_X^1,L_Y^1,L_Z^1$. Equation (1) can be written as

$$\left[\begin{array}{c}{I}_1\\ I_2\\ I_3\\ ···\\ I_8\end{array}\right]=\rho \left[\begin{array}{c}{L}_X^1,L_Y^1,L_Z^1\\ L_X^2,L_Y^2,L_Z^2\\ L_X^3,L_Y^3,L_Z^3\\ ···\\ L_X^8,L_Y^8,L_Z^8\end{array}\right]\left[\begin{array}{c}{N}_X\\ N_Y\\ N_Z\end{array}\right]$$

(2)

Since the number of light sources used is greater than 3, the approximate solution is obtained using the least squares method:

$$N={\displaystyle \frac{\left(L^{T}L{)}^{-1}\right(L^{T}I)}{\rho }}$$

(3)

$$\rho =‖L^{-1}I‖$$

(4)

The surface gradient values $p$ and $q$ of the material surface in the $x,y$ directions can be obtained denoted as

$$p={\displaystyle \frac{{\partial }_z}{{\partial }_x}}=-{\displaystyle \frac{N_x}{N_z}}$$

(5)

$$q={\displaystyle \frac{{\partial }_z}{{\partial }_y}}=-{\displaystyle \frac{N_y}{N_z}}$$

(6)

Through the image acquisition system designed in this paper, with the collected images of 8 light angles as input objects, the photometric stereo vision algorithm of 8 light sources is completed to realize the acquisition of the material surface information, and to obtain the surface normal phase information, Albedo information, and gradient information. As shown in Figure 5, we show that the normal phase information of the material surface image is calculated based on the images acquired by the image acquisition device under 8 lighting angles by means of the photometric stereo algorithm mentioned above. Based on the normal phase information, the Albedo image and the curvature gradient image of the textured material are obtained.

For the sake of experimental rigor, we show the acquisition effect for different textured materials in Figure 6. A represents coarse textured leather; B represents fine textured leather; C represents textile fabric; and D represents textured kraft paper. We show the samples of different textures, the acquisition area, and the synthesized surface normal information map, Albedo image, and Curl Gradient image of the material by the images under different lighting angles. It was observed that all defective scratches could be observed in the obtained Curl Gradient image, although some scratches were not clearly distinguished. The experiment verifies the effectiveness of the acquisition device designed in this paper and the effectiveness of the idea of ‘scratch defect detection of textured materials based on photometric stereoscopic vision optimization’ proposed in this paper.

2.2. Scratch Defect Detection on Textured Material’s Surface Based on Image Enhancement Algorithm

Aimed at studying the influence of the texture of the material itself caused by the material surface’s texture and the surface scratch defects that make it difficult to distinguish the difficulties [32,33], this paper proposes a detection method for a textured material’s surface scratch defects based on image enhancement algorithms. As shown in Figure 7, we have designed a Gabor filter based on fast Fourier transform. The frequency domain information of the image is obtained by the method of transforming the image frequency domain and spatial domain by fast Fourier transform. Then, the background information in the frequency domain of the image is obtained by introducing the Gabor filter convolution kernel for convolution operation in the frequency domain. Then, the conversion of the image frequency domain and the spatial domain is performed again by fast Fourier transform to obtain the spatial domain image of the image background. Then, through the original image and the spatial domain of the background image, difference subtraction is performed to realize the textured region; the background region of the grayscale difference becomes larger, and we can realize the image of the scratch defective region and the contrast enhancement of its own textured background. Finally, by introducing the threshold segmentation method, we can realize the detection of scratches on the surface of the textured materials.

The fast Fourier transform is based on the mathematical Fourier series to realize the conversion of images between the spatial domain and the frequency domain [34,35,36]. In the spatial domain, the presence of various noises makes it difficult to accurately localize the defective region, while the fast Fourier transform can describe the defective features in the frequency domain, thus detecting the defective location [10]. It is worth mentioning that the Gabor filtering algorithm is still an image enhancement algorithm based on the fast Fourier transform [37,38,39]. It uses the idea of refined time on the basis of the Fourier transform, eliminating the limitation that the fast Fourier transform is unable to analyze the local signals of the image [40,41,42].

The Fourier positive transform equation is expressed as

$$\mathrm{F}\left(\mathrm{u},\mathrm{v}\right)={\displaystyle \frac{1}{\mathrm{M}\mathrm{N}}}\sum _{\mathrm{x}=0}^{\mathrm{M}-1}\sum _{\mathrm{y}=0}^{\mathrm{N}-1}\mathrm{f}(\mathrm{x},\mathrm{y})\exp (-\mathrm{j}2\mathsf{\pi }\left({\displaystyle \frac{\mathrm{u}\mathrm{x}}{\mathrm{M}}}+{\displaystyle \frac{\mathrm{v}\mathrm{y}}{\mathrm{N}}}\right))$$

(7)

For an ordinary two-dimensional image, assume that the spatial domain of the image is $f\left(x,y\right)$; according to the Fourier transform Formula (7), the frequency domain of the image $F\left(u,v\right)$ is obtained. In the formula, u = 0, 1, 2, 3, …, M − 1; v = 0, 1, 2, 3, …, N − 1. u and v represent frequency variables; $x$ and $y$ represent spatial domain variables; and M and N represent the size of the image.

The Fourier inverse transform equation is expressed as

$$f(x,y)=\sum _{u=0}^{M-1}\sum _{v=0}^{N-1}F(u,v)e^{-j2\pi ({\displaystyle \frac{ux}{M}}+{\displaystyle \frac{vy}{N}})}$$

(8)

According to Equation (8), the image can be inverted from the frequency domain $F\left(u,v\right)$ to the spatial domain $f(x,y)$.

Gabor filtering was first proposed by Gabor [43], and the window function used for the Gabor filtering transform is a Gaussian function [44]. In space, the two-dimensional Gabor filter is obtained by modulating a two-dimensional Gaussian function with a sinusoidal plane wave, and the two-dimensional Gabor filter function is expressed as

$$G_{\sigma ,\phi ,\theta }\left(x,y\right)={\displaystyle \frac{1}{2\pi {\sigma }_x{\sigma }_y}} exp[-{\displaystyle \frac{1}{2}}/[({\displaystyle \frac{x^{\prime }}{{\sigma }_x}}{)}^2+({\displaystyle \frac{y^{\prime }}{{\sigma }_y}}{)}^2]]\mathit{exp}\left(2j\pi \phi x^{\prime }\right),j=\sqrt{-1}$$

(9)

In Equation (9), $\sigma$ is the frequency of the Gabor filter; ${\sigma }_x,{\sigma }_y$ are the effective width and height, where we default to ${\sigma }_x$ = ${\sigma }_y$, which means the filter is a circular domain; $\theta$ is denoted as the direction of the Gabor filter; and $\phi$ stands for the meridional center frequency. $x^{\prime },y^{\prime }$ are obtained by rotating $x,y$, and $x^{\prime }=xcos\theta +ysin\theta ; y^{\prime }=-xsin\theta +ycos\theta$.

The two-dimensional Gabor filter function can also be represented as a real and imaginary part. The plural form of Gabor filter $G_{\sigma ,\phi ,\theta }\left(x,y\right)$ is expressed as (10). The real part is expressed as Formula (11). The imaginary part is expressed as Formula (12). The cosine wave included in the real part is near the point of crossing zero, and the transformation is more obvious in the alternating part, so it can be used to detect abnormal defective scratches.

$$G_{\sigma ,\phi ,\theta }\left(x,y\right)=G_e\left(x,y\right)+j{G}_o\left(x,y\right)$$

(10)

$$G_e\left(x,y\right)=\exp [-{\displaystyle \frac{1}{2}}({\displaystyle \frac{x^{\prime }}{{\sigma }_x}}{)}^2+({\displaystyle \frac{y^{\prime }}{{\sigma }_y}}{)}^2]\mathrm{c}\mathrm{o}\mathrm{s}(2\mathsf{\pi }\phi x^{\prime })$$

(11)

$$G_o\left(x,y\right)=\exp [-{\displaystyle \frac{1}{2}}({\displaystyle \frac{x^{\prime }}{{\sigma }_x}}{)}^2+({\displaystyle \frac{y^{\prime }}{{\sigma }_y}}{)}^2]\mathrm{s}\mathrm{i}\mathrm{n}(2\mathsf{\pi }\phi x^{\prime })$$

(12)

The mathematical representation of the convolution operation with the Gabor filter is Equation (13):

$${\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }f(x,y) G_{\sigma ,\phi ,\theta }\left(x,y\right)\mathrm{d}\mathrm{x}\mathrm{d}\mathrm{y}$$

(13)

Threshold segmentation, as a typical region segmentation algorithm, is based on the principle of segmenting the image according to a reasonable threshold value, and the mathematical formula is expressed as Equation (14):

$$g(x,y)=\left\{\begin{array}{c}1, f(x,y)>T\\ 0, f(x,y)\le T\end{array}\right.$$

(14)

where $f(x,y)$ is the pixel point of point $(x,y)$; $g\left(x,y\right)$ is the segmented image; and $T$ is the threshold.

We use the machine vision program HALCON (mvtec.com), where the operator $fft\_generic$ is called to implement the fast Fourier transform of the image between the frequency and spatial domains, and the operator $convol\_fft$ is called to implement the convolution of the image with a Gabor filter. A threshold segmentation method (OTSU) is introduced to realize the detection and marking of scratches on the surface of the textured material [23,45]. On the basis of Section 2.1, we show the effect of image contrast enhancement after fast Fourier transform based on Gabor filter, as shown in Figure 8. We sequentially show the Curl Gradient image synthesized based on photometric stereo vision; the background image obtained by the fast Fourier transform of the Gabor filter; the contrast enhancement of the scratched defective region obtained by subtracting the background image from the Curl Gradient image and the background image; and the image which is obtained by introducing a threshold segmentation method (OTSU) for detecting and localizing the scratched area.

At the same time, in order to demonstrate more intuitively and three-dimensionally the effect of the contrast enhancement between the texture of the material surface and the defects of the surface scratches after the fast Fourier transform based on Gabor filtering, we show the 3D surface map of the contrast-enhanced image in Figure 8. A gradual shift towards bluer colors in the images indicates lower heights, aiding in distinguishing scratches from background textures. Observing the above picture and 3D surface map data after the contrast enhancement of the fast Fourier transform image, we can see that the scratch information on the material’s surface is clearly distinguished, and the contrast between its own texture and the scratch defects on the surface is obviously enhanced. Through the threshold segmentation method, it can effectively locate the scratch defect area on the material surface.

3. Experimentation and Evaluation

In this paper, we selected a diverse array of 36 commonplace materials, distinguished by their varied textural characteristics. Our selection encompasses an assortment of items encountered in daily life, such as leathers, fabrics, textured papers, wooden panels, textured plastics, and metallic goods. To rigorously assess the efficacy of our proposed methodology, we subjected these materials to a standardized procedure. We tested a total of 144 samples by manually creating four random scratch defects for each material. The parameters of these induced flaws were meticulously controlled to ensure a wide spectrum of defect severity; the least number of scratches imposed on any given sample was one, escalating up to a maximum of twenty-five. Similarly, the dimensions of these blemishes ranged from a minimum length of 5 mm to an upper limit of 88 mm, thereby encapsulating a broad gamut of potential damage scenarios. The minimum number of scratches was 1 while the maximum was 25; the minimum length of scratches was 5 mm, and the maximum length was 88 mm.

In this chapter, we are dedicated to corroborating the superiority and the broad applicability of our novel methodology entitled “Enhanced Scratch Detection for Textured Materials Based on Optimized Photometric Stereo Vision and FFT-Gabor Filtering”. Our validation strategy is meticulously crafted to serve dual purposes: firstly, to affirm the broad applicability of our proposed technique across a variety of material types, and secondly, to underscore its distinctive advantages over conventional approaches within the domain of scratch detection on textured surfaces.

3.1. Validation of Textured Material Applicability of Detection Methods

In this section, we present several common materials from daily life as examples to illustrate the effectiveness of our method, as shown in Figure 9. Following the methodology, we display the images that appear during the detection process. Specifically, these include, in order, the material sample; the measured detection area; the Curl Gradient image of the material surface optimized by photometric stereo vision; the background texture image and the contrast-enhanced material image based on fast Fourier transform (FFT) processing; and the image detected by the OTSU threshold segmentation method. The images after scratches are detected and marked; we then analyze the correct rate of the number of scratches detected for scratch defects in different textured materials, the correct percentage of the length of scratches detected versus the actual length, and the percentage of the area of scratches marked versus the actual area of scratches, as shown in

Table 1. Objective evaluation of textured material applicability in detection methods.

Object/Evaluation	Number of Scratches Detected	Correct Rate	Scratch Detection Length	Correct Rate	Detection Coverage Rate
A	14	100%	148.54 mm	99.87%	98.91%
B	2	100%	87.88 mm	98.60%	98.43%
C	7	100%	186.14 mm	97.24%	97.97%
D	3	100%	71.23 mm	101.18%	101.67%
E	4	100%	74.91 mm	102.51%	103.42%

.

By observing the detection effect of all the samples and analyzing the experimental data, we find that the ratio of the number of detected scratches to the actual number of scratches is consistently at 100%; the ratio of correctly identified scratches is stable at 98.43% ± 1.0%; the accuracy of the detected scratch lengths is at 97.84% ± 2.0%; and the coverage rate of the detected scratches over the real area is stable at 99.51% ± 5.0%. We can conclude that the method proposed in this paper, “Enhanced Scratch Detection for Textured Materials Based on Optimized Photometric Stereo Vision and FFT-Gabor Filtering”, is applicable to the detection of scratch defects on most textured materials encountered in everyday life.

3.2. Validation of Methodological Superiority

In the preliminary phase of our study, we conducted comparative experiments to evaluate the improvement in accuracy and reliability of defect detection on textured materials using our proposed composite-enhanced defect detection method.

To validate the superiority of the method proposed in this paper, we used the same batch of textured materials as experimental subjects and compared the defect information enhancement and scratch defect detection performance of our method with mainstream, commonly used defect detection methods. Given the significant technical differences between our method, which is based on traditional machine vision technology, and methods based on deep learning, we did not consider deep learning methods in our comparative trials.

The comparative trials were divided into two parts:

Comparison of Two-Dimensional Detection Methods: We compared our method with automatic threshold segmentation [12,46] and fast Fourier transform based on Gaussian filtering (FFT-Gauss) [47]. Automatic threshold segmentation can achieve the fastest binary segmentation of an image; however, due to the influence of the material’s texture, it fails to distinguish between scratches and the texture on the surface of the material. The FFT enhances the high-frequency information of the image, but the FFT alone tends to enhance both scratches and texture simultaneously and is affected by the lighting angle, making it difficult to fully observe the scratches. The limitations of these methods in detecting defects on textured materials are evident, as they often fail to distinguish between scratches and surface textures. For clarity, the detection results are shown in the first three columns of Figure 10.

Comparison of Three-Dimensional Detection Methods: Given the limitations of two-dimensional methods, we also conducted a comparison with three-dimensional detection methods. We evaluated the performance of our method against photometric stereo vision alone [48,49] as well as a combination of photometric stereo vision and FFT-Gauss [50]. The results of these comparisons are displayed in the last three columns of Figure 10.

Using photometric stereo vision overcomes the effect of a single lighting angle, allowing for a full observation of the scratches, but it does not filter out the texture to a degree that allows for a clear distinction between scratches and texture. The photometric stereo vision + FFT-Gauss method, while effective in detecting anomalous scratch defects, exhibits significant inaccuracies due to its inability to mitigate the influence of the background texture, frequently confusing inherent texture variations with actual defects.

To further validate the superiority of our method, we provide a more comprehensive comparison of the performance metrics in

Table 2. The more comprehensive comparison of the performance of our method against photometric stereo vision alone [48,49] and a combination of photometric stereo vision and FFT-Gauss [50].

Object/Evaluation	Method	Number of Scratches Detected	Correct Rate	The Number of False Positives Marked as Scratches	Scratch Detection Length Error	Scratch Area/Area Identified as Scratches
A	Photometric Stereo [48,49]	2/2	100%	87	−14.8 mm	88.43%
	Photometric Stereo + FFT-gauss [50]	2/2	100%	674	+9.3 mm	86.31%
	Our Method	2/2	100%	0	−0.4 mm	98.43%
B	Photometric Stereo [48,49]	3/3	100%	187	−31.4 mm	78.33%
	Photometric Stereo + FFT-gauss [50]	3/3	100%	1316	+24.0 mm	42.74%
	Our Method	3/3	100%	1	−0.2 mm	99.12%
C	Photometric Stereo [48,49]	5/6	80%	143	−13.1 mm	86.49%
	Photometric Stereo + FFT-gauss [50]	6/6	100%	978	+8.1 mm	72.31%
	Our Method	6/6	100%	0	−0.2 mm	99.77%

. As shown in the table, our method consistently demonstrates lower detection errors and a higher coverage of the original scratch areas when compared to the other methodologies. As the data in Table 2 show, our method consistently outperforms the alternatives in terms of correct rate, false positives, and scratch detection length error. The results clearly indicate that our method, which combines optimized photometric stereo techniques with FFT-Gabor filtering, successfully mitigates the influence of background texture and provides a more accurate detection of scratch defects on textured surfaces.

Our method displays lower detection errors and a higher coverage of the original scratch areas. These findings support the conclusion that, for the detection of scratch defects on textured materials, our method, which builds upon optimized photometric stereo techniques and integrates FFT-Gabor filtering, overcomes the shortcomings of conventional Gaussian filtering in differentiating between surface texture and anomalous defects. The key advantage of our proposed method is its ability to discern anomalous scratches from the inherent surface texture of textured materials, thus robustly identifying defects on textured surfaces. By leveraging optimized photometric stereo techniques, our approach overcomes the limitations associated with single-source illumination. Furthermore, the application of FFT-Gabor filtering enhances the visibility of defects by suppressing the intrinsic textures. In summary, our methodology demonstrates superior stability and robustness by effectively distinguishing true defects from natural material variations, which is essential for accurate defect detection on complex textured surfaces.

4. Conclusions

In conclusion, this paper has successfully addressed the critical challenge of detecting scratches on textured materials by developing an enhanced scratch defect detection system. Our approach combines optimized photometric stereo vision with FFT-Gabor filtering, enabling a more accurate and robust detection of defects. The optimized photometric stereo vision system captures images under various lighting conditions, which are then processed to generate a surface gradient image that mitigates the effects of high reflections and shadows. The FFT-Gabor filtering technique selectively enhances the visibility of defects while suppressing the inherent texture patterns, thereby improving the detectability of scratches.

The experimental results demonstrate the effectiveness and superiority of our method, achieving a 100% success rate in scratch capture and a recognition detection rate of 98.43% ± 1.0%, validating its applicability across a range of textured materials. However, it is acknowledged that the proposed system faces limitations, such as increased computational complexity due to the use of advanced imaging techniques and the potential variability in performance across different textures. Future work will focus on optimizing the algorithm to reduce computational demands, making the system suitable for real-time applications. Additionally, we aim to enhance the adaptability of the system to accommodate a wider variety of lighting conditions and texture variations, ensuring its robustness across diverse scenarios. These improvements will further solidify the practical utility of our method in industrial settings and contribute to advancements in automated quality control systems for textured materials.