Application of computer vision techniques to estimate surface roughness on wood-based sanded workpieces

Accepted manuscript 1 Application of computer vision techniques to estimate surface roughness on wood-based sanded workpieces. [Accepted manuscript] F. Iglesiasa, A. Aguilerab, A. Padillaa, A. Vizanc, E. Dieza,⁎ a Department of Mechanical Engineering, Universidad de La Frontera, Temuco, Chile. b Instituto de Bosques y Sociedad, Universidad Austral de Chile, Valdivia, Chile. c Department of Mechanical Engineering, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid, España. ⁎ Corresponding author. E-mail address: e[email protected] (E. Diez). Please cite this article as: F. Iglesias, A. Aguilera, A. Padilla, A. Vizan, E. Diez, Application of computer vision techniques to estimate surface roughness on wood-based sanded workpieces, Measurement (2023), doi: https://doi.org/10.1016/j.measurement.2023.113917 Abstract In the wood industry, surface inspection post-sanding is critical during the final production stages. This inspection relies on subjective assessments made by operators due to the challenges of adapting traditional measuring techniques to industrial environments. This study introduces an innovative artificial vision approach for the in-line inspection of surface roughness applied to wood and wood-based products in highly automated manufacturing systems. The procedure is based on extracting features from the grey-level co-occurrence matrix in images processed with edge-detection algorithms. Images are derived from photographs of sanded medium-density fibreboard, and models predicting surface roughness were formulated and compared with direct measurements using a stylus profilometer and a confocal microscope. Results showed that the most effective algorithm-feature combination was Roberts and Uniformity of Energy, with consistent performance for different roughness parameters. This approach can improve quality control and extend to a broader range of materials and applications. Keywords: wood-based products; finishing operations; artificial vision; stylus profilometry; confocal microscopy; roughness models. Accepted manuscript 2 1. Introduction In the wood products manufacturing industry, it is necessary to continuously improve the quality of products and components by optimising the operations involved in the manufacturing process. Finishing operations are of great relevance in the definition of final quality, a stage in which it is essential to conduct a detailed inspection to detect manufacturing errors according to the product's dimensional, geometric, and surface finish specifications. In addition, developing emerging manufacturing systems that aim to automate finishing operations using industrial robots [1] brings new challenges in designing quality inspection technologies to operate in highly automated environments. Inspecting the surface finish of a sanded wooden workpiece determines if the workpiece is accepted, rejected, or requires an additional operation. The surface finish will affect the adhesion force in applying coatings [2] and the user's perception of the product's final quality. Inspecting sanded workpieces is a critical task that is difficult to automate due to its multiparametric nature, which motivates, in the wood furniture industry, the inspection to be usually carried out through the subjective perception of the operator [3]. To quantitatively determine the quality of a surface, roughness measurement is used after an intermediate or final operation. However, using roughness measurement instruments in wood product manufacturing is infrequent due to the costs of purchasing measurement equipment, personnel training, measurement times, and the difficulties when measuring curved geometries if a contact stylus profilometer is used. Additionally, evaluating the surface roughness of wood products is a complex procedure, and there still needs to be an accepted methodology for performing roughness measurements on wood [4]. The results of the surface roughness measurement in processed wood vary depending on multiple factors, some associated with the type of wood, type of cut, structural characteristics, operating conditions, the measuring instrument used, and the processing of the wood profile, a representation of the measured surface texture to which different filters are applied before the roughness parameters are calculated. So many factors increase the difficulty in determining the influence of the process on the roughness of the piece. In the case of homogeneous materials such as medium-density fibreboard (MDF), since there is no fibre orientation [5], there are more appropriate conditions to determine the influence of the operation on the surface quality, decreasing the variability in the roughness present in the sanded workpiece. However, it is recognised that the roughness might change for varying depths in MDF due to changes in density as a result of the MDF manufacturing process [6]. Accepted manuscript 3 Gurau & Irle [4] reviewed methods to evaluate the wood surface roughness. Those approaches show that some researchers emphasise the elimination of cracks in the roughness profile, which are frequent in wood pieces, before calculating the amplitude parameters, thus improving the sensitivity of roughness to changes in operating conditions. This review also gathers different roughness measurement methods, from which it follows that conventional measuring instruments, commonly used in the laboratory, can be categorised as contact measuring equipment (i.e., stylus profilometer, atomic force microscope), and contactless measuring equipment (i.e., autofocus roughness meter, white light interferometer, confocal microscope). These instruments measure surface texture parameters associated with a profile or a surface according to ISO Geometrical Product Specifications (GPS) standards. There is currently no agreement about the preference for using contact or contactless methods to evaluate the surface finish of wood products. Magoss et al. [7] studied the use of confocal microscopy in the evaluation of the surface roughness of wood, obtaining that the mean of the parameters 𝑅𝑎, 𝑅𝑞, 𝑅𝑧, 𝑅𝑘 and 𝑅𝑣𝑘 were close to the parameters calculated from data measured with a stylus profilometer. In the case of the 𝑅𝑝𝑘 parameter, the values measured with the confocal microscope turned out to be higher than when using the conventional stylus profilometer due to the higher resolution available in the microscope, which does not apply a mechanical filter as the stylus tip does (Figure 1), and when anomalous values are recorded by the sensor light saturation, reported by Caja García et al. [8]. However, Magoss et al. [7] concluded that the observed differences could be corrected by applying filters and eliminating artificial peaks, proving that confocal microscopy is an adaptable method for measuring the surface quality of wood pieces. Figure 1. Stylus profilometer and confocal microscope behaviour when measuring a surface. Accepted manuscript 4 Among the instruments mentioned above, only the stylus profilometer is feasible to use at an industrial level due to its costs and measurement times. However, its use is limited to flat surfaces. To develop automated inspection systems, it is necessary to test fast, non-conventional techniques for evaluating wood parts that can be applied in the industry. Liu et al. [9], who reviewed cutting tool failure diagnostic procedures by monitoring the surface texture of machined metal parts, pointed out the advantages of evaluating surface roughness through machine vision-based inspection systems, which take measurements faster and without scratching the surface. On the other hand, machine vision-based techniques proved to be more convenient and consistent than manual inspections in evaluating surface roughness. Techniques based on two-dimensional images allow fast and low-cost results, apply to surfaces that are difficult to measure using conventional instruments due to geometric or dimensional factors of the parts, and allow for an easy integration into automated systems, inspection stations, or intelligent systems [9]. In recent years, there has been a significant development in machine vision techniques to inspect the quality of parts [10]. Regarding surface roughness, tests have been carried out using algorithms that consider direct calculations on the pixels of a digital image, applying filters, statistical techniques, and machine learning algorithms through artificial intelligence algorithms [11]. In the literature, there are examples of different techniques to assess the surface quality of parts from images, such as the extraction of roughness parameters from the grey-level histogram [12], the measurement of the intensity of light reflected by the surface in MDF boards [13] or the roughness estimation from analysis of light intensity differences in wood workpieces [14]. A method that showed a high correlation between the features extracted from the images and the standardised roughness evaluation parameters corresponds to the one proposed by Ghodrati et al. [15], who used image edge detection algorithms to estimate the roughness of plastic parts. Other examples of roughness estimation are those proposed by Lu et al. [16], who applied Laplacian-based edge enhancement on surfaces of casting components, Koblar & Filipič [17], presented the design of an online algorithm that applies an FFT filter and extracts features, which are used in a machine learning algorithm to predict roughness, and Kilinçarslan et al. [18] used an artificial neural network and random forest algorithm to predict roughness in heat-treated spruce wood surfaces. Another technique applied in studies that seek to determine roughness from images is obtaining features from the grey-level co-occurrence matrix (GLCM), which measures Accepted manuscript 5 the frequency of grey-level patterns between neighbouring pixels in an image. The first use based on the GLCM associated with the roughness evaluation was made by Gadelmawla [19]. Co-occurrence matrix-based techniques to measure roughness may vary depending on the specific material and the roughness range evaluated, which is why a previous calibration step is necessary [20]. Moreover, there are studies in the literature on using features extracted from the GLCM in the training of neural networks to estimate surface roughness, like the works done by Joshi & Patil [21] and Kumar et al. [22]. Some investigations have focused on developing deep learning models, such as using a convolutional network to evaluate roughness in machined parts processed by turning and milling [23] and in assessing roughness and defects [24]. Rifai et al. [25] estimated surface roughness and identified chatter vibration using vision-based deep learning. Lu et al. [26] developed a deep learning model combined with simulation data to recognise surface roughness in milling; Bhandari et al. [27] implemented a transformer-based deep learning architecture to classify surface roughness using sound and cutting force signals in end-milling; and He et al. [28] developed a theoretical and deep learning hybrid model to predict the surface roughness of diamond-turned polycrystalline materials. However, machine learning-based techniques, such as those mentioned above, require a large amount of data in the training stage and bring difficulties that need attention, such as model overfitting and out-of-range prediction problems. Based on the review outlined here, there is still no suitable method to evaluate the roughness of wood pieces using machine vision. To contribute to the advancement of the study of artificial vision techniques to inspect surfaces and, at the same time, compare different instruments for measuring roughness on sanded wood pieces, in this work, a novel method is developed to estimate the surface roughness of wood pieces based on combining GLCM and edge detection algorithms to obtain roughness parameters from photographic images. The proposed method is conceived to apply to in-line roughness inspection in highly automated sanding and polishing robotised stations. 2. Methodology Automating sanding processes with industrial robots requires the development of fast and reliable inspection systems, which allow roughness to be measured with sufficient precision. The proposed method based on artificial vision requires previous calibration against known input values of roughness. In this study, the calibration is carried out with state-of-the-art instruments: contact measurement with a stylus profilometer and Accepted manuscript 6 contactless measurement with a confocal microscope. The calibration process begins with the photographic capture of the surface of the pieces. These images can be acquired from specimens taken from the product across its different sanding stages. The images are transformed to greyscale and then processed with five edge detection algorithms. Then, the GLCM is calculated for each image resulting from the above processing, including the original greyscale image, and five features are obtained from the matrix. With the roughness parameters and the features of the images, the best models are fit and selected, making it possible to estimate the roughness from new images. Next, the materials and methods considered in this study are described in detail. 2.1 MDF sanded workpieces Sanded MDF workpieces, 180 x 110 x 15 mm3, were used. An aerosol polyurethane coating was applied to the lower surface of the specimens for correct attachment with the vacuum fixture. Figure 2. Robotic sanding station in which the MDF specimens were prepared. Accepted manuscript 7 Two experimental robotic sanding campaigns were carried out with the same operating conditions: one for obtaining estimation data (15 workpieces) and the other one for validation data (9 workpieces). The sanding process was carried out with a sander of inhouse design [1], driven by a servo motor mounted on the flange of a collaborative robot UR10e (Figure 2). A force of 20 N was applied to the specimen perpendicular to the feed direction, controlled by the collaborative robot; a rotating speed of 2000 min-1 in the servomotor; and a feed speed of 0.02 m/s, defined through a linear movement of the sanding pad, parallel to the surface of the specimen. The three types of circular sandpaper were 3M™ Cubitron™ II Hookit™ 127 mm diameter, with perforations for particle suction. In both experimental campaigns, the total number of specimens was subdivided into three groups: the first was processed with coarse P80 grit size (one pass), the second with P120 (one pass), and the third was sanded with two passes, one with P120 and the other, finer, with P240, considering the need to apply incremental sanding when using finer grits. In the sanding tests, the minimum number of passes was considered to avoid the variations in density present in MDF boards at different depths [29]. 2.2 Roughness measurement To measure roughness, three measurement methods have been considered. One is a classic measurement by contact, a stylus profilometer, and two are optical, one based on a confocal microscope, which provides a high-precision digital definition of the surface geometry of the part, and another based on computer vision, where a general evaluation of the image is made. These methods exhibit advantages and limitations related to the nature of their measurement principles. Contact profilometer measurement is fast, reliable, robust, and can be applied to any part size. The confocal measurement is slow and limits the dimensions of the piece to be explored, but the high precision of the geometric model obtained provides excellent flexibility for the measurement and the definition of any normalised roughness parameter. It also performs a superficial scan instead of a linear scan. Vision-based measurement is fast and easy to incorporate into production lines, although it can have limited accuracy. The system proposed in this work is based on this type of measurement. In this study, the confocal evaluation of the roughness will be intercompared with the measurement by contact of the workpiece. At the same time, the normalised roughness Accepted manuscript 8 parameters obtained with these procedures will be intercompared with the parameters obtained by visual image processing. To obtain a comprehensive description of surface roughness, it is necessary to use more than one roughness parameter, even if the part surface is homogeneous [30]. For this reason, five parameters were selected based on the physical information provided by the sanding operation: the arithmetic mean height 𝑅𝑎, the maximum height 𝑅𝑧, the mean peak height 𝑅𝑝, the mean profile element spacing 𝑅𝑠𝑚, and the skewness 𝑅𝑠𝑘, according to ISO 21920-2. The measurements were made in the central area of the specimen in the feed direction of the rotating sanding pad (see Figure 2). 2.3 Roughness parameters The surface roughness parameters are defined by the ISO 21920-2 [31] standard, published in December 2021, which replaces the ISO 4287, ISO 13565-2 and ISO 135653 standards and implements some modifications in the stages of the profile processing and the way to calculate some roughness parameters. The new standard also increases the available parameters to describe surface roughness. For profile processing, the new standard considers the application of three filters in the order shown in Figure 3. Once the mechanical profile is obtained with the stylus tip, an S profile filter is applied to eliminate the small lateral scale components (short wavelength), with nesting index 𝑁𝑖𝑠, to obtain the primary surface profile. Then, operation F is applied to eliminate the profile form, using an association method and element (for example, a polynomial fit of order n by least squares), a filter L, which removes the large lateral scale components (long wavelength), with nesting index 𝑁𝑖𝑓, or a combination of stages. Once the form has been subtracted from the profile, the primary profile P is obtained, to which a filter L or a filter S with nesting index 𝑁𝑖𝑐 is applied to get the roughness profile R or the waviness profile W, respectively. Accepted manuscript 9 Figure 3. Profile processing scheme based on ISO 21920-2. In the new standard, the classification of roughness parameters changes. Previously, the amplitude parameters of mean values were an average of the calculation at each sample length (now section length); in the new standard, some of these parameters are calculated directly from the evaluation length. The parameters selected in this work are defined below, based on the ISO 21920-2 standard, and have been adapted for digital implementation. In addition, the changes observed in the new standard are mentioned. Arithmetic mean height (𝑅𝑎) The 𝑅𝑎 parameter is considered since it is a good representation of the distribution of profile deviations from the mean line, and its use is widespread in the industry. The height parameter 𝑅𝑎 does not experience changes in the renewal of the standard; it was previously calculated as the average of 𝑅𝑎 for each section; now, it is obtained directly from the evaluation length, which is mathematically equivalent in the case of this parameter. 𝑅a=1 𝑛∑|𝑧𝑖|, 𝑛 𝑖=1 (1) Accepted manuscript 16 3. Results and discussion The dataset in this study, which includes roughness data measured with the confocal microscope and the stylus profilometer, and the corresponding photographic images of each sanding test, is available for the reader in [40]. 3.1 Roughness evaluation For an adequate analysis of the results, it is necessary to check if the identification of the micro geometric profiles (mechanical and optical) is equivalent and provides similar information for calculating the normalised roughness parameters. Figure 6 shows the mechanical profile obtained with the roughness tester for specimens sanded with sandpaper of different grain sizes. As expected, smaller grain sizes give rise to profiles with smaller deviations from the zero line. It can also be observed that the profile distribution is highly symmetrical, which is attributable to the regular shape of the abrasive grain. In the collected profiles, no influence of the previous processes to which the piece has been subjected is observed. Figure 6. Roughness profiles obtained with the stylus profilometer and different grit sizes. Accepted manuscript 17 The confocal method identifies the micro-geometric surface according to the profiles obtained by the stylus profilometer (Figure 7). The distribution of the profile around the mean line is also very symmetrical and with a slightly more extended distribution, which confirms that the optical (confocal) method can obtain a profile with more resolution than a contact-based method (stylus). Similarly, smaller grain sizes result in narrower distributions of the profile deviation. The characterisation of the surface microgeometry by both methods is similar, with greater resolution of the confocal method in the case of sanded MDF pieces. Figure 7: Examples of images obtained with the confocal microscope on specimens sanded with different grit sizes. To analyse the associated dispersion when measuring with the stylus and the confocal microscope, the roughness measurements for each estimation specimen were plotted in Figure 8. While there is a natural tendency to reduce roughness using finer sandpaper, it is realised that a specific grit size does not necessarily imply a particular roughness level. When performing rough sanding with P80 sandpaper, there is a higher dispersion of roughness than in finer sanding. The roughness distribution in Figure 7 represents all Accepted manuscript 18 points of the multifocal reconstruction, which is more representative of the roughness behaviour than a specific line in the image. Figure 8: Confidence intervals (95%) of 𝑅𝑎 for each specimen of the estimation tests. Table 1 shows, for each grain size, the mean, median and standard deviation of 𝑅𝑎 for the different confidence intervals. It is observed that the confidence interval ranges are reduced as sanding with finer grits; the same happens with the standard deviation of those ranges. It also follows that the confidence intervals of the parameters measured with the confocal microscope are usually larger than those obtained with the stylus profilometer, although similar results are obtained with the finest grain P240. A reduced dispersion is a good indicator of the instrument’s performance. However, it must be considered that, due to the nature of the material, there is variability present on the surface. Table 1. Summary of the confidence interval (95%) ranges of 𝑅𝑎 for each grit size. Grit size Instrument Mean [µm] Median [µm] Standard Deviation [µm] P80 Stylus 2.28 1.95 1.03 Confocal 2.94 2.45 1.08 P120 Stylus 1.32 0.73 0.99 Confocal 2.13 2.17 0.75 P240 Stylus 0.88 0.57 0.66 Confocal 0.88 0.81 0.64 In the graphs of Figure 9, a reduction in the magnitude of the roughness parameters can be seen as a finer grit is used (something similar occurs in the case of the confidence Accepted manuscript 19 intervals in the three height parameters: 𝑅𝑎, 𝑅𝑧, and 𝑅𝑝), which implies that the roughness parameters are not strictly independent in this particular operation. It can also be seen that with the confocal microscope, parameters of greater magnitude are usually obtained, especially in the case of the parameters 𝑅𝑧 and 𝑅𝑝. Figure 9. Roughness parameters measured with both instruments. The intercomparison of the normalised roughness parameters calculated from not exactly equal profiles endeavours to determine if there is a correlation between these parameters. To this end, a linear fit of the measurement data recorded by both techniques was carried out for each one of the roughness parameters obtained in the first 15 MDF workpieces, generating models defined by Equation 9, which were validated with the remaining nine workpieces (Figure 10). Table 2 shows the coefficients and some goodness of fit; note that RMSE is computed both with estimation and validation data. 𝑅𝑐𝑜𝑛𝑓𝑜𝑐𝑎𝑙=𝑤0+𝑤1∙𝑅𝑠𝑡𝑦𝑙𝑢𝑠 (9) Accepted manuscript 20 Table 2. Coefficients and goodness of fit of the models defined by Equation 9. The comparison shows that the confocal measurement has a higher resolution in the determination of 𝑅𝑧 and 𝑅𝑝, since the range of the stylus is smaller than the one provided by the confocal method for the same measurements. This range is appreciably greater and about double. This demonstrates that the optical measurement better determines the pits and peaks of the profile. On the other hand, it is confirmed that the parameters 𝑅𝑧 and 𝑅𝑝 for a sanded MDF piece have a similar evolution, and therefore, they do not provide any additional information about each other as to the surface state of the workpiece. As occurs with other processes, the parameters 𝑅𝑎 and 𝑅𝑧 (𝑅𝑝) calculated by both methods are closely correlated, allowing an approximate conversion between them for the MDF sanding process. The measure of the profile skewness expressed according to 𝑅𝑠𝑘 and the spacing defined by 𝑅𝑠𝑚 are very similar for both methods, which shows that these open surface characteristics can be evaluated without distinction by any of the methods. Roughness parameter (Confocal) Interception 𝑤0 Coefficient 𝑤1 𝑅2 estimation data RMSE estimation data RMSE validation data 𝑅𝑎 [µm] -0.2857 1.2933 0.95 0.60 µm 0.93 µm 𝑅𝑧 [µm] -6.8871 1.9463 0.95 4.31 µm 8.12 µm 𝑅𝑝 [µm] 0.0458 2.5238 0.93 3.72 µm 5.41 µm 𝑅𝑠𝑚 [mm] 0.0433 0.6730 0.83 0.01 mm 0.01 mm 𝑅𝑠𝑘 [-] 0.7330 0.7349 0.47 0.40 0.17 Accepted manuscript 21 Figure 10. Comparison of roughness parameters obtained from measurements with the confocal microscope and the stylus profilometer. 3.2 Determination of surface finish through vision Figure 11 presents cutouts of greyscale images that show the surface finish after the sanding operation using different grit sizes. The result is delivered to the right of each image after applying the various edge detection algorithms considered in this study. These images were captured to extract the features and fit the models. For expository reasons, we increased the brightness and contrast of the images, and a gradient map was applied so that the reader could better visualise the surface marks after processing with different edge detection algorithms. Like the Laplacian algorithm, the Roberts algorithm tends to obscure the marks but does not remove them. On the other hand, Sobel, Prewitt, and the Laplacian of Gaussian enhance markings to a greater degree. Accepted manuscript 22 Figure 11. Images of MDF specimens sanded with different grit sizes and the result after applying the edge detection algorithms. As specified in the methodology, for calculating the GLCM, a vertical displacement coinciding with the sanding feed was used to consider thereby the same measurement direction made with the stylus profilometer and the traces extracted from the image obtained with the confocal microscope (Figure 5). Due to the difference observed between the contact and confocal measurement systems, models were made (Equation 10) comparing the features obtained when using vision algorithms with both measurement instruments separately. It is considered that, during the calibration stage, one of the two instruments will be selected, depending on availability, to perform calibration measurements on small-sized specimens made of the material to be processed. The vision algorithms analysed showed different performances when estimating roughness. Tables 3 and 4 show some results for selected combinations of algorithm and feature in the estimation of the parameter 𝑅𝑎. The RMSE values in Table 3 are calculated from the fitted model between the stylus measurements and the features extracted from the photographed images processed with edge detection algorithms. Table 4 presents the RMSE values of the fitted model between the confocal microscope and image Accepted manuscript 23 features. Henceforth, the Roberts algorithm for edge detection and the Uniformity of Energy (U) feature were selected, which yielded the best RMSE results compared to all the other combinations. In addition, the mean absolute percentage error (MAPE) was calculated to evaluate the models. MAPE values, presented in Appendix 2, are consistent with the RMSE results. Table 3. RMSE for stylus-based models (in µm). Uniformity of Energy (U) Entropy (S) Contrast (C) Homogeneity (H) Autocorrelation (A) Original 1.16 1.07 1.16 1.37 1.84 Roberts 0.66 0.67 0.69 0.70 1.94 Sobel 1.62 1.29 0.91 1.32 2.32 Prewitt 1.43 1.18 0.86 1.22 2.14 Laplaci an 0.91 0.92 0.89 0.94 1.49 LoG 1.93 1.74 1.54 1.89 2.71 Table 4. RMSE for confocal-based models (in µm). Uniformity of Energy (U) Entropy (S) Contrast (C) Homogeneity (H) Autocorrelation (A) Original 1.60 1.42 1.69 1.94 2.17 Roberts 1.03 1.06 1.06 1.07 2.65 Sobel 2.19 1.82 1.33 1.80 3.28 Prewitt 1.96 1.70 1.28 1.69 3.05 Laplaci an 1.41 1.44 1.37 1.41 2.26 LoG 2.51 2.22 2.11 2.44 3.76 A similar behaviour was observed with the parameters 𝑅𝑧 and 𝑅𝑝. In the case of the 𝑅𝑠𝑚 parameter, the best result was Roberts with Entropy, although with a negligible difference from the result with Roberts and Uniformity of Energy. The parameter that performed worst was 𝑅𝑠𝑘. To facilitate the comparison between the estimated models for each Accepted manuscript 24 parameter, it was deemed necessary to plot them maintaining the Roberts combination with Uniformity of Energy. Figure 12 shows the models obtained by comparing the vision method with the stylus profilometer based on Equation 10. A Bayesian linear fit was used, and ±2𝜎 prediction intervals were obtained. Table 5 shows the model coefficients, the precision 𝛽= 1 𝜎2 and the coefficient of determination in the estimation 𝑅2, together with the RMSE evaluations in the estimation and validation. 𝑅=𝑤0+𝑤1∙𝑣𝑓𝑒𝑎𝑡𝑢𝑟𝑒 (10) Table 5. Coefficients and goodness of fit of the models defined by Equation 10, using the stylus profilometer. Parameter stylus Interceptio n 𝑤0 Coefficient 𝑤1 Precision 𝛽 𝑅2 estimation RMSE estimation data RMSE validation data 𝑅𝑎 [µm] 57.2507 -55.2224 2.67 0.90 0.61 µm 0.73 µm 𝑅𝑧 [µm] 300.9354 -281.1843 0.06 0.85 4.05 µm 5.31 µm 𝑅𝑝 [µm] 162.1268 -157.2091 0.34 0.91 1.71 µm 3.90 µm 𝑅𝑠𝑚 [mm] 1.2324 -1.1371 4231 0.86 0.02 mm 0.02 mm 𝑅𝑠𝑘 [-] 11.5163 -13.0721 11.61 0.69 0.29 0.57 Figure 12. Bayesian linear models relating roughness and features obtained from the GLCM, based on the values of the stylus profilometer. Similarly to the previous models, Figure 13 shows the models obtained by comparing the vision method with the parameters measured with the confocal microscope. Table 6 gathers the coefficients and evaluations of the proposed models. Accepted manuscript 25 Table 6. Coefficients and goodness of fit the models defined by Equation 10, using the confocal microscope. Roughnes s Parameter confocal Interceptio n 𝑤0 Coefficient 𝑤1 Precision 𝛽 𝑅2 estimation RMSE estimation data RMSE validation data 𝑅𝑎 [µm] 77.6082 -75.3876 1.55 0.91 0.80 µm 1.43 µm 𝑅𝑧 [µm] 592.2905 -560.8858 0.01 0.83 8.51 µm 12.16 µm 𝑅𝑝 [µm] 404.1223 -390.9245 0.02 0.79 6.84 µm 8.89 µm 𝑅𝑠𝑚 [mm] 0.8819 -0.7777 2657 0.65 0.02 mm 0.02 mm 𝑅𝑠𝑘 [-] 10.8143 -11.3263 4.77 0.41 0.46 0.53 Again, the Roberts and Uniformity of Energy combination delivered the best models. Figure 13. Bayesian linear models relating the roughness and features obtained from the GLCM, based on the values of the confocal microscope. 3.3 Analysis of results For the developed models, the evaluation of error (RMSE) between each combination of algorithm-feature and surface roughness parameter, shows that the best performance was found in the combination of the Roberts algorithm and the Uniformity of Energy feature; thus, this selection was presented in the results. Based on the results, the repetition of the same algorithm-feature combinations may be due to the high correlation that the roughness parameters present with each other, as reported in previous investigations [41]. Accepted manuscript 32 Appendix 3 Table 10 and Table 11 present the mean absolute percentage error (MAPE) for Ra in stylus and confocal models. Table 10. MAPE for stylus-based models. Uniformity of Energy (U) Entropy (S) Contrast (C) Homogeneity (H) Autocorrelation (A) Original 0.27 0.24 0.27 0.32 0.41 Roberts 0.12 0.14 0.13 0.13 0.39 Sobel 0.37 0.29 0.21 0.29 0.50 Prewitt 0.32 0.28 0.20 0.28 0.46 Laplaci an 0.20 0.21 0.19 0.20 0.32 LoG 0.47 0.39 0.31 0.46 0.53 Table 11. MAPE for confocal-based models. Uniformity of Energy (U) Entropy (S) Contrast (C) Homogeneity (H) Autocorrelation (A) Original 0.29 0.25 0.30 0.34 0.37 Roberts 0.16 0.17 0.16 0.17 0.43 Sobel 0.36 0.31 0.23 0.30 0.55 Prewitt 0.33 0.30 0.23 0.29 0.51 Laplaci an 0.23 0.25 0.23 0.23 0.35 LoG 0.47 0.38 0.34 0.45 0.58 Accepted manuscript 33 References [1] E. Diez Cifuentes, R. Alzugaray Franz, A. Padilla Bernedo, E. Leal Muñoz, and M. Madaf Poblete, “Robotized workstation for intelligent sanding processes of wooden workpieces,” DYNA, vol. 98, no. 4, pp. 362–368, 2023, doi: 10.6036/10873. [2] P. L. Tan, S. Sharif, and I. Sudin, “Roughness models for sanded wood surfaces,” Wood Sci. 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