Modelling the orange-peel texture for chromatic and achromatic samples

Progress in Organic Coatings 135 (2019) 148–155

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Modelling the orange-peel texture for chromatic and achromatic samples a

a,⁎

b

T

c

Ali Mohammadalizadeh , Farhad Ameri , Siamak Moradian , Manuel Melgosa , Fereshteh Mirjalilid a

Department of Color Physics, Institute for Color Science and Technology, P.O. Box 16765-654, Tehran, Iran Center of Excellence for Color Science and Technology, Institute for Color Science and Technology, P.O. Box 1668814811, Tehran, Iran Faculty of Sciences, Department of Optics, University of Granada, 18071, Granada, Spain d State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China b c

A R T I C LE I N FO

A B S T R A C T

Keywords: Orange peel texture Color appearance Visual assessment Waviness perception ACT panels

The aim of this study was to quantify orange-peel texture with an instrumentally based single-number index highly correlated with equivalent visual assessments. We prepared 3 achromatic (black, grey, and white) and 4 chromatic (red, green, blue, and yellow) scales, each with 8 different levels of orange-peel texture. Each scale had a sample with a minimum degree of orange peel, which was considered to be the standard sample. The visual differences between the standard sample and the remaining ones with progressively increasing degrees of orange peel in each scale were assessed by a panel of 28 observers using a prepared one dimensional lightness scale based on CIELAB. The usual parameters for surface texture provided by the BYK instrument were measured for each of the 56 paint samples and used to develop different models under the assumption of the additivity principle. The coefficients of these models and their performance with respect to visually assessed equivalent differences in orange peel were determined. Ridge regression was used to address multicollinearity between parameters. The validity of the models derived as well as other indices were further tested using the ACT (Advanced Coating Technologies) standard panels. ANOVA analyses indicate that chromatic samples have no adverse significant effects on the orange peel. Predictions of visual orange peel texture results by one of our models are considerably good [R2 = 0.98; STRESS (Standardized Residual Sum of Squares) = 6.3] and therefore, this index is recommended as an index of orange peel.

1. Introduction

texture, gloss, transparency, opacity, etc., separately or in some combination [5]. The visual appearance perceived by humans is the result of complex interactions between an object and the incident light falling upon it, these interactions including specular reflection, scattering, absorption, and transmission [6]. Hunter subdivided the visual appearance of materials into two categories, namely chromatic attributes and geometric attributes [4]. All geometric attributes of visual appearance originate from distribution of white light in space [7]. The International Commission on Illumination (CIE) categorized the optical properties of a material into four aspects (color, gloss, translucency, and texture) [8], for which measurements may be possible now or in the near future [9]. Due to the importance of the high correlation between instrumental measurements and visual assessment of geometric appearance attributes, a vast amount of research has been conducted in this field [1,3,9–17]. The present study focuses on the quantification of only one key attribute of texture appearance, which is known as ‘orange peel’. According to ASTM, texture is the visible surface structure depending

The visual appearance of objects is important in everyday life, particularly in the selling of manufactured products. Therefore, it has been a challenge to identify and measure different aspects of appearance in consumer-goods industries such as automotive, printing, packaging, textile, food, cosmetics, etc. The measurement of appearance requires knowledge of optical processes (interaction of light with objects) and visual pathways (psychophysical interpretation by the eye/ brain combination) involved in creating specific object appearances [1–3]. Traditionally, the visual appearance of items was subjectively evaluated by experts, a practice still maintained in many industries. However, modern demands by customers for a high-quality appearance of goods have prompted extensive studies to develop measuring devices and methods, together with mathematical models, that can quantify appearance attributes which correlate with human perception [4]. The American Society for Testing and Materials (ASTM) defined the appearance of an object as the visual perception of size, shape, color,

⁎

Corresponding author:Tel.: +98 21 22945301; fax: +98 21 22947537. E-mail address: [email protected] (F. Ameri).

https://doi.org/10.1016/j.porgcoat.2019.06.003 Received 28 April 2019; Received in revised form 28 May 2019; Accepted 1 June 2019 0300-9440/ © 2019 Elsevier B.V. All rights reserved.

Progress in Organic Coatings 135 (2019) 148–155

A. Mohammadalizadeh, et al.

same for both classes, and vertical surfaces such as doors had a higher LW than horizontal surfaces in both car classes. In addition, the results for LW, SW, and DOI were used to provide a structure space with short and long wave combinations. In this space, the x and y axes represented the values of the Longwave Coverage (LC) and Wet look (WL) parameters, respectively, while the z axis represented Wd. The appearance of coatings with low LC and high WL values was wavy, while for a high LC value and low WL value the appearance moved from clear to fuzzy, the change being related to the Wb/Wd and Wd/Wc ratios. In 2012, Henshaw et al. studied the correlation between visual perception and waviness measurements for coated surfaces using painted panels with three different colors (silver, white and blue) [23] and a panel of 30 observers. The correlation between the BYK wavescan results of panels and the median rank was investigated. In 2014, Ameri et al. investigated the effectiveness of the “Structure Balance Index” correlating visual assessments for white, metallic grey and metallic black samples [3]. A panel of 16 observers participated in the visual assessments. It was reported that the balance chart cannot be extended to all lightness levels and the acceptability regions are not symmetrical for different lightness values, which can be regarded as a secondary fine-tuning correction of the Wd and LW parameters. In the last two decades, computer graphic images have also been used to investigate the relationship between the physical and perceptual dimensions of visual appearance [29–31]. The rendering of orange peel as an attribute of texture according to wave-scan instrumental measurements and related models has been studied [32–35]. In 2012, Konieczny et al. investigated the simulation of orange peel on a computer monitor, by comparison with the appearance of real neutrally colored (grey) samples, concluding that the software used for simulation of the orange peel had the potential to be used for prototype surface roughness [36]. Regarding the preparation of samples for visual assessments of orange peel, it is possible to use real plates or samples simulated on a computer monitor. Although it is much harder to prepare real samples, it seems that the results using real samples are much more reliable. Therefore, in the present study, real samples were used to quantify orange peel. The literature indicates that more research is necessary in order to quantify orange peel using a single instrumentally based number representing physical texture. The need for a single number measuring orange peel can be exemplified by the fact that BYK Gardner has provided a single number OP (Orange Peel) as a scale for a levelling parameter which was measured by their instruments, in addition to many other parameters. Recently, BYK Gardner has also included a new CF (Combined Ford) parameter on some of its instruments to denote an overall quality scale that includes physical surface textures [37]. However, no literature is available on the extent to which the OP and CF parameters suggested by BYK Gardner and certified by the Ford automotive manufacturer are equivalent to visual physical texture. The present study evaluates and recommends a single-number instrumentally based index for orange-peel, which is highly correlated with visual assessments in chromatic and achromatic samples.

on the size and organization of small constituent parts of a material, and orange peel is the appearance of irregularity of a surface resembling the surface texture of the skin of an orange [5,18]. The orange-peel phenomenon on glossy surfaces is seen as a wave pattern of dark and bright areas. Various factors such as substrate roughness, film thickness and its formulation, and manufacturing processes, cause a height difference on the surface of a coating. These height differences, referred to as wavelengths, are described by the size, shape, and depth of such surface structures. Coatings with different sizes of surface structures are judged differently in visual evaluations [19]. The clarity of these structures depends not only on the size of the structures, but also on the viewing distance, so that the sizes of 3–100 mm are visible at a distance of 3 m and are known as long waves. On the other hand, small structures in the range of 0.1–1 mm are visible only at very close distances and are known as short waves [20]. Very fine surface structures even smaller than 0.1 mm cannot be detected by the naked eye, but they also contribute to reducing the clarity of the coated surface, and ultimately affect the visual appearance of the coating. Similarly, surface structures with sizes of 1–3 mm are difficult to detect at a distance of 3 m, but they also affect the appearance of the coating [3,21–23]. BYK Gardner is a manufacturer of devices used to measure different properties of surface structures. For example, the wave-scan produced by the BYK Gardner company is released in several models, such as wave-scan DOI, micro-wave-scan and wave-scan dual, with similar functions for measuring the wavelength of surface structures. Generally, in such devices, a laser light shines on the surface of a coating at an incidence angle of 60° and the intensity of the reflected laser light from the surface is measured by the detector of the device at an equal angle on the other side of normal. Next, the device moves over the surface for approximately 10 cm and reflected laser light is measured, recording data points at 0.027-mm intervals to simulate the resolution of the human eye. The values of the signals measured are converted to a scale from 0 to 100 by the use of specific mathematical functions [2,21–24]. For the visual evaluation of orange-peel texture, the ACT (Advanced Coating Technologies) standard panels can also be used. These are a set of 10 black panels with different degrees of orange peel, on a scale from 1 to 10, according to visual evaluations in which panels 1 and 10 show the highest and lowest amount of orange peel, respectively [25]. Given the importance of orange peel in industry, this topic has been investigated by many researchers, as described in the next section. 1.1. Background In 2003, Giroux evaluated relationships between visual and instrumental assessments of appearance, using three different measurement methods and three different devices (Autospect, BYK Gardner wavescan Plus, and BYK Gardner wave-scan DOI) [26]. From 25 black panels evaluated by 45 observers using the ACT panels, they reported that the results of wave-scan DOI correlated well with human perception. In 2004, Gradischnig investigated the correlation between visual perception and measurements made by the wave-scan DOI for the structures of automotive finishes [27], using a set of 18 black panels from vertical and horizontal surfaces of 4 vehicles evaluated by 20 observers. The results showed high correlation coefficients for horizontal and vertical samples of 0.90 and 0.98, respectively. The model proposed from these results was independent of refractive index, and it was suggested that panels with a structure spectrum of Wb > 25 and Wd > 13 had a small visual effect. In 2004, Kigle-Böckler studied differences in appearance of painted bodies for cars in the top and middle classes [28]. The middle class had 7 different models and the top class had 5 models in black and silver. Horizontal surfaces such as hood and vertical surfaces such as doors were selected for measurements. The results showed that the SW:LW ratio for a metallic black color was higher in the highest class than in the middle class, the DOI values measured in metallic silver were the

2. Experimental 2.1. Preparation of orange peel scales Seven physical orange-peel scales were prepared on a tinplate substrate of size 10 × 20 cm² at the paint shop of the Iranian Gamma Thinner paint manufacturing company. Firstly, a basecoat was applied on the substrate. In total, seven base coats were applied, three achromatic (white, grey, and black), and four chromatic (red, green, blue and yellow). After a flash-off time of 15 min, a clear coat was applied by the wet-on-wet method. The simultaneous curing process for the basecoat/ clear coat system was carried out at 145 °C for 20 min. The thickness of cured base and clear coats were 13–15 μm and 10–50 μm, respectively. The reason for the broad range of clear-coat thicknesses was to create 149

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Table 1 Characteristics of the 8 samples in each of the 7 orange−peel scales (56 painted samples). The first sample in each scale (superscript a) was the one used as standard sample in our visual assessments. Scale

Sample

a*10

b*10

L*10

LW

SW

Wa

Wb

Wc

Wd

We

CF

OP

Du

DOI

Specular gloss (60°)

Black

OPS1a OPS2 OPS3 OPS4 OPS5 OPS6 OPS7 OPS8 OPN1a OPN2 OPN3 OPN4 OPN5 OPN6 OPN7 OPN8 OPW1a OPW2 OPW3 OPW4 OPW5 OPW6 OPW7 OPW8 OPR1a OPR2 OPR3 OPR4 OPR5 OPR6 OPR7 OPR8 OPG1a OPG2 OPG3 OPG4 OPG5 OPG6 OPG7 OPG8 OPB1a OPB2 OPB3 OPB4 OPB5 OPB6 OPB7 OPB8 OPY1a OPY2 OPY3 OPY4 OPY5 OPY6 OPY7 OPY8

0 0 0 0 0 0 0 0 −0.5 −0.5 −0.5 −0.5 −0.5 −0.5 −0.5 −0.5 −1.6 −1.5 −1.5 −1.6 −1.6 −1.5 −1.5 −1.5 28.2 27.9 27.9 27.9 27.8 27.9 27.7 27.6 −35.7 −36.1 −36.5 −35.8 −36.1 −36.2 −36.1 −36.1 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.6 11.4 11.0 11.3 10.8 10.8 10.8 10.9 11.0

−0.7 −0.6 −0.7 −0.7 −0.6 −0.7 −0.6 −0.7 2.7 2.8 2.9 2.9 2.9 2.9 2.8 2.8 1.4 1.3 1.3 1.9 1.9 1.5 1.3 1.6 8.0 8.0 8.1 7.9 8.1 8.1 8.1 8.0 10.6 10.8 11.0 10.6 10.7 10.6 10.7 10.8 32.6 32.6 32.7 32.8 32.7 32.7 32.8 32.7 61.0 60.8 60.9 60.7 60.6 60.6 60.7 60.8

25.8 25.8 25.8 25.8 25.8 25.8 25.8 25.8 35.4 35.2 35.1 35.2 35.3 35.3 35.3 35.1 93.4 93.9 93.9 92.8 92.7 92.8 93.4 93.5 34.9 34.7 34.6 34.5 34.5 34.5 34.5 34.4 43.7 43.9 43.9 43.6 43.8 43.7 43.8 43.7 39.5 39.5 39.3 39.6 39.3 39.3 39.4 39.5 78.2 78.3 78.7 78.2 78.3 78.3 78.4 78.5

5.5 9.8 17.4 22.5 31.4 39.4 45.3 49.0 5.4 9.2 17.4 21.0 33.3 39.0 46.3 51.9 5.0 9.3 16.4 22.8 30.6 42.4 47.0 53.3 5.0 8.9 15.8 25.6 33.1 42.9 47.6 53.3 5.0 9.6 15.9 21.5 33.3 41.0 46.3 50.2 5.2 9.2 16.5 21.9 34.4 43.5 46.6 54.6 3.1 10.4 17.5 22.5 32.2 42.2 46.8 57.4

5.8 7.6 15.0 11.8 33.3 20.6 24.6 42.3 4.7 8.7 16.4 8.4 23.9 20.6 23.7 33.9 5.6 7.5 14.7 22.3 22.2 33.4 37.4 40.1 8.2 15.1 21.6 32.1 43.1 48.6 56.4 54.7 7.1 15.7 25.7 34.5 37.3 46.8 45.8 56.0 5.3 9.6 10.0 12.9 41.9 48.2 51.5 50.2 7.0 11.4 28.9 17.2 32.0 39.9 38.0 55.2

4.7 6.8 9.9 6.3 11.5 8.4 9.5 15.4 5.4 7.0 9.7 7.8 11.2 9.7 10.9 11.4 5.3 5.4 10.2 10.0 11.0 18.0 20.1 17.7 3.1 10.1 10.5 14.7 24.9 21.6 23.9 31.8 7.8 10.6 14.6 22.6 20.4 24.5 23.6 30.4 3.9 4.8 8.4 8.7 15.8 18.0 17.2 26.0 5.9 6.7 9.4 7.3 9.6 13.8 15.3 24.5

11.3 12.8 18.5 13.9 28.6 20.4 23.8 43.5 8.6 13.5 21.3 12.8 28.2 22.6 26.1 36.3 9.6 9.6 17.6 22.5 23.5 35.8 40.0 39.2 12.1 20.6 24.5 35.3 48.0 46.5 51.0 56.8 12.7 22.4 34.9 43.3 40.7 50.2 49.7 58.7 8.2 12.7 14.4 17.6 40.9 46.9 52.3 52.0 12.7 14.2 26.0 17.9 30.4 39.8 40.1 52.8

13.5 16.5 30.2 27.1 40.8 45.2 46.7 62.3 14.4 12.9 29.0 25.4 42.4 47.1 50.8 60.2 11.2 14.1 19.4 26.4 37.1 52.8 59.0 58.1 9.7 15.0 26.4 33.1 41.0 49.7 48.0 63.4 13.0 16.9 25.4 34.1 46.0 53.4 46.7 63.8 11.5 14.6 22.0 30.5 40.8 53.2 52.9 66.9 11.2 19.8 29.6 28.2 39.3 55.8 48.4 70.1

14.0 24.1 30.7 35.0 37.4 43.8 44.4 45.0 20.1 25.2 30.8 31.6 42.7 44.7 49.3 51.4 14.0 21.2 30.9 36.6 38.7 44.5 47.2 48.0 15.0 24.0 35.5 38 40.7 45.5 50.5 53.3 13.7 24.3 29.9 32.5 34.9 45.8 47.7 49.2 16.4 21.7 31.8 32.9 39.5 44.6 47.9 48.9 12.7 25.0 2.09 34.3 38.0 42.8 47.5 50.7

14.4 16.8 23.8 19.9 30.5 36.0 39.6 25.0 19.8 23.9 25.9 30.2 35.2 38.5 36.2 33.0 13.9 15.8 17.6 18.1 27.4 28.0 31.6 30.2 14.8 19.4 24.8 23.0 27.7 40.8 43.0 37.2 17.9 16.5 19.3 20.5 28.6 29.5 33.3 30.0 22.6 23.3 17.3 20 23.3 29 33 30 15.9 21.2 18.0 20.3 22.1 19.2 21.3 24.0

65.7 57.0 46.7 49.5 44.1 44.8 43.2 42.2 59.0 55.9 50.0 49.4 43.8 43.2 44.6 45.3 62.7 55.3 47.7 39.5 42.6 39.4 39.6 40.2 68.0 59.0 46.9 46.4 41.9 41.9 39.4 36.7 65.5 56.4 52.0 48.3 43.8 41.8 40.6 38.7 65.8 58.7 49 47.4 45.4 41.8 40.3 35.2 66 54 50.4 46.6 44.3 41.4 38.5 35.6

63 48.6 33.5 32 25 25 25 25 52.6 47.8 37 35 25 25 25 25 61.4 49.1 37.1 25 25 25 25 25 64 52.3 32.3 30.2 25 25 25 25 64.2 50.1 42.5 37 26.2 25 25 25 60.7 51.5 35.8 32 26.4 25 25 25 65.3 45.1 38.9 30.5 25 25 25 25

2.4 3.4 11.7 1.7 9.9 6.9 7.1 10.2 4.9 6.2 6.3 4.9 10.1 11.2 8.3 2.6 10.1 10.9 11.6 18.4 13.4 19.1 21.0 15.9 1.0 2.7 7.2 6.6 12.6 11.1 10.3 19.9 3.8 5.9 6.5 9.8 8.9 9.8 10 15.2 1 4 6.4 7.3 6.4 12 12.8 25.1 5.6 6.4 8.4 7.1 9.4 14.2 14.7 24.4

95.0 94.3 89.9 94.9 88.7 91.7 87.7 84.6 94.2 93.1 91.8 93.7 88.8 89.5 89.4 89.6 91.8 91.5 90.1 86.1 88.2 83.1 83.8 83.6 95.6 93.3 90.8 88.4 82.7 83.5 80.0 77.7 94.1 91.7 88.5 85.2 86.2 83.0 80.7 78.7 95.9 94.2 92.8 92 86.8 82.9 80.5 76.4 93.5 92.9 90 92.1 88.5 84.1 81.5 76.4

94.9 94.6 94.3 93.8 95.1 93.7 93.2 93.8 96.4 92.6 95.2 94.8 96.5 93.5 93.1 92.1 96.7 95.7 94.9 96.7 95.9 92.6 94.6 95.4 95.3 94.0 96.1 93.3 92.8 92.6 92.0 91.8 94.4 92.4 93.2 91.3 93.8 93.8 93.5 94.0 95.0 94.9 93.9 92.7 91.6 94.4 93.2 93.9 96.4 96.0 91.6 95.4 94.5 93.3 94.2 95.4

Grey

White

Red

Green

Blue

Yellow

functions from size measurements of surface structures. Specifically, wavelength sizes lower than 0.1 mm are associated with Du, from 0.1 to 0.3 mm with Wa, from 0.3 to 1.0 mm with Wb, from 1.0 to 3.0 mm with Wc, from 3.0 to 10.0 mm with Wd, and from 10 to 30 mm with We [37]. To measure the CIELAB colorimetric coordinates of the samples, we used a Gretag Macbeth Color-Eye 7000A spectrophotometer [38]. The coordinates were calculated for the CIE 1964 standard colorimetric observer and CIE D65 illuminant. Table 1 shows the CIELAB coordinates, different wave-scan parameters, and specular gloss at 60°, for each sample. As mentioned above, three achromatic (black, grey and white) plus four chromatic colors (red, green, blue, yellow) were used as base coats. Each base coat was made at 8 levels, from low to high degree of orange peel, providing a total of 56 samples. In Table 1 it is

different orange-peel levels on the panels. Other application parameters such as viscosity and the spraying distance are important in preparing orange-peel scales. This resulted in eight orange peel levels, from low to high degree, separately for each of the seven scales, providing a total of 56 painted samples. Maximum effort was made to ensure the same level of orange peel in each paint scale. 2.2. Instrumental measurements The BYK Gadner dual wave-scan instrument was used to measure surface structures, and the values of parameters Du (dullness), Wa, Wb, Wc, Wd, and We were recorded for each painted panel. These parameters are determined by the instrument using mathematical filter 150

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noteworthy that the other geometric attributes namely DOI and specular gloss have, as far as possible, been kept constant. 2.3. Visual assessments Visual assessments were performed in a dark room using a VeriVide CAC 120 light cabinet with a light source simulating D65. The illuminance at the centre of the floor of the cabinet was 1070 lx. Observers were positioned at a distance of 45–50 cm from the surface of the samples and the viewing direction was about 60° with respect to the perpendicular to the samples. A panel of 28 observers (16 males and 12 females), with normal color vision screened by the Ishihara test for color blindness, participated in the visual assessments. When making the visual assessments, observers were required to wear cotton gloves to avoid marring the samples. Visual assessments were conducted without time limitations, and the time for each assessment session was around 30–45 min. A total of 1372 visual assessments (28 observers x 7 scales x 7 color pairs in each scale) were performed in the current experiment, discounting the repeated assessments made to estimate observers’ variability. Previous researchers have stated that human-perception tasks quantifying the differences in any visual attribute are basically zero balancing operations, and the easiest differences that can be discerned by the visual system are lightness differences [7,39–43]. Therefore, for our current experiment, we used a common lightness scale, produced by us and composed by eight 10 × 20 cm² samples (same size as the test samples) made of grey matte polyester fabrics [44]. This lightness scale is analogous to the 9-steps ‘Grey Scales for Color Change’ manufactured by the American Association of Textile Chemists and Colorists (AATCC) or the Society of Dyers and Colourists (SDC) which are frequently used in fastness tests and other applications. Table 2 shows the CIELAB coordinates of the eight samples in our scale for the CIE D65 illuminant and the CIE 1964 standard colorimetric observer. With sample 1 used as the standard, the last two columns in Table 2 show the CIELAB color differences (ΔE*ab,10) and lightness differences (ΔL*10) for the 7 color pairs in our lightness scale. Table 2 indicates that L*10 increases from sample 1 to 8, while their a*10 and b*10 coordinates remain almost constant. The common lightness scale was employed to evaluate differences in orange-peel appearance had lightness differences (ΔL*10) in the range 1.6–13.1 CIELAB units. There is a nonlinear relationship between the lightness scale numbers and the actual lightness differences as shown in Fig.1 and Eq. (1). Although this lightness scale can also be defined in terms of other CIE recommended color-difference equations, regarding the range of difference values in our experiment, the CIELAB color-difference equation (ΔE*ab,10) was preferred. ΔE*ab,10 = 0.1073(LS)² + 0.8359(LS) - 0.6873

Fig. 1. Color differences (ΔE*ab,10) against Common lightness scale numbers (LS). The model fitted in Eq. 1 with different performance measurements (R2, STRESS, CV and γ) are also indicated.

compare each sample in any paint scale with the selected standard of that same scale, and quantify its difference in terms of lightness differences shown by the prepared lightness scale (Table 2). For evaluating the correlation between visually assessed differences and differences in various instrumental parameters, four statistical parameters, namely, coefficient of determination (R²), standard residual sum of squares (STRESS) [45,46], coefficient of variation (CV) [47], and gamma (γ) were utilised [47,48]. For example, the values of these statistical parameters are shown in Fig. 1, indicating a very good agreement between the lightness differences measured (Table 2) and the results provided by Eq. (1) [49]. The reason for using more than one statistical parameter in our analyses is that, as long as they give consistent results, the conclusions drawn will be accurate and precise.

3. Results and discussion 3.1. Intra- and inter-observer variability The robustness of the visual assessments can be evaluated in terms of intra-observer and inter-observer variability. Seven samples were presented for a second assessment by each observer that participated in the experiment in order to evaluate intra-observer variability. Table 3 shows values of different statistical parameters measuring the average intra-observer and inter-observer variability for all our observers. The lowest variability corresponds to zero values for all these parameters, except γ, which has a value of 1. For example, STRESS values are always in the range 0–100, a value equal to zero indicating zero intra- or interobserver variability [15]. In comparison with STRESS values reported in previous visual assessments experiments [50–54], the values shown in Table 3 (15.2 and 19.6 units for intra- and inter-observer variability, respectively) indicate that our visual experiment register lower average intra- and inter-observer variability than in previous works, which are attributed to the use of a common lightness scale procedure for visual assessments of all differences.

(1)

Regarding the visual task performed by the observers, the first step was to select the sample with the lowest orange peel in each base-coat paint scale as the standard for that scale. In practice, the best standard orange peel sample is the lowest orange-peel sample that any individual manufacturer is capable of producing. Next, the second step was to Table 2 Specifications of samples in the prepared lightness scale for the CIE D65 illuminant and the CIE 1964 standard observer. Samples

L*10

a*10

b*10

ΔE*ab,10

ΔL*10

1 (Standard) 2 3 4 5 6 7 8

37.79 39.41 40.57 42.51 44.17 45.13 48.22 50.92

−2.97 −2.77 −2.94 −3.21 −3.07 −3.15 −3.30 −3.11

−3.93 3.93 3.77 4.00 3.92 3.58 3.95 3.36

0 1.64 2.79 4.73 6.39 7.36 10.44 13.14

0 1.62 2.78 4.72 6.38 7.34 10.43 13.13

Table 3 Average intra- and inter-observer variability for visual assessments of orange peel.

151

Statistical parameters

Average intra-observer variability

Average inter-observer variability

STRESS CV γ

15.2 15.7 1.19

19.6 19.7 1.25

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Table 4 Average visual difference ΔV (CIELAB units, 28 observers) of orange peel for each sample in the 7 scales. Black

Grey

White

Red

Green

Blue

Yellow

Sample

ΔV

Sample

ΔV

Sample

ΔV

Sample

ΔV

Sample

ΔV

Sample

ΔV

Sample

ΔV

OPS2 OPS3 OPS4 OPS5 OPS6 OPS7 OPS8

4.54 6.11 8.1 9.98 10.74 11.70 12.43

OPN2 OPN3 OPN4 OPN5 OPN6 OPN7 OPN8

4.68 7.08 7.4 7.66 8.92 10.31 11.9

OPW2 OPW3 OPW4 OPW5 OPW6 OPW7 OPW8

3.09 5.07 7.36 8.88 9.51 10.06 10.43

OPR2 OPR3 OPR4 OPR5 OPR6 OPR7 OPR8

2.53 5.49 7.65 9.0 10.32 11.19 11.91

OPG2 OPG3 OPG4 OPG5 OPG6 OPG7 OPG8

2.97 4.48 7.43 9.59 10.20 10.96 11.47

OPB2 OPB3 OPB4 OPB5 OPB6 OPB7 OPB8

3.36 5.13 6.26 8.88 10.01 10.97 11.93

OPY2 OPY3 OPY4 OPY5 OPY6 OPY7 OPY8

2.86 4.06 6.51 8.23 9.67 10.92 11.84

3.2. Visual and instrumental measurements

Table 5 Results of the test of multicollinearity for wave-scan parameters.

The visual difference of each sample in Table 1 for the orange peel attribute compared to the standard sample (i.e. samples ended with “1” in Table 1), in terms of lightness scale was converted to the corresponding color difference value (ΔV). For each sample, the average value of color difference obtained for all observers was calculated. The calculated ΔV values from the standard sample for each orange peel scale are illustrated in Table 4.

3.3. Derivation and performance of different orange-peel indices

BYK wave-scan parameters

Tolerance

VIF

ΔDu ΔWa ΔWb ΔWc ΔWd ΔWe

0.107 0.026 0.017 0.024 0.037 0.165

9.367 38.854 58.181 41.042 26.708 6.054

Kennard, who devised ridge regression, proposed an estimation procedure based on adding a small positive quantity (k), known as the ridge parameter, to the diagonal elements of the information matrix (X′X) [56,59,60]. In ordinary least square (OLS) regression, the coefficients are estimated by using the formula BOLS= (X′X)−1X′Y, while the ordinary ridge-regression method (ORR) proceeds by adding a small value, k, to the diagonal elements of the information matrix [i.e. BORR= ((X′X) + kI)−1X′Y; where I is the identity matrix]. When k is considered in the ORR method, the variation in the parameters estimated proves lower than when using the OLS method [56,59,60]. Among the methods available to determine the appropriate value for k, an optimal iterative method proposed by Hoerl et al. [61] was used in the current paper. The determination of coefficients by the ridge-regression method and optimal k value from Hoerl et al. method can be made using the NCSS software [56]. Specifically, we have used the NCSS 2007 software to statistically analyse our data. This software has a variety of outputs in ridge regression, one of which being the estimation of standardized regression coefficients, when each independent variable is first standardized by subtracting the mean and dividing by the standard deviation. Using ridge regression between visual assessments of orange peel and BYK wave-scan instrumental parameters, we can calculate the coefficients in Eq. (2). These coefficients are illustrated for OPIi in Table 6. In the first model (OPI1), all independent variables in Eq. (2) were considered in the ridge regression and the rest of the indices resulted from the combination of the independent variables in terms of choosing the parameter with the largest coefficient value than the other parameters in the respective standardized coefficients. The extent of the power of these indices to predict visual orange peel from instrumental parameters exemplified by statistical parameters (STRESS, CV and R2 values) for OPIi coefficients are given in Table 6. Some BYK instruments provide values for other indices such as CF (overall quality factor certified by the Ford automotive company) and OP (Orange Peel, denoting levelling), in addition to the LW and SW indices [37]. Table 7 shows the performance of these four indices with respect to our visual data using STRESS, CV, and R2. The ΔLW, ΔSW, ΔCF, and ΔOP in Table 7 represent the differences between values measured for each sample and the standard sample (the one with minimum orange peel in each scale). Low R² values (0.66 and 0.65) for ΔCF and ΔSW in Table 7 suggest that CF and SW are not appropriate indices for orange peel. This is not surprising because CF is a combined overall index related to orange

Model estimation methods such as regression can be used [23]. The interpretation and use of a multiple regression model often depends explicitly or implicitly on estimates of the individual regression coefficients. Regression models are used to identify the relative effects of dependent variables, prediction and selection of right sets of variables for a model, etc. [55]. To derive an Orange-Peel Index (OPI) predicting the amount of visual orange-peel texture in terms of instrumental measurements, the general additive format in Eq. (2) was assumed: OPIi = ui ΔDu + ai ΔWa + bi ΔWb + ci ΔWc + di ΔWd + ei ΔWe + fi (i = 1 to n) (2) Where Δ’s denote the differences between each parameter measured by the BYK instrument for the test sample and the standard sample (i.e. samples ended with “1” in Table 1, which consistently had the minimum orange-peel); ui, ai, bi, ci, di and ei are coefficients; fi is a constant; and i denotes one of the n models proposed in this subsection. Analysis of variance (ANOVA) was used to study the variance of the parameters [56,57], and p-values showed no significant difference in the visual assessments of orange peel when considering the seven orange-peel scales [i.e. 3 achromatic (black, grey, and white) and 4 chromatic (red, green, blue and yellow)]. To develop an Orange-Peel Index, we analysed the results of visual assessments and the wave-scan results, and used ridge-regression modelling because multicollinearity was found between wave-scan parameters. Multicollinearity, or collinearity, is the existence of nearlinear relationships among the independent variables [56]. In some cases, independent variables have multicollinearity, and deduction based on a regression model can be misleading. The existence of multicollinearity may hamper the estimation and interpretation of results but it does not invalidate the regression analysis [55]. SPSS 22 software was used to statistically analyse the variance inflation factor (VIF) and tolerance for the data in this study. The variance inflation factor (VIF) is the reciprocal of 1-R2x (named tolerance), where R2x is the R2 found when a variable is regressed on the remaining independent variables [56]. For the diagnosis of multicollinearity between independent variables of various scales, the tolerances and VIFs were calculated (Table 5), leading to the conclusion that multicollinearity exists because VIFs of all independent variables are greater than 2.5 [56,58]. The ridge-regression method is one of the most widely used techniques to address the problem of multicollinearity [59]. Hoerl & 152

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Table 6 The six orange-peel indices (OPIi) developed by using ridge regression, together with their performances for visual assessments of orange peel, using STRESS, CV, and R2. Indices (OPIi)

Coefficients

Independent Variables

STRESS

CV

R2

OPI1 OPI2 OPI3 OPI4 OPI5 OPI6

u1 = 0.03; a1 = 0.024; b1 = 0.0271; c1 = 0.0396; d1 = 0.0726; e1 = 0.0608; f1 = 3.769 a2 = 0.0298; b2 = 0.0289; c2 = 0.0412; d2 = 0.0744; e2 = 0.0606; f2 = 3.792 b3 = 0.0338; c3 = 0.0432; d3 = 0.0773; e3 = 0.0626; f3 = 3.821 c4 = 0.0518; d4 = 0.089; e4 = 0.0654; f4 = 3.979 c5 = 0.073; d5 = 0.1375; f5 = 2.902 d6 = 0.236; f6 = 2.619

ΔDu;ΔWa;ΔWb;ΔWc;ΔWd;ΔWe ΔWa;ΔWb;ΔWc;ΔWd;ΔWe ΔWb;ΔWc;ΔWd;ΔWe ΔWc;ΔWd;ΔWe ΔWc;ΔWd ΔWd

10.6 10.3 9.7 8.8 10.8 10.5

11.0 10.6 9.9 9.0 11.3 10.8

0.84 0.85 0.86 0.87 0.86 0.85

Table 7 Performance of 4 orange-peel indices given by the BYK instrument. Orange-peel indices

STRESS

CV

R2

ΔCF ΔOP ΔLW ΔSW

21.0 18.3 17.3 32.2

22.0 19.1 19.7 36.4

0.66 0.69 0.88 0.65

Table 9 Ranking of performance of different orange-peel indices for the ACT standard panels.

peel, DOI (distinction of image) and gloss, certified by the Ford automotive company [37]. Additionally, the STRESS values of 21.0 and 32.2 found for ΔCF and ΔSW, respectively, are above mean STRESS values found in our experiment for intra- and inter-observer variability (15.2 and 19.6, respectively; see Table 3). Therefore, both ΔCF and ΔSW indices were omitted for further investigation. On the other hand, the six instrumentally based indices derived in this paper (Table 6) provided STRESS values in the range 8.8–10.8, clearly below the intra- and interobserver variability in Table 3, and also below STRESS values given by the OP and LW indices in Table 7.

Indices (OPIi)

Independent variables

STRESS

CV

R2

OPI6 OPI5 OPI4 OPI2 OPI3 OPI1 ΔOP ΔLW

ΔWd ΔWc;ΔWd ΔWc;ΔWd;ΔWe ΔWa;ΔWb;ΔWc;ΔWd;ΔWe ΔWb;ΔWc;ΔWd;ΔWe ΔDu;ΔWa;ΔWb;ΔWc;ΔWd;ΔWe ΔOP ΔLW

6.3 8.6 10.0 11.4 11.9 12.4 15.5 19.1

6.9 9.6 10.9 12.5 12.9 13.6 18.3 25.9

0.98 0.96 0.94 0.92 0.92 0.91 0.92 0.92

study is in full agreement with our previous statement that a common lightness scale alleviates the process of perception in technical visual assessments. Since it provides effortless quantification of visual differences in geometric attributes with enhanced perceptibility of observers. The overall conclusions which can be drawn from the present study are as follows:

3.4. Performance of orange-peel indices using the ACT standard panels

1) ANOVA analyses indicated that chromaticity had no significant effects on orange peel. 2) The CF index, certified by the Ford company as a combined quality indicator of orange peel, DOI, and gloss, was not a good predictor of just visual orange peel, because R2 =0.66 and a STRESS value of 21.0 was clearly above average values of intra- and inter-observer variability in our visual experiment. 3) Similarly, the SW index, with R2 = 0.65 and STRESS = 32.2 for our visual results, was not a good index for orange peel. 4) The LW index achieved R2 = 0.92 and STRESS=19.1 for our visual results, and therefore it can be considered a better index than SW, but the STRESS value was still somewhat high. 5) The OP index with R2 = 0.92 and STRESS = 15.5 was the best predictor of levelling, but its performance for our visual results could be improved using the orange-peel indices derived in the present study. 6) The six indices of orange peel derived in the present study (Table 6) are good to excellent indicators of orange peel for our visual experiment, achieving values of R2 in the range 0.91-0.98 and STRESS

Table 8 shows the results of measurements made by a glossmeter and using a BYK wave-scan instrument for the 10 ACT standard panels. As an additional validity test, the six indices derived by us (Table 6) plus the OP and LW indices in BYK instruments were regressed against the visual values of the ACT standard panels [25], and the results are shown in Table 9. Finally, Fig. 2 shows three plots comparing our best-derived index of orange peel (i.e. OPI6) plus the OP and LW indices against the values of the ACT standard panels, with the corresponding linear fits. Fig. 2 shows that the OP and LW indices did not perform well as indicators of orange peel, but our OPI6 index achieves very satisfactory results as an orange-peel index [R2 = 0.98; CV = 6.9; STRESS = 6.3]. 4. Conclusions The goal of the present research was to achieve a single-number instrumentally based index for orange peel in good agreement with mean visual assessments. The initial conclusion reached in the present Table 8 Wave-scan measured parameters for each of the ACT standard panels. Panels

Du

Wa

Wb

Wc

Wd

We

CF

OP

LW

SW

DOI

Specular gloss(60º)

ACT ACT ACT ACT ACT ACT ACT ACT ACT ACT

36.7 26.2 19.7 10.7 6.9 4.4 5.4 1.2 1.0 1.0

32.6 25.0 15.0 22.3 16.2 13.3 12.3 10.5 7.3 5.1

58.0 63.9 32.4 34.4 18.0 22.4 20.6 28.6 23.3 15.1

72.5 75.3 51.5 41.0 24.9 21.1 14.8 15.1 9.6 8.9

58.6 51.1 43.5 37.4 30.4 29.2 23.7 11.5 9.9 7.7

45.6 25.2 24.5 13.5 14.2 11.2 9.4 9.0 6.3 11.3

27.9 33.3 39.6 43.3 50.0 53.2 57.5 68.5 72.4 74.1

25.0 25.0 25.0 26.0 39.3 43.5 51.8 68.2 73.0 75.0

65.4 53.2 42.8 35.1 18.4 16.5 9.8 6.1 4.1 3.1

50.3 52.2 34.3 36.8 13.8 20.1 14.9 25.9 26.5 12.7

70.2 78.0 83.5 87.4 92.1 92.3 92.2 92.2 93.5 95.1

90.1 89.7 90.8 91.2 89.4 89.8 90.6 90.1 90.3 89.7

1 2 3 4 5 6 7 8 9 10

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Fig. 2. Plots of best derived index (OPI6) (a), plus the OP (b) and LW indices (c) for the ACT standard panels.

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Acknowledgements The authors wish to thank all the observers who agreed to participate in the visual assessments. We are also grateful to the support received from Gamma Thinner paint manufacturing company, the Centre of Excellence for Color Science and Technology (Tehran, Iran) and the research project FIS2016-80983-P (National Government of Spain and European Regional Development Fund).

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