Instrumentation system for objective evaluation of wrinkle appearance in fabrics using a standardized inspection booth

Abstract

The appliance industry requires a reliable method for wrinkle evaluation in textile materials. This method is necessary to assess the performance of new designs of tumble dryers. In this paper, we describe an objective evaluation system for wrinkle appearance grading based on the digital analysis of luminance images. The system is capable of evaluating wrinkles in real garments using the legacy inspection booth designed for subjective evaluation. Therefore, the results from the objective evaluation of wrinkles can be compared to the historical records. The dependence of luminance on the three-dimensional characteristics of the wrinkles is modeled and discussed. Based on this analysis, we propose a method supported by two descriptors closely related with the wrinkle characteristics as appreciated by trained evaluators. The design incorporates filtering algorithms that eliminate the influence of undulations and the non-uniform illumination. The objective wrinkle evaluation showed high correlation with human experts and robust performance, as demonstrated by the repeatability and reproducibility study.

Keywords

wrinkle image processing objective evaluation

Every engineering effort oriented to the optimization of a process involves the acquisition of objective, quantitative, and accurate information about performance in order to assess the improvement. In recent years, innovative functions have been incorporated to laundry dryers in order to eliminate wrinkles or minimize their generation in clothes. The efficacy of new designs is usually evaluated by a subjective test where the wrinkle degree of a batch of shirts is evaluated before and after being smoothed by a prototype dryer. This information is used as feedback for the process of dryer design optimization. The subjective test is based on the Method 124, “Appearance of fabrics after repeated home laundering”, published by the American Association of Textile Chemists and Colorists (AATCC).¹ This method was designed to evaluate the smoothness appearance (SA) of flat fabric specimens. The SA is defined as the visual impression of planarity of a specimen, quantified by comparison with a set of reference standards. These reference standards are six fabric wrinkle replicas commercialized by the AATCC. The replicas, shown in Figure 1, are three-dimensional (3D) reproductions of fabric wrinkles with nominal SA grades from 1 to 5. According to this method, three trained observers should rate each specimen using the inspection booth shown in Figure 2. The overhead fluorescent lamps should be the only light source for the viewing board. All other lights in the room should be turned off. The observer stands directly in front of the specimen, 120 cm away from the board. The test specimen is mounted on the viewing board, as illustrated in Figure 2. The most similar 3D plastic replicas are placed on each side of the test specimen to facilitate comparative rating. The wrinkle grade is the quantitative value of SA obtained by comparison with the replicas. The observer assigns the numerical grade of the replica that most nearly matches the SA of the test specimen, or assigns a grade midway between two standards if the appearance of the test specimen warrants it. Frequently, this evaluation must be repeated due the low correlation between the grades assigned by the evaluators. As a result, the test is a potentially unreliable indicator of the performance of the appliance. To overcome these limitations, a major appliance manufacturer demanded an objective method, capable of repeatable and reproducible results, but comparable to the current standard of the industry, the AATCC method no. 124. The objective method must adhere to the following restrictions, as defined by the final user. Firstly, the objective evaluation must be performed using the current inspection booth and commercially available shirts on regular cloth hangers. In addition, the evaluation of SA must show high correlation with the human evaluators using the legacy method. Finally, the objective system must pass the repeatability and reproducibility test, according to the Six Sigma strategy adopted by the final user for all testing procedures.
Figure 1.
Smoothness appearance replicas.

Figure 2.
Schematic drawing of the inspection booth.

The study of objective methods for wrinkle evaluation in fabrics has been an active research field, given the disadvantages of the subjective evaluation. Objective methods based on two-dimensional (2D) images^2–5 and 3D topography evaluation has been previously proposed. The 3D information from fabric is usually extracted by laser line projection^6–12 or different stereo techniques.^13–15 These systems are usually tested using wrinkle replicas or fabric samples of simple geometry, instead of actual clothes. The use of the former is of particular importance in the home appliances industry, since sleeves of shirts can undergo tangling and wrinkle generation in washing machines and tumble dryers. In most reported experiments, the samples lie on a horizontal table. Therefore, they are not subjected to gravity-induced smoothing and curtain-like undulations that are present while using the current inspection booth. Moreover, while the clothes are supported on a horizontal table, they are usually smoothed by hand in order to remove undulations. This hand-smoothing is hardly repeatable or reproducible. Furthermore, the human perception of wrinkles is no longer accounted for when using a surface topography scanning technique. It will be shown later that the visibility of the wrinkles depends strongly on their orientation when the samples are evaluated as described by method 124. As a result, the evaluators consistently underrate vertical wrinkles. Moreover, some 3D features, such as smooth undulations, are not associated with wrinkles and the evaluators ignore them. In addition, the wrinkle sharpness^16,17 strongly influences the perception of the evaluators. The combined effects of these factors are not considered by the previously reported systems. Therefore, agreement with the evaluation performed using the method 124 cannot be assured.

We propose a system for objective evaluation of fabric wrinkle appearance that is compliant with the geometry and testing conditions of the legacy method, but designed to overcome the uncertainty associated with the subjective evaluation. The system is composed of a digital camera controlled by a computer, and the software application that processes the images in order to assign an objective grade. The objective system operates using the standard inspection booth, regular shirts, and cloth hangers defined by the legacy method. Consequently, the results can be compared to the historical records. Moreover, the objective evaluation is performed based on the same visual information used by the trained evaluators.

System setup

The inspection booth used by the objective system is shown in Figure 2. This booth is similar to that referenced by AATCC method No. 124. It was originally conceived to perform evaluations by trained evaluators, and the geometry must be respected by the objective system in order to maintain compliance with the legacy procedure. A plywood board with a slight inclination serves as support for hanging the specimen. The specimen is illuminated exclusively by two 8-ft (244-cm) fluorescent lamps installed on a standard white enamel reflector, without baffle or glass. The board is painted in black, as well as all exposed surfaces of the room. The specimens are commercially available white cotton, long sleeve shirts, displayed on regular cloth hangers. The shirts have a pocket at the front. The front and back of the shirts are both evaluated. As a result of the geometry of the shirt and the cloth hanger, curtain-like undulations are usually present. The use of devices to stretch or tension the shirts is not allowed since that manipulation would affect the appearance of wrinkles. The only modification introduced to the legacy method was the replacement of the evaluator by the camera, but maintaining his/her location, as shown in Figure 3.
Figure 3.
Location of the camera.

A charge-coupled device (CCD) camera to acquire images of the specimen was used. It is located at 120 cm from the board. The line of sight is horizontal and centered to the specimen. The camera incorporates a 1/3” CCD with a resolution of 1024 by 768 pixels. Shirts are evaluated defining regions of interest (ROIs) of 350 by 350 pixels that correspond to an effective area of 15 by 15 cm. Three regions are measured at the front and four at the back for shirts with a front pocket, as shown in Figure 4. The area where the pocket is located is not evaluated, because the SA is greatly influenced by the conformation of the pocket. An IEEE-1394a interface is used to communicate the camera with the computer. The software application developed in language Visual C# controls the camera and processes the images in real time. The exposure time is fixed to a multiple of 1/120 s in order to avoid flicker from the oscillation of the fluorescent lamps. The camera is configured to operate with a data depth of 12 bits and linear response (Gamma = 1).
Figure 4.
The shirts are evaluated averaging three regions of interest for the front and four for the back.

Principle of measurement

When the samples with wrinkles are observed by the naked eye, it is possible to identify dark and bright areas, as shown by the images from the AATCC replicas shown in Figure 5. The dark areas are not generated by the interception of light. Therefore, they are not strictly considered as shadows. The presence of dark and bright areas can be explained by the local values of illuminance and their relationship with the topography of the fabric. The illuminance depends on the relative orientation of the vector normal to the surface with respect to the position of the light source. On surfaces that present diffuse reflection, such as these fabrics, the brightness is independent from the direction of observation and depends mostly on illuminance.¹⁸
Figure 5.
Filtered images of the six fabric wrinkle replicas made by the American Association of Textile Chemists and Colorists.

The geometric description of the setup is shown in Figure 6. Only one lamp is shown in order to simplify the schema. Nevertheless, the analysis can be extended by superposition to the two parallel lamps mounted on the luminaire. On this schema, the x–y plane is parallel to the board where the specimen rests. A segment of the surface of the specimen at the position (x, y) is illuminated by the extended light source of length l. Here, d is the vector from the point (x, y) at the surface of the sample to the position p_l at the surface of the lamp, $\overset{\land}{n}$ is the unit vector normal to the surfaces of the sample at (x, y), α is the angle between the vectors d and $\overset{\land}{n}$ , and β is the angle between $\overset{\land}{n}$ and the optical axis of the camera. According to this geometry, the illuminance E_v measured at (x, y) depends on the luminous intensity of the light source, the distance between the surface and the source, and the angle α. The illuminance E_v is the result of the integration of the contributions along the whole length of the source of light:
${dE}_{v} (x, y) = \frac{{dI}_{v} (p_{l})}{‖ d (x, y, p_{l}) ‖^{2}} \cos (α (x, y, p_{l}))$
(1)
Here, E_v is the illuminance measured at a segment of the surface of the fabric at position (x, y) and dI_v is the luminous intensity of the lamp at position p_l. When the light from the lamps impinges upon the surface of the fabric, the resulting reflections are mostly diffuse with a small portion of specular reflection. Given the nature of fabrics, their reflection characteristics are close to that of a Lambertian surface, and appear to be almost equally bright from all directions. Therefore, the luminance of the fabric measured from the location of the camera depends mostly on the illuminance E_v and the luminance factor ρ:¹⁹
$dL (x, y) = \frac{{dE}_{v} (x, y) \cdot ρ}{π}$
(2)
Here, L is the luminance of the fabric at position (x, y), E_v is the illuminance measured at location (x, y) of the surface, and ρ is the luminance factor of the fabric at the direction of the camera. The luminance factor ρ depends on the reflectivity of the material, given by the color and appearance of the fabrics. The constant value of ρ implies that the color of the fabric is uniform. These equations predict that the luminance of the fabric increases as the angle α decreases. Moreover, luminance depends on the distance between the sample and the lamp, resulting in an additional dependence on the y position. We found that the dependence of luminance factor ρ on angle β is measurable in fabric samples, but it is small enough to approximate ρ as a constant for this specific geometry.
Figure 6.
Geometrical description of the setup.

Considering the setup of the Figures 2 and 3, the value of α is 52.4° when measured at the center of a flat sample. The length of d calculated from this position to the center of the lamp is approximately 100 cm. We measured the average value of E_v as 211 lx for the inspection booth implemented at our laboratory. Using a calibrated image photometer, we measure the average value of luminance L as 56.5 cd/m² for samples of white cotton fabric. Therefore, the estimated valued of ρ is 0.84.

The relative position of the lamps limits the value of slope at the surface of the fabric to the interval [–35°, 35°], in order to avoid shadows. We found that the luminance L depends mostly on the component of the slope in the direction of y when using the inspection booth. In order to illustrate this behavior, we model the vector $\overset{\land}{n}$ as the result of two consecutives rotations of a unit vector that is originally parallel to the z-axis. The first rotation is executed around the x-axis by an angle γ. The resulting vector lies on the plane y–z. The second rotation is executed around the y-axis by an angle θ. The resulting vector is the vector $\overset{\land}{n}$ . The predicted value of illuminance E_v is shown in Figure 7 as a function of angles γ and θ, considering the geometry of the described setup and the use of two lamps in the luminaire. The dependence of E_v on γ is approximately linear for the interval [–35°, 35°] with an average slope of 2.7%/1°. The dependence on θ is much smaller, with a slope of –0.015%/1°. Therefore, Equations (1) and (2) predict that horizontal wrinkles will be evident, while vertical wrinkles are hardly visible when using the inspection booth shown in Figure 2. An important consequence from this fact is that wrinkle appearance depends on relative wrinkle orientation. By example, the two creases of the specimen shown in Figure 6 could be invisible if it is rotated 90° around the z-axis. As a result, the evaluators consistently underrate vertical wrinkles. The current setup provides information about SA, rather than surface topography.
Figure 7.
Illuminance E_v as a function of angles γ and θ.

The gray level value of each pixel from the camera is proportional to the luminance value predicted by Equation (3):
$g (m, n) = \frac{G_{2}}{16} \cdot ⌊ G_{1} \cdot k \cdot \frac{E_{v} (x, y) \cdot ρ}{π} ⌋$
(3)
Here, g is the gray level value of the pixel at the position (m, n) of the image; G₁ is the gain of the camera; G₂ is the complementary fine gain factor applied by the computer; and k is a factor that depends on the sensitivity of the CCD, the exposure time, the aperture of the lens, and the analog to digital converter. The factor 1/16 is used to adjust the 12-bit grayscale interval from the camera to the commonly used 8-bit interval. The relationship between the position (m, n) at the image and the spatial location (x, y) at the sample is not shown for simplicity. The luminance of the sample described by Equations (1) and (2) depends mostly on the component y of the slope of the sample. Therefore, the gray level value of each pixel is approximately proportional to the vertical component of the slope at the surface of the sample. We implemented an automatic gain control (AGC) algorithm in order to maintain the proportionality factor between the gray level and slope as a constant for all measurements. The objective of the AGC algorithm is to keep the average gray value of all images equal to 127, the middle point of the grayscale interval. The average slope of the sample is parallel to the support board. Therefore, by implementing the AGC algorithm we obtain pixels with a gray value of 127 when a region of the sample is parallel to the board (γ ≈ 0). Given the current dependence of E_v on γ, the expected relationship between the gray level value and the angle γ is approximately lineal with a slope of 3.43 units/1°. At this point, this statement is true only at the center of the image, because the illuminance also depends on the y position, but this issue is solved by the preprocessing and filtering algorithms described in the fourth section. The camera has a gain range of 0–25 dB with an increment resolution of approximately 0.0345 dB/step. The AGC algorithm adjusts the gain G₁ based on the acquisition of multiple images. After each acquisition, the error is calculated as the difference between the mean gray value of the image and the target value 127. The gain value G₁ is increased or decreased, depending on the calculated error value, and a new image is acquired. This procedure is repeated until the calculated error is smaller than 2% of the target value. Finally, the complementary digital fine gain G₂ is applied by the computer to the acquired image in order to compensate the small remaining error. The resulting image has a mean gain value of 127.

The AGC algorithm compensates for color differences of the samples, as well as the aging of the lamps. Color fabrics reflect only a portion of the incident light from the lamps, compared to white fabrics. As the camera is monochrome, this is observed as a lower value of ρ. The effect of the aging of the lamps is similar, diminishing the luminous intensity I_v. Equation (3) shows that changes in ρ and I_v can be compensated by G₁ and G₂. By example, Figure 8 shows the images of two swatches, one white and one blue. The total gain G₁ + G₂ applied by the AGC algorithm for the white swatch was 9.1 dB, while the gain necessary for the blue swatch was 12.7 dB. After the gain adjustment by the AGC algorithm, both images present an average gray value of 127, as shown by the histograms. By using the AGC algorithm, we estimate that the current objective system is insensitive to the color of the fabrics with a reflectivity as low as 20%. Currently, the AGC algorithm is applied to all measurements. Nevertheless, there is a possible variation to this technique. The gain factors G₁ and G₂ can be calculated using the replica SA-5 at the beginning of the session, and then used as constants for all measurements. This variation mimics the perception of the evaluators that underrate dark fabrics because the wrinkles are less visible. In this case, the relationship between grayscale value and angle γ is not longer constant.
Figure 8.
Images and histograms for two swatches of different colors.

Objective evaluation of wrinkle appearance

The objective system for wrinkle evaluation is based on the use of two quantitative descriptors of wrinkles. These descriptors are calculated from images of the AATCC replicas to establish the calibration scale. In order to evaluate a sample, their descriptors are calculated and the grade is determined using the calibration scale. This process involves the stages of image preprocessing, descriptor evaluation, system calibration, and sample evaluation.

Preprocessing and noise filtering

We implemented the preprocessing functions in order to minimize the noise influence and eliminate information that is not related to wrinkles from the luminance images. Figure 9 shows a typical raw image from a fabric sample. This image presents noise from the four main sources that we distinguish. The first noise source is intrinsic to the electronic nature of the camera. The second source of noise arises from the illumination function given by the dependence of the illuminance to the y position of the sample. This multiplicative noise is observed as a vertical luminance gradient, where the highest part of the sample (closer to the lamp) appears brighter than the lower one. The third source of noise is related to the soft undulations that are present when shirts are displayed using regular cloth hangers. These curtain-like undulations modify the local slope of the surface, and we treat them as additive noise. The last source of noise comes from the high resolution of the images, where the thread pattern of the fabrics is registered. We found that the preprocessing functions are of uppermost importance in terms of the reliability of the system, since the magnitude of multiplicative and additive noise on luminance images are comparable to that of the wrinkle information. The measurements are not repeatable if the information from illumination and undulations is not eliminated from the images prior to the grading.
Figure 9.
An example of the original image (matrix I₁).

We reduce the intrinsic additive noise of the camera by averaging eight consecutive frames, as the first step of preprocessing. This process allows us to achieve an effective value of signal-to-noise ratio (SNR) equal to 57.3dB. The image averaging is performed in real time, at a rate of 15 frames per second. The image averaging routine also incorporates the AGC algorithm functionality. When the image is transferred to the computer, it is stored and processed as a floating point matrix, in order to minimize quantization errors. The image of 12-bit depth is scaled by a constant factor of 1/16 in order to handle it as a regular grayscale interval of [0,255]. This image is stored as the matrix I₁.

The second preprocessing algorithm was designed to eliminate the vertical luminance gradient that is constant along the width of the sample. This luminance gradient is treated as multiplicative noise because it depends on the factor 1/‖d(x,y,p_l)‖² of Equation (1). In order to extract the illumination function from the image, we calculate the column vector V _mean as the average of all columns of the image:
$V_{mean} (m) = \frac{1}{N} \sum_{n = 0}^{N - 1} I_{1} (m, n)$
(4)
Here, V _mean is the column vector that results from the average of all columns of the image. The value of V _mean is dominated by the illumination function, since the wrinkle information average tends to zero. The illumination function is determined fitting a polynomial of order 2 to the V _mean vector. The multiplicative noise is eliminated from the image dividing by the local value of this illumination function. The result is scaled by the factor mean(I₁), in order to preserve the average gray value of the image:
$I_{2} (m, n) = \frac{I_{1} (m, n)}{a_{0} + a_{1} m + a_{2} m^{2}} \cdot mean (I_{1})$
(5)
Here, the matrix I₂ is the image obtained with the multiplicative noise filter; the matrix I₁ is the original image; (m,n) represents the row and column location at the matrix; a₀, a₁, and a₂ are the coefficients of the second-order polynomial of the illumination function; and mean(I₁) represents the average gray value of I₁. Figure 10 shows the image from the matrix I₂ calculated after the matrix I₁ from Figure 9. In addition, we calculate the difference matrix D₁₂ as (I₁ – I₂)·5 + 127 in order to show the information from the illumination function that is removed from I₁. The factor 5 is included to enhance the visibility of the differences, and the constant 127 is added to display D₁₂ as an image. This filter corrects the brightness of the higher and lower areas, as well as the strength of the wrinkles of I₁, as shown in Figure 10.
Figure 10.
Image from matrix I₂ after Figure 9, and the image of difference D₁₂.

The third preprocessing algorithm was implemented in order to eliminate the information of soft undulations. These undulations are present because the shirt is displayed using a regular cloth hanger. The undulations are mostly vertical because they are induced by gravity. The luminance information from the wrinkles is superimposed to the low-frequency information of the undulations. The filtering algorithm is similar to that used to filter multiplicative noise, but modified to filter additive noise. We determine the additive noise function from the image by fitting a polynomial of order 10 to each column. Then, the additive noise is eliminated by subtracting the additive noise function from each column:
$I_{3} (m, n) = I_{2} (m, n) - \sum_{r = 0}^{10} b_{r} (n) m^{r} + mean (I_{2})$
(6)
Here, the matrix I₃ is the resulting image from the additive noise filter, the matrix I₂ is the images previously obtained by the multiplicative noise filter, and the coefficients b_r(n) are the coefficients of the additive noise function calculated for column n. The mean value of I₂ must be added to preserve the average gray value of the image, because the first coefficient of the summation (r = 0) subtracts this value. Figure 11 shows the image from matrix I₃, calculated after the matrix I₂ of Figure 10. We calculate the difference matrix D₂₃ as (I₂ – I₃) + 127 in order to show the information from soft undulations that is eliminated by Equation (6). It can be observed that the matrix I₃ preserves the wrinkle information from I₂, but the information from soft undulations has been removed. We determined the order of the polynomial that represents the additive noise function analyzing the luminance distribution in wrinkle images. We found that the luminance histogram of samples without soft undulations (such as the AATCC wrinkle replicas) is symmetrical and resembles a normal distribution. When soft undulations are present, the distribution is asymmetrical and it is possible to find more than one local maximum, as shown in Figure 12. The additive noise filtering by a polynomial function of order 10 results in images with symmetrical and approximately normal distribution of luminance. This filter eliminates soft undulations and preserves the sharpness of the wrinkles on images of real shirts.
Figure 11.
Image from matrix I₃ after Figure 10, and the image of difference D₂₃.

Figure 12.
Histograms of matrixes I₁ and I₃, calculated from the images of Figures 9 and 11.

The last step of the image preprocessing is the elimination of high-frequency components derived from the texture and thread patterns of the fabric. This information must be filtered because the combination of CCD and amplification from the lens results in images that include details that cannot be observed by the naked eye from the distance defined by the legacy procedure. Moreover, the AATCC wrinkle replicas do not reproduce the fine thread pattern of fabrics. Therefore, this information should be eliminated before comparison. The high-frequency filtering is performed in the frequency domain implementing a low-pass Butterworth filter²⁰ of order n equal to 3 with a cutoff frequency D₀ equal to 50. This filter is applied to the matrix I₃ and the resulting image is stored as the matrix I₄. Figure 13 shows the image of matrix I₄ calculated after the matrix I₃ from Figure 11. We calculate the matrix of difference D₃₄ as (I₃ – I₄)·10 + 127, in order to show the information of texture that is eliminated by the Butterworth filter. The factor 10 is included to increase the visibility of the differences. In addition, the image of D₃₄ in Figure 13 is amplified by a factor of 2, compared to the image of I₄, in order to reveal the details of the difference. The cutoff frequency and the order of the filter were defined based on the current size of the inspection area, 15 by 15 cm, and the wrinkle replica SA-1, with the help of the difference matrix D₃₄. The information from wrinkles can be found at the low-frequency components of the Fourier spectrum, while the fabric texture and thread information are present at the higher frequency components. The objective of the low-pass filter is to attenuate all high-frequency components that do not carry information of wrinkles. Therefore, the cutoff frequency D₀ must be located close to the higher frequency components of the wrinkles of SA-1. Hence, we sought for a filter with the lowest values of D₀ and n that does not remove the information of wrinkles from matrix I₃. Figure 14 shows the image of D₃₄ for different values of D₀ and n. Some information from wrinkles is visible at D₃₄ for values of D₀ equal to 30 or n equal to 1. This indicates that the filter removes information of wrinkles from I₃, which is undesirable. As D₀ and n are increased, the undesired effect of the filter on the wrinkles is decreased. We found that the low-pass filter with D₀ = 50 and n = 3 represents the best compromise to filter most high-frequency components without losing information from wrinkles. Given the current field of view, the cutoff frequency can be expressed as a spatial frequency of 50 cycles/15 cm, or 3.33 cycles/cm. In comparison, the spatial frequency expected from a fabric with a thread count of 25 (per square inch) is 9.8 cycles/cm. Therefore, the filter does not need to be modified to adapt to different fabrics with thread count greater than or equal to 25 (per square inch), because the spatial frequency of the threads is much higher than the current cutoff frequency. Moreover, D₀ does not depend on image resolution while the current field of view of 15 by 15 cm is preserved. This is an advantage of the filters implemented at the frequency domain. Nevertheless, if the field of view is modified, then D₀ should be adjusted in order to maintain the value of the spatial frequency.
Figure 13.
Image from matrix I₄ after Figure 11, and the image of difference D₃₄.

Figure 14.
Image of difference matrix D₃₄ for different values of cutoff frequency D₀ and order n.

The preprocessing functions previously described are applied to the images from fabric samples as well as the wrinkle replicas used to calibrate the system. All descriptors used to characterize samples and wrinkle replicas are calculated from matrix I₄.

Definition of descriptors

We identify three characteristics that describe the fabric wrinkles. These properties are mutually independent. Nevertheless, they are correlated in real samples of fabric. The first characteristic is the average peak-valley height of wrinkles. The second is the wrinkle density, also expressed as the inverse value of the average distance between wrinkles. The last characteristic is the wrinkle sharpness. We evaluated several descriptors suitable for wrinkle evaluation, including luminance statistical functions, Haralick textural features,³ frequency and amplitude analysis based on 2D-fast Fourier transform (FFT)^2,5 fractal dimension calculation,^7,15 wavelet analysis,⁶ and edge detection-based descriptors.⁴ We selected two quantitative descriptors to evaluate wrinkles that are closely related to the wrinkle properties as perceived by the evaluators: the standard deviation of luminance, and the summation of wrinkle edge strength. These descriptors allowed us to achieve a high correlation between the grades assigned by the computer-assisted system and those assigned by a jury of trained evaluators.

Standard deviation of luminance

As predicted by Equations (1) and (2), the luminance depends on the local slope on each segment of the fabric surface. An ideally flat sample should present a constant slope. Therefore, it is expected that the matrix I₄ from a plane presents a nearly constant value and a very narrow luminance distribution. On the other hand, a sample with wrinkles will present regions with different values of slope and the luminance histogram will present a wider distribution and higher standard deviation. We found that the standard deviation of luminance depends linearly on the average peak-valley height value, as well as on the wrinkle density. Then, the first descriptor is calculated from the matrix I₄ as shown:
$D 1 = \sqrt{\frac{1}{M} \frac{1}{N} \sum_{m = 0}^{M - 1} \sum_{n = 0}^{N - 1} (I 4 (m, n) - μ) 2}$
(7)
Here, D₁ is the first descriptor, matrix I₄ is the image obtained after the preprocessing filters, M and N are the number or rows and columns, respectively, and μ is the average value of matrix I₄. In Figure 15, we show the value of the first descriptor for each replica of the AATCC. The value of D₁ decreases with the nominal wrinkle grade value of each plate, but the relationship between wrinkle grade and D₁ is not linear.
Figure 15.
Descriptor D₁ as a function of wrinkle grade for the American Association of Textile Chemists and Colorists (AATCC) replicas.

Wrinkle sharpness

The wrinkles are temporal deformations that results from folds of the fabric. These creases are visible at the border between two segments of the surface of different slopes, analogous to the peak where two sloped roof sections meet. The border is visible due to the contrast resulting from the luminance difference between the surfaces and the width of the transition zone. The wrinkle sharpness appearance is directly related with the visibility of the borders. We quantify the wrinkle sharpness implementing an algorithm based on the Canny edge detection filter.²¹ This implementation includes only the stages of Gaussian smoothing, Sobel edge detections, and non-maximum suppression. The filter is applied to matrix I₄ and the resulting image is stored as matrix S. The summation of the strength of the detected borders is proportional to the contrast of the wrinkles, providing the information of sharpness:
$D_{2} = \frac{1}{M} \frac{1}{N} \sum_{m = 0}^{M - 1} \sum_{n = 0}^{N - 1} S (m, n)$
(8)
Here, D₂ is the second descriptor that depends on wrinkle sharpness, S is the resulting image from the edge detection algorithm. Figure 16 shows the value of D₂ calculated from images of the AATCC replicas. Similar to D₁, the relationship between wrinkle grade and D₂ is not linear.
Figure 16.
Descriptor D₂ as a function of wrinkle grade for the American Association of Textile Chemists and Colorists (AATCC) replicas.

System calibration

The grades assigned to the samples are determined by comparison to the AATCC replicas. These samples define a wrinkle degree scale from 1 to 5, where 1 corresponds to a sample with heavy wrinkles and 5 to a flat sample. In order to calibrate the system, an image of each replica is acquired. The images are processed by the preprocessing filters and both descriptors are calculated for each replica. For each descriptor, we generate an interpolated calibration function by fitting a polynomial of order 3, as show in Figures 15 and 16. This allows us to evaluate samples using a continuous wrinkle grade scale, interpolating from the six discrete values that the replicas define. The replica labeled as SA-5 is not used for fitting because this replica is too similar to replica SA-4. Therefore, we defined that wrinkle grade 5 should be applied to an ideally flat sample. Then, descriptors 1 and 2 are fixed to be zero for this wrinkle grade. The calibration process is complete after the interpolation functions for D₁ and D₂ are calculated.

In order to assign a grade for a sample, we quantify both descriptors. One wrinkle grade is determined for each descriptor using the corresponding interpolation function and a successive approximations algorithm. Both grades usually converge to the same value, but a small difference is present because descriptors D₁ and D₂ depend on different characteristics of wrinkles. The final grade is calculated by the weighted average of the partial grades. We determined the weight of each grade by a correlation evaluation between grades assigned by the system and a jury of evaluators:
$G_{s} = \frac{{AG}_{D 1} + {BG}_{D 2}}{A + B}$
(9)
Here, G_s is the final wrinkle grade assigned to the sample, G_D₁ and G_D₂ are the partial grades calculated from D₁ (Equation (6)) and D₂ (Equation (7)) using the respective calibration functions, and A and B are the weight coefficients used for the weighted average.

Correlation between the system and the jury of evaluators

In order to determine the constants A and B, we performed a correlation test using a batch of 18 shirts. The shirts were simultaneously graded by a jury of evaluators and the objective system. These specimens were commercially available dress shirts with a front pocket, made of white Pinpoint Oxford fabric (40% cotton, 60% polyester, thread count: 80). They were previously wrinkled by tying knots. We obtained a batch with wrinkle grade values from 1 to 4 by controlling the tension of the knots, processing some samples in a steam-dewrinkle tumble dryer, and also using a steam iron. Regular cloth hangers were used to display the shirts. The front opening was fastened using the top three buttons. The objective grade calculated by the system resulted from averaging the seven ROIs shown in Figure 4. The size of each ROI was 15 by 15 cm, equivalent to images of 350 by 350 pixels as described in the second section. The AGC algorithm was configured in continuous mode, adjusting the exposure on each measurement. All preprocessing and filtering algorithms were enabled. The information from soft undulations was eliminated by the respective filter using a polynomial of order 10. The high-frequency filter was operating with a cutoff frequency D₀ equal to 50, and order n equal to 3. Three expert evaluators integrated the jury that graded the shirts, assigning quantitative grades to each garment with a resolution of 0.5 units. The pocket and sleeves were not evaluated by the observers, in agreement with the legacy procedure and the objective system. The subjective grades from the jury for each shirt were averaged and compared to those assigned by the objective system. We calculated the square of the correlation coefficient R² for different values of A from 0 to 1.0 and B = 1.0–A, as shown in Figure 17. The highest correlation was found when descriptor 2 dominates the weighted average, demonstrating that experts are considerably more sensible to wrinkle sharpness than wrinkle depth. We fixed the weight coefficients as A = 0.3 and B = 0.7 in order to obtain a high correlation (R² = 0.91) and a robust performance. Figure 18 shows the correlation between the grades assigned by the jury and those assigned by the system using the selected weight coefficients.
Figure 17.
The square of the correlation coefficient R² between the objective system and the experts as a function of weight coefficients A and B.

Figure 18.
Correlation between the objective system (system grading) and the jury of evaluators (expert grading).

The previous evaluation shows high correlation between the objective system and the jury of evaluators. The evaluation performed by the objective system required one third of the effort compared to the jury of evaluators, because only one operator is necessary. After reviewing the grades assigned by the system, the evaluators agreed that the differences were originated by the difficulty to mentally integrate the degree and frequency of wrinkles in the specimens. In most cases, the wrinkles are not uniform in the shirts. Therefore, it is not possible to match a single replica to the whole surface. This difficulty contributes to the relatively low repeatability that can be observed between human evaluators, compared to the objective system.

Analysis of variance Gage for Repeatability and Reproducibility

The Gage for Repeatability and Reproducibility (R&R) is a powerful statistical tool to qualify a measurement system as a reliable one. The Gage R&R is based on a classical analysis of variance (ANOVA) study to assess the robustness of gages, measuring instruments, test methods, and other measurement systems. It is used to determine the amount of variability induced in the measurements by the measurement system itself, and compares it to the total variability observed. There are several factors affecting a measurement system, including measuring instruments, operators (people), test methods, specification or reference value, and the parts or specimens. There are two important aspects of Gage R&R, namely repeatability and reproducibility. Gage Repeatability measures the consistency of the results with the same operator, whereas Gage Reproducibility evaluates the consistency of results between operators. Through repetitive data collection and ANOVA calculations, we can measure test validity, operator differences, specification validity, and the clarity of standard operating procedures.

Prior to the implementation at the production environment, we evaluated the performance of the system using a Gage R&R study. We perform this analysis to estimate the contribution of variation attributable to the measurement system itself. The theory of the R&R study is beyond the scope of this work, but the objective can be explained in simple words. With this study we want to demonstrate that a sample can be evaluated repeatedly by one operator, or different operators, obtaining consistent grades. In addition, two samples with a grade difference as small as 0.5 should be clearly differentiated by the system. Gage R&R studies should be performed over the range of expected observations. As discussed by Montgomery and Runger,²² the ANOVA method is usually preferred for continuous data, where the operators and parts are considered to be random factors. The Gage R&R was performed grading two batches of 15 shirts each. The first batch was composed of shirts wrinkled following a repeatable procedure. The average wrinkle grade for this batch was approximately 1.8. The second batch was prepared smoothing the shirts from the first batch, using a tumble dryer featuring a steam de-wrinkle cycle. The average wrinkle grade of the second batch was 2.5. The test was repeated by two different operators. Each operator evaluated each batch twice using the objective system. On each measurement, the shirts were mounted and dismounted from their respective hangers. Each shirt was graded by the front and the back, resulting in two grades by garment. The test comprised 30 measurements by batch, for a total of 240 measurements for the Gage R&R, as shown in Table 1. In this table, the repetitions of the first operator are labeled as the columns A and B for the first batch, and columns E and F for the second batch. The repetitions for the second evaluator are labeled as C and D for the first batch, and G and H for the second batch. The columns labeled as average show the calculated grades for the front and the back of the shirts for each repetition. All measurements were performed in a darkened room, as recommended by AATCC method No. 124. The only source of light is the overhead lighting arrangement of the inspection booth. The Minitab® software was used to perform the study with a risk level at α = 0.05.
Table 1.
Detailed results from the Gage Repeatability and Reproducibility

Shirt Side ROI Batch 1 Batch 2

Operator 1 Operator 2 Operator 1 Operator 2

Repetition A Repetition B Repetition C Repetition D Repetition E Evaluation F Repetition G Repetition H

Grade Average Grade Average Grade Average Grade Average Grade Average Grade Average Grade Average Grade Average

1 Front 1 2.5 2.10 2.6 2.11 2.2 2.00 2.4 2.13 2.6 2.59 2.8 2.53 2.4 2.55 3.0 2.68

2 1.4 1.6 1.7 1.8 2.5 2.3 2.6 2.4

3 2.4 2.0 2.1 2.2 2.7 2.5 2.7 2.7

Back 4 2.0 1.68 2.0 1.79 1.9 1.65 1.9 1.65 2.4 2.37 2.4 2.42 2.5 2.48 2.5 2.37

5 1.9 2.0 1.8 1.8 2.6 2.8 2.8 2.5

6 1.5 1.6 1.6 1.4 2.2 2.3 2.2 2.2

7 1.3 1.6 1.3 1.5 2.3 2.3 2.4 2.3

2 Front 1 2.1 2.17 2.2 2.09 2.3 2.17 2.3 2.03 2.8 2.63 2.5 2.47 2.9 2.65 2.8 2.73

2 1.8 1.7 1.7 1.6 2.3 2.2 2.4 2.4

3 2.6 2.3 2.5 2.2 2.7 2.7 2.6 2.9

Back 4 2.1 1.80 2.1 1.90 2.1 1.75 2.0 1.75 2.6 2.50 2.6 2.54 2.6 2.53 2.5 2.50

5 2.1 2.3 2.0 2.0 2.8 2.9 2.8 3.0

6 1.7 1.6 1.5 1.5 2.4 2.3 2.3 2.2

7 1.3 1.6 1.4 1.5 2.3 2.4 2.4 2.3

3 Front 1 2.1 1.67 2.2 1.74 2.1 1.57 2.0 1.80 2.7 2.64 2.5 2.33 2.2 2.07 2.2 2.09

2 1.2 1.5 1.3 1.5 2.6 2.1 1.8 1.9

3 1.7 1.5 1.3 1.9 2.6 2.4 2.2 2.1

Back 4 1.5 1.38 1.7 1.45 1.6 1.45 1.5 1.48 2.6 2.59 2.4 2.24 2.7 2.38 2.5 2.33

5 2.0 1.8 1.9 2.1 2.9 2.5 2.6 2.3

6 1.0 1.2 1.1 1.1 2.5 1.9 2.2 2.3

7 1.0 1.2 1.2 1.2 2.3 2.2 2.1 2.3

4 Front 1 2.3 2.13 2.1 1.98 2.1 2.00 2.1 2.10 2.3 2.38 2.8 2.74 2.7 2.55 2.8 2.77

2 2.0 1.9 1.9 1.8 2.2 2.4 2.4 2.7

3 2.1 2.0 2.0 2.4 2.7 3.1 2.6 2.8

Back 4 2.1 1.88 1.9 1.85 2.0 1.85 2.0 1.83 2.3 2.29 2.7 2.58 2.8 2.62 2.8 2.60

5 2.0 2.1 2.1 2.1 2.6 2.9 2.8 2.8

6 1.8 1.6 1.7 1.6 2.0 2.4 2.6 2.5

7 1.6 1.8 1.7 1.6 2.3 2.4 2.2 2.3

5 Front 1 1.7 1.63 1.8 1.65 1.7 1.63 1.9 1.77 2.3 2.35 2.4 2.43 2.5 2.40 2.4 2.41

2 1.2 1.4 1.3 1.3 2.2 2.3 2.1 2.3

3 2.0 1.8 1.9 2.1 2.5 2.6 2.6 2.5

Back 4 1.4 1.25 1.4 1.37 1.5 1.33 1.5 1.25 2.8 2.33 2.5 2.27 2.3 2.37 2.4 2.27

5 1.7 1.7 1.7 1.6 2.0 2.3 2.3 2.2

6 1.1 1.2 1.2 1.1 2.4 2.2 2.4 2.3

7 0.8 1.2 0.9 0.8 2.2 2.2 2.5 2.2

6 Front 1 1.6 1.73 1.4 1.47 1.7 1.63 1.7 1.70 2.7 2.52 2.7 2.50 2.4 2.16 2.7 2.47

2 1.2 1.2 1.0 1.2 2.4 2.4 2.2 2.3

3 2.4 1.8 2.2 2.2 2.4 2.5 2.0 2.4

Back 4 1.7 1.63 1.6 1.58 1.7 1.73 1.5 1.63 2.5 2.52 2.4 2.63 2.6 2.64 2.5 2.58

5 2.2 2.0 2.1 2.2 2.7 3.1 3.0 3.0

6 1.3 1.4 1.4 1.3 2.3 2.4 2.4 2.3

7 1.3 1.3 1.7 1.5 2.5 2.7 2.6 2.6

7 Front 1 2.2 2.03 2.2 1.89 2.1 1.87 2.3 2.00 2.5 2.58 2.5 2.62 2.4 2.56 2.6 2.64

2 1.9 1.7 1.7 1.8 2.5 2.5 2.5 2.6

3 2.0 1.7 1.8 1.9 2.7 2.8 2.8 2.8

Back 4 2.0 1.70 2.0 1.85 1.8 1.68 2.0 1.73 2.5 2.46 2.5 2.51 2.5 2.51 2.7 2.52

5 2.0 2.2 2.1 2.1 2.6 2.7 2.7 2.6

6 1.3 1.5 1.3 1.4 2.3 2.3 2.4 2.5

7 1.5 1.7 1.5 1.4 2.4 2.5 2.4 2.3

8 Front 1 1.9 1.90 1.8 1.91 1.7 1.80 1.8 1.90 2.3 2.37 2.6 2.37 2.7 2.36 2.3 2.37

2 1.6 1.5 1.5 1.6 2.0 2.0 1.9 2.2

3 2.2 2.4 2.2 2.3 2.8 2.5 2.4 2.6

Back 4 1.7 1.75 1.6 1.77 1.5 1.63 1.4 1.75 2.5 2.48 2.5 2.51 2.5 2.45 2.4 2.40

5 2.3 2.3 2.2 2.7 2.8 2.6 2.7 2.7

6 1.5 1.4 1.3 1.2 2.3 2.4 2.4 2.2

7 1.5 1.7 1.5 1.7 2.3 2.6 2.3 2.3

9 Front 1 1.9 1.63 1.9 1.64 1.9 1.60 2.0 1.70 3.0 2.63 2.6 2.29 2.5 2.18 2.7 2.39

2 1.1 1.2 1.1 1.0 2.2 1.9 1.9 2.2

3 1.9 1.9 1.8 2.1 2.8 2.4 2.2 2.4

Back 4 1.4 1.45 1.4 1.41 1.6 1.55 1.8 1.63 2.7 2.59 2.5 2.53 2.4 2.51 2.5 2.42

5 1.7 1.6 1.6 1.8 2.9 3.1 3.0 2.9

6 1.2 1.2 1.3 1.4 2.4 2.4 2.3 2.1

7 1.5 1.5 1.7 1.5 2.4 2.2 2.4 2.2

10 Front 1 2.6 1.97 2.4 1.92 2.3 1.93 2.4 1.97 2.6 2.63 2.8 2.70 2.6 2.47 2.8 2.70

2 1.4 1.3 1.5 1.4 2.5 2.5 2.3 2.4

3 1.9 2.0 2.0 2.1 2.9 2.8 2.5 2.9

Back 4 1.8 1.88 1.9 1.86 1.9 1.85 2.0 1.85 2.6 2.46 2.7 2.40 2.2 2.31 2.4 2.36

5 2.4 2.4 2.3 2.5 2.6 2.4 2.6 2.6

6 1.6 1.4 1.7 1.4 2.2 2.2 2.1 2.1

7 1.7 1.7 1.5 1.5 2.3 2.3 2.3 2.3

11 Front 1 1.9 1.83 1.8 1.77 1.9 1.90 1.8 1.80 2.7 2.31 2.6 2.48 2.3 2.23 2.6 2.24

2 1.8 1.9 1.8 1.7 2.3 2.2 2.1 1.8

3 1.8 1.7 2.0 1.9 2.0 2.6 2.3 2.3

Back 4 1.7 1.60 1.8 1.62 1.8 1.65 2.0 1.75 2.5 2.32 2.4 2.30 2.4 2.38 2.6 2.40

5 2.0 2.0 2.0 1.9 2.7 2.7 2.4 2.6

6 1.2 1.2 1.2 1.5 2.1 1.9 2.5 2.3

7 1.5 1.5 1.6 1.6 2.0 2.2 2.2 2.1

12 Front 1 2.0 2.13 2.0 2.16 2.1 2.13 2.5 2.43 2.7 2.67 2.9 2.75 2.7 2.63 2.8 2.63

2 1.6 1.7 1.6 1.9 2.6 2.6 2.4 2.5

3 2.8 2.8 2.7 2.9 2.8 2.8 2.8 2.5

Back 4 2.1 2.08 2.2 2.04 2.1 2.05 2.1 2.03 2.6 2.52 2.9 2.77 2.6 2.60 2.6 2.62

5 2.5 2.4 2.4 2.4 2.8 3.1 2.9 3.0

6 2.1 2.0 2.1 2.0 2.2 2.6 2.3 2.5

7 1.6 1.6 1.6 1.6 2.4 2.5 2.6 2.3

13 Front 1 1.7 1.87 2.1 1.99 2.0 2.00 1.9 1.93 2.6 2.59 2.9 2.75 2.5 2.72 2.0 2.37

2 1.6 1.8 1.7 1.4 2.5 2.5 2.5 2.3

3 2.3 2.1 2.3 2.5 2.8 2.9 3.2 2.8

Back 4 1.9 2.03 1.9 1.87 1.9 2.05 2.0 1.93 3.1 2.59 2.7 2.46 2.4 2.49 2.7 2.48

5 2.7 2.3 2.6 2.4 2.6 2.5 2.6 2.7

6 1.8 1.5 1.9 1.7 2.4 2.4 2.4 2.3

7 1.7 1.7 1.8 1.6 2.3 2.2 2.5 2.2

14 Front 1 2.2 2.13 2.4 2.30 2.3 2.20 2.4 2.23 2.7 2.65 2.7 2.52 2.8 2.63 2.9 2.68

2 2.0 2.1 2.0 2.1 2.3 2.3 2.7 2.5

3 2.2 2.4 2.3 2.2 2.9 2.6 2.4 2.7

Back 4 1.9 1.90 1.8 1.94 1.9 1.95 1.8 2.03 2.4 2.33 2.4 2.38 2.3 2.34 2.3 2.31

5 2.2 2.3 2.3 2.6 2.5 2.6 2.6 2.7

6 1.7 1.7 1.8 1.7 2.2 2.3 2.2 2.2

7 1.8 1.9 1.8 2.0 2.2 2.2 2.2 2.2

15 Front 1 1.2 1.47 1.5 1.51 1.2 1.43 1.3 1.57 2.6 2.41 2.7 2.54 2.6 2.58 2.6 2.37

2 1.4 1.3 1.3 1.3 2.2 2.4 2.4 2.2

3 1.8 1.7 1.8 2.1 2.5 2.6 2.7 2.3

Back 4 1.8 1.50 2.0 1.59 1.7 1.55 1.8 1.60 2.7 2.48 2.6 2.41 2.7 2.45 2.5 2.40

5 1.5 1.5 1.6 1.5 2.4 2.3 2.5 2.5

6 1.5 1.5 1.5 1.7 2.4 2.2 2.5 2.4

7 1.2 1.3 1.4 1.4 2.4 2.5 2.2 2.2

ROI: region of interest.

Table 2 summarizes the Gage R&R study results. Frequently, practitioners investigate the relationship between allowable study variation and tolerance with the total Gage R&R computations. According to Pareto’s law, 80% of the variance can be explained by 20% of the variables, deemed as the vital few.²² This has given foundations to the Gage R&R contribution to both percentage of variation and percentage of tolerance to be less than 20% as qualifying acceptance criteria. On the other hand, a widespread practice is to accept a number greater than or equal to five categories in the Six Sigma industry. The distinct categories are computed by dividing the part variation by the combined repeatability and reproducibility variation, multiplying by 1.41, and rounding down to the nearest whole number. Therefore, with 51 distinct categories, the system is very capable of discerning between garment wrinkles grades with a resolution better than 0.1.
Table 2.
Gage Repeatability and Reproducibility (R&R) summary

Gage R&R parameter Acceptance criteria Contributor/quantity

Reproducibility It is sought that operator and operator by part are both not statistically significant for good reproducibility. Ho: The factor does not contribute the Gage R&R total variation. Unable to reject the null hypothesis of those factors whose p > 0.05 Unable to reject the null hypothesis that the operator and operator by batch interactions effects is equal to zero at 95% confidence level

Repeatability-total variation [%] <20 0.08

Study of variation [%] <20 2.78

Tolerance [wrinkle levels] Current resolution of the evaluators subjective grading 0.5

Study of tolerance [%] <20 13.87

Categories [dimensionless] ≥5 51

Figure 19 shows the customary charts used to evaluate the repeatability and reproducibility based on the results from the Gage R&R.²² These charts compare the average grades obtained by the two operators for both batches. The graphical output showing the “Components of Variation” illustrates how most of the variation is due to the part-to-part component, as one would desire. In other words, the variation comes from the shirt specimens and not from the operators. The “R-chart by operator” shows that the two operators (1 and 2) recorded the values for each part with a similar amount of variability, meaning that the test procedure is similarly understood and followed by both operators. On the other hand, the “Xbar chart by operator” represents the variability between different shirts. There are out of control points, indicating that the measurement system can discriminate points outside of the specification limits. In other words, the operators are very capable of distinguishing different shirts with different wrinkling grades when using the objective system. The average values on all parts measured twice by the two operators are represented in the “By operator” chart, and indicate that both the overall means and dispersion recorded by the two operators are similar. The chart “Operatorbatch interaction” shows that there is no interaction effect between these two factors, given that the interaction lines exhibit parallelism. Therefore, the operatorbatch term is removed from the statistical model that describes the system variation. Finally, the graph entitled “By batch” shows that both batches have very different wrinkle levels, covering the total range of expected observations.
Figure 19.
Gage Repeatability and Reproducibility graphical output from Minitab.

Using the information obtained from the Gage R&R, we evaluate the effect of the weight of the fabric on the SA, as well as the influence of the geometry of the shirts on wrinkle generation. This evaluation provides information regarding the appearance of wrinkles in shirts displayed on cloth hangers, as well as the sensitivity of the method to evaluate them. For this purpose, we use the grades obtained from repetitions A (first batch) and E (second batch) of operator 1, but similar results can be obtained from other repetitions of the Gage. Figure 20 shows the average value for the seven ROIs, calculated from the grades of repetitions A and E. The difference between the different ROIs of batch 1 is not produced by random factors. Using the technique of one-way ANOVA, we rejected the null hypothesis that the samples of these regions belong to populations with the same mean value (p < 0.00001). In other words, the wrinkles of the shirt are not uniform and depend on the region. The wrinkles from batch 2, after the smoothing process by the tumble dryer, are still not uniform and the difference is very statistically significant (p < 0.00001).
Figure 20.
Average wrinkle grade value for each region of interest (ROI), calculated from evaluations A (batch 1) and E (batch 2) of operator 1.

Now, we analyze the effect of gravity on the SA. The mean value of the grades for the upper regions (4 and 5) at the back of the shirts from batch 1 is 1.94, while the mean value for the lower regions (6 and 7) is 1.45. The difference of 0.49 is very statistically significant, as demonstrated by the t-test (t = 12.6317, df = 14, p < 0.0001). The same effect can be observed from the grades of batch 2, where the mean values of the grades for the upper and lower regions of the back are 2.64 and 2.30, respectively. The difference of 0.34 is also statistically significant (t = 9.7399, df = 14, p < 0.0001). This effect is present because the tension due to the weight of the fabric is higher close to the shoulders, and it smoothes the wrinkles at the upper region of the shirts. The same conclusion can be obtained by comparing regions 1 and 2 at the front of the shirt. The smoothing due to weight of the fabric is highly repeatable, as demonstrated by the Gage. It does not introduce an error while comparing the performance of different appliances, unless samples of different geometry are used. In addition, the gravity-induced smoothing would not be observable if the shirts were evaluated over a horizontal plane.

The information from the Gage also indicates that there is some asymmetry in the wrinkles of batch 1. By example, the mean values for regions 4 and 5 from the back of shirts 1 are 1.81 and 2.08, respectively. The difference of 0.273 is small, but very significant (t = 3.3849, df = 14, p < 0.0044). This indicates that there is an asymmetry on the procedure used to generate wrinkles. Nevertheless, after the process of smoothing by the tumble dryer (batch 2), the mean values of regions 4 and 5 were 2.587 and 2.633, respectively. This difference is not significant (t = 0.5564, df = 14, p = 0.5867), indicating that the wrinkles tend to be uniform after the smoothing process.

The wrinkles generated at the back of the shirts from batch 1 are heavier than those generated at the front, 1.70 and 1.92 being the mean values of the grades. This significant difference of 0.22 (t = 4.2340, df = 14, p = 0.0007) could be attributed to the procedure used to generate the wrinkles. Nevertheless, the difference remains after the smoothing process. The mean values for the front and back of shirts of batch 2 are 2.56 and 2.45, respectively. The back of the shirts remain the most wrinkled. The difference of 0.10 is small, but significant (t = 3.4670, df = 14, p < 0.0038). Compared to the results from regions 4 and 5 from the back, where the non-uniformity of the wrinkles disappeared after the smoothing process, the non-uniformity between the front and the back of the shirt was not eliminated. This indicates that there is some influence of the geometry of the shirt on the remaining wrinkles after the smoothing process by the tumble dryer.

An unexpected asymmetry was found between regions 2 and 3 from the front of the shirt. For batch 1, the mean grade values for these regions were 1.55 and 2.14, respectively. This indicates that the appearance of wrinkles is heavier in region 2 than in region 3. Actually, region 3 exhibits the smoothest appearance of the garment. The difference remains after the smoothing cycle. For batch 2, the mean grades for regions 2 and 3 are 2.35 and 2.65, respectively. Region 3 is the least wrinkled for batch 2, despite being at the lower region of the shirt, where the smoothing effect of the gravity is less noticeable. It can be inferred that the pocket of the shirt and the placket influence the SA of region 3.

The previous results indicate that there are differences between the seven regions of the shirts, originated by the geometry of the garment, the use of cloth hangers, and the procedure to generate wrinkles. Therefore, shirts cannot be replaced by swatches of different geometry nor evaluated over a horizontal plane without introducing a statistically significant difference, compared to the results obtained by the legacy procedure.

Conclusions

We described an objective system developed for wrinkle appearance evaluation in fabrics. This system is compliant with the geometry of the inspection booth designed for subjective evaluation by trained experts, and was tested grading real clothes. The wrinkle grading method is based on luminance image analysis and incorporates two quantitative descriptors that are closely related with wrinkle characteristics as perceived by evaluators: peak-valley height, wrinkle density, and wrinkle sharpness. The incorporation of specially designed additive and multiplicative noise filters resulted in highly repeatable results. The results from the objective evaluation are comparable to the historical records because they are based on the same visual information. The square of the correlation coefficient of the system with expert evaluators was calculated as R²= 0.91. The reliable performance of the system was demonstrated by the repeatability and reproducibility study performed according to the Six Sigma methodology.

Shirt	Side	ROI	Batch 1	Batch 2
1	Front	1	2.5	2.10	2.6	2.11	2.2	2.00	2.4	2.13	2.6	2.59	2.8	2.53	2.4	2.55	3.0	2.68
2	1.4	1.6	1.7	1.8	2.5	2.3	2.6	2.4
3	2.4	2.0	2.1	2.2	2.7	2.5	2.7	2.7
Back	4	2.0	1.68	2.0	1.79	1.9	1.65	1.9	1.65	2.4	2.37	2.4	2.42	2.5	2.48	2.5	2.37
5	1.9	2.0	1.8	1.8	2.6	2.8	2.8	2.5
6	1.5	1.6	1.6	1.4	2.2	2.3	2.2	2.2
7	1.3	1.6	1.3	1.5	2.3	2.3	2.4	2.3
2	Front	1	2.1	2.17	2.2	2.09	2.3	2.17	2.3	2.03	2.8	2.63	2.5	2.47	2.9	2.65	2.8	2.73
2	1.8	1.7	1.7	1.6	2.3	2.2	2.4	2.4
3	2.6	2.3	2.5	2.2	2.7	2.7	2.6	2.9
Back	4	2.1	1.80	2.1	1.90	2.1	1.75	2.0	1.75	2.6	2.50	2.6	2.54	2.6	2.53	2.5	2.50
5	2.1	2.3	2.0	2.0	2.8	2.9	2.8	3.0
6	1.7	1.6	1.5	1.5	2.4	2.3	2.3	2.2
7	1.3	1.6	1.4	1.5	2.3	2.4	2.4	2.3
3	Front	1	2.1	1.67	2.2	1.74	2.1	1.57	2.0	1.80	2.7	2.64	2.5	2.33	2.2	2.07	2.2	2.09
2	1.2	1.5	1.3	1.5	2.6	2.1	1.8	1.9
3	1.7	1.5	1.3	1.9	2.6	2.4	2.2	2.1
Back	4	1.5	1.38	1.7	1.45	1.6	1.45	1.5	1.48	2.6	2.59	2.4	2.24	2.7	2.38	2.5	2.33
5	2.0	1.8	1.9	2.1	2.9	2.5	2.6	2.3
6	1.0	1.2	1.1	1.1	2.5	1.9	2.2	2.3
7	1.0	1.2	1.2	1.2	2.3	2.2	2.1	2.3
4	Front	1	2.3	2.13	2.1	1.98	2.1	2.00	2.1	2.10	2.3	2.38	2.8	2.74	2.7	2.55	2.8	2.77
2	2.0	1.9	1.9	1.8	2.2	2.4	2.4	2.7
3	2.1	2.0	2.0	2.4	2.7	3.1	2.6	2.8
Back	4	2.1	1.88	1.9	1.85	2.0	1.85	2.0	1.83	2.3	2.29	2.7	2.58	2.8	2.62	2.8	2.60
5	2.0	2.1	2.1	2.1	2.6	2.9	2.8	2.8
6	1.8	1.6	1.7	1.6	2.0	2.4	2.6	2.5
7	1.6	1.8	1.7	1.6	2.3	2.4	2.2	2.3
5	Front	1	1.7	1.63	1.8	1.65	1.7	1.63	1.9	1.77	2.3	2.35	2.4	2.43	2.5	2.40	2.4	2.41
2	1.2	1.4	1.3	1.3	2.2	2.3	2.1	2.3
3	2.0	1.8	1.9	2.1	2.5	2.6	2.6	2.5
Back	4	1.4	1.25	1.4	1.37	1.5	1.33	1.5	1.25	2.8	2.33	2.5	2.27	2.3	2.37	2.4	2.27
5	1.7	1.7	1.7	1.6	2.0	2.3	2.3	2.2
6	1.1	1.2	1.2	1.1	2.4	2.2	2.4	2.3
7	0.8	1.2	0.9	0.8	2.2	2.2	2.5	2.2
6	Front	1	1.6	1.73	1.4	1.47	1.7	1.63	1.7	1.70	2.7	2.52	2.7	2.50	2.4	2.16	2.7	2.47
2	1.2	1.2	1.0	1.2	2.4	2.4	2.2	2.3
3	2.4	1.8	2.2	2.2	2.4	2.5	2.0	2.4
Back	4	1.7	1.63	1.6	1.58	1.7	1.73	1.5	1.63	2.5	2.52	2.4	2.63	2.6	2.64	2.5	2.58
5	2.2	2.0	2.1	2.2	2.7	3.1	3.0	3.0
6	1.3	1.4	1.4	1.3	2.3	2.4	2.4	2.3
7	1.3	1.3	1.7	1.5	2.5	2.7	2.6	2.6
7	Front	1	2.2	2.03	2.2	1.89	2.1	1.87	2.3	2.00	2.5	2.58	2.5	2.62	2.4	2.56	2.6	2.64
2	1.9	1.7	1.7	1.8	2.5	2.5	2.5	2.6
3	2.0	1.7	1.8	1.9	2.7	2.8	2.8	2.8
Back	4	2.0	1.70	2.0	1.85	1.8	1.68	2.0	1.73	2.5	2.46	2.5	2.51	2.5	2.51	2.7	2.52
5	2.0	2.2	2.1	2.1	2.6	2.7	2.7	2.6
6	1.3	1.5	1.3	1.4	2.3	2.3	2.4	2.5
7	1.5	1.7	1.5	1.4	2.4	2.5	2.4	2.3
8	Front	1	1.9	1.90	1.8	1.91	1.7	1.80	1.8	1.90	2.3	2.37	2.6	2.37	2.7	2.36	2.3	2.37
2	1.6	1.5	1.5	1.6	2.0	2.0	1.9	2.2
3	2.2	2.4	2.2	2.3	2.8	2.5	2.4	2.6
Back	4	1.7	1.75	1.6	1.77	1.5	1.63	1.4	1.75	2.5	2.48	2.5	2.51	2.5	2.45	2.4	2.40
5	2.3	2.3	2.2	2.7	2.8	2.6	2.7	2.7
6	1.5	1.4	1.3	1.2	2.3	2.4	2.4	2.2
7	1.5	1.7	1.5	1.7	2.3	2.6	2.3	2.3
9	Front	1	1.9	1.63	1.9	1.64	1.9	1.60	2.0	1.70	3.0	2.63	2.6	2.29	2.5	2.18	2.7	2.39
2	1.1	1.2	1.1	1.0	2.2	1.9	1.9	2.2
3	1.9	1.9	1.8	2.1	2.8	2.4	2.2	2.4
Back	4	1.4	1.45	1.4	1.41	1.6	1.55	1.8	1.63	2.7	2.59	2.5	2.53	2.4	2.51	2.5	2.42
5	1.7	1.6	1.6	1.8	2.9	3.1	3.0	2.9
6	1.2	1.2	1.3	1.4	2.4	2.4	2.3	2.1
7	1.5	1.5	1.7	1.5	2.4	2.2	2.4	2.2
10	Front	1	2.6	1.97	2.4	1.92	2.3	1.93	2.4	1.97	2.6	2.63	2.8	2.70	2.6	2.47	2.8	2.70
2	1.4	1.3	1.5	1.4	2.5	2.5	2.3	2.4
3	1.9	2.0	2.0	2.1	2.9	2.8	2.5	2.9
Back	4	1.8	1.88	1.9	1.86	1.9	1.85	2.0	1.85	2.6	2.46	2.7	2.40	2.2	2.31	2.4	2.36
5	2.4	2.4	2.3	2.5	2.6	2.4	2.6	2.6
6	1.6	1.4	1.7	1.4	2.2	2.2	2.1	2.1
7	1.7	1.7	1.5	1.5	2.3	2.3	2.3	2.3
11	Front	1	1.9	1.83	1.8	1.77	1.9	1.90	1.8	1.80	2.7	2.31	2.6	2.48	2.3	2.23	2.6	2.24
2	1.8	1.9	1.8	1.7	2.3	2.2	2.1	1.8
3	1.8	1.7	2.0	1.9	2.0	2.6	2.3	2.3
Back	4	1.7	1.60	1.8	1.62	1.8	1.65	2.0	1.75	2.5	2.32	2.4	2.30	2.4	2.38	2.6	2.40
5	2.0	2.0	2.0	1.9	2.7	2.7	2.4	2.6
6	1.2	1.2	1.2	1.5	2.1	1.9	2.5	2.3
7	1.5	1.5	1.6	1.6	2.0	2.2	2.2	2.1
12	Front	1	2.0	2.13	2.0	2.16	2.1	2.13	2.5	2.43	2.7	2.67	2.9	2.75	2.7	2.63	2.8	2.63
2	1.6	1.7	1.6	1.9	2.6	2.6	2.4	2.5
3	2.8	2.8	2.7	2.9	2.8	2.8	2.8	2.5
Back	4	2.1	2.08	2.2	2.04	2.1	2.05	2.1	2.03	2.6	2.52	2.9	2.77	2.6	2.60	2.6	2.62
5	2.5	2.4	2.4	2.4	2.8	3.1	2.9	3.0
6	2.1	2.0	2.1	2.0	2.2	2.6	2.3	2.5
7	1.6	1.6	1.6	1.6	2.4	2.5	2.6	2.3
13	Front	1	1.7	1.87	2.1	1.99	2.0	2.00	1.9	1.93	2.6	2.59	2.9	2.75	2.5	2.72	2.0	2.37
2	1.6	1.8	1.7	1.4	2.5	2.5	2.5	2.3
3	2.3	2.1	2.3	2.5	2.8	2.9	3.2	2.8
Back	4	1.9	2.03	1.9	1.87	1.9	2.05	2.0	1.93	3.1	2.59	2.7	2.46	2.4	2.49	2.7	2.48
5	2.7	2.3	2.6	2.4	2.6	2.5	2.6	2.7
6	1.8	1.5	1.9	1.7	2.4	2.4	2.4	2.3
7	1.7	1.7	1.8	1.6	2.3	2.2	2.5	2.2
14	Front	1	2.2	2.13	2.4	2.30	2.3	2.20	2.4	2.23	2.7	2.65	2.7	2.52	2.8	2.63	2.9	2.68
2	2.0	2.1	2.0	2.1	2.3	2.3	2.7	2.5
3	2.2	2.4	2.3	2.2	2.9	2.6	2.4	2.7
Back	4	1.9	1.90	1.8	1.94	1.9	1.95	1.8	2.03	2.4	2.33	2.4	2.38	2.3	2.34	2.3	2.31
5	2.2	2.3	2.3	2.6	2.5	2.6	2.6	2.7
6	1.7	1.7	1.8	1.7	2.2	2.3	2.2	2.2
7	1.8	1.9	1.8	2.0	2.2	2.2	2.2	2.2
15	Front	1	1.2	1.47	1.5	1.51	1.2	1.43	1.3	1.57	2.6	2.41	2.7	2.54	2.6	2.58	2.6	2.37
2	1.4	1.3	1.3	1.3	2.2	2.4	2.4	2.2
3	1.8	1.7	1.8	2.1	2.5	2.6	2.7	2.3
Back	4	1.8	1.50	2.0	1.59	1.7	1.55	1.8	1.60	2.7	2.48	2.6	2.41	2.7	2.45	2.5	2.40
5	1.5	1.5	1.6	1.5	2.4	2.3	2.5	2.5
6	1.5	1.5	1.5	1.7	2.4	2.2	2.5	2.4
7	1.2	1.3	1.4	1.4	2.4	2.5	2.2	2.2

Gage R&R parameter	Acceptance criteria	Contributor/quantity
Reproducibility	It is sought that operator and operator by part are both not statistically significant for good reproducibility. Ho: The factor does not contribute the Gage R&R total variation. Unable to reject the null hypothesis of those factors whose p > 0.05	Unable to reject the null hypothesis that the operator and operator by batch interactions effects is equal to zero at 95% confidence level
Repeatability-total variation [%]	<20	0.08
Study of variation [%]	<20	2.78
Tolerance [wrinkle levels]	Current resolution of the evaluators subjective grading	0.5
Study of tolerance [%]	<20	13.87
Categories [dimensionless]	≥5	51

Footnotes

Acknowledgments

The authors are thankful to Darío Martínez for his assistance in the experimental tests, to José Berrondo Mir Mabe TyP operation’s vice-president, Salvador Cossio, dryer engineering manager, as well as to Francisco Antón, I + D manager, for their support on this project.

Funding

This work was supported by Mabe and Consejo Nacional de Ciencia y Tecnología (CONACYT) under the 2009 PROINNOVA funding program, Project grant: 111905, Fortalecimiento del sector de electrodomésticos, AERI Electrodomésticos.

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Shirt	Side	ROI	Batch 1								Batch 2
			Operator 1				Operator 2				Operator 1				Operator 2
			Repetition A		Repetition B		Repetition C		Repetition D		Repetition E		Evaluation F		Repetition G		Repetition H
			Grade	Average	Grade	Average	Grade	Average	Grade	Average	Grade	Average	Grade	Average	Grade	Average	Grade	Average
1	Front	1	2.5	2.10	2.6	2.11	2.2	2.00	2.4	2.13	2.6	2.59	2.8	2.53	2.4	2.55	3.0	2.68
		2	1.4		1.6		1.7		1.8		2.5		2.3		2.6		2.4
		3	2.4		2.0		2.1		2.2		2.7		2.5		2.7		2.7
	Back	4	2.0	1.68	2.0	1.79	1.9	1.65	1.9	1.65	2.4	2.37	2.4	2.42	2.5	2.48	2.5	2.37
		5	1.9		2.0		1.8		1.8		2.6		2.8		2.8		2.5
		6	1.5		1.6		1.6		1.4		2.2		2.3		2.2		2.2
		7	1.3		1.6		1.3		1.5		2.3		2.3		2.4		2.3
2	Front	1	2.1	2.17	2.2	2.09	2.3	2.17	2.3	2.03	2.8	2.63	2.5	2.47	2.9	2.65	2.8	2.73
		2	1.8		1.7		1.7		1.6		2.3		2.2		2.4		2.4
		3	2.6		2.3		2.5		2.2		2.7		2.7		2.6		2.9
	Back	4	2.1	1.80	2.1	1.90	2.1	1.75	2.0	1.75	2.6	2.50	2.6	2.54	2.6	2.53	2.5	2.50
		5	2.1		2.3		2.0		2.0		2.8		2.9		2.8		3.0
		6	1.7		1.6		1.5		1.5		2.4		2.3		2.3		2.2
		7	1.3		1.6		1.4		1.5		2.3		2.4		2.4		2.3
3	Front	1	2.1	1.67	2.2	1.74	2.1	1.57	2.0	1.80	2.7	2.64	2.5	2.33	2.2	2.07	2.2	2.09
		2	1.2		1.5		1.3		1.5		2.6		2.1		1.8		1.9
		3	1.7		1.5		1.3		1.9		2.6		2.4		2.2		2.1
	Back	4	1.5	1.38	1.7	1.45	1.6	1.45	1.5	1.48	2.6	2.59	2.4	2.24	2.7	2.38	2.5	2.33
		5	2.0		1.8		1.9		2.1		2.9		2.5		2.6		2.3
		6	1.0		1.2		1.1		1.1		2.5		1.9		2.2		2.3
		7	1.0		1.2		1.2		1.2		2.3		2.2		2.1		2.3
4	Front	1	2.3	2.13	2.1	1.98	2.1	2.00	2.1	2.10	2.3	2.38	2.8	2.74	2.7	2.55	2.8	2.77
		2	2.0		1.9		1.9		1.8		2.2		2.4		2.4		2.7
		3	2.1		2.0		2.0		2.4		2.7		3.1		2.6		2.8
	Back	4	2.1	1.88	1.9	1.85	2.0	1.85	2.0	1.83	2.3	2.29	2.7	2.58	2.8	2.62	2.8	2.60
		5	2.0		2.1		2.1		2.1		2.6		2.9		2.8		2.8
		6	1.8		1.6		1.7		1.6		2.0		2.4		2.6		2.5
		7	1.6		1.8		1.7		1.6		2.3		2.4		2.2		2.3
5	Front	1	1.7	1.63	1.8	1.65	1.7	1.63	1.9	1.77	2.3	2.35	2.4	2.43	2.5	2.40	2.4	2.41
		2	1.2		1.4		1.3		1.3		2.2		2.3		2.1		2.3
		3	2.0		1.8		1.9		2.1		2.5		2.6		2.6		2.5
	Back	4	1.4	1.25	1.4	1.37	1.5	1.33	1.5	1.25	2.8	2.33	2.5	2.27	2.3	2.37	2.4	2.27
		5	1.7		1.7		1.7		1.6		2.0		2.3		2.3		2.2
		6	1.1		1.2		1.2		1.1		2.4		2.2		2.4		2.3
		7	0.8		1.2		0.9		0.8		2.2		2.2		2.5		2.2
6	Front	1	1.6	1.73	1.4	1.47	1.7	1.63	1.7	1.70	2.7	2.52	2.7	2.50	2.4	2.16	2.7	2.47
		2	1.2		1.2		1.0		1.2		2.4		2.4		2.2		2.3
		3	2.4		1.8		2.2		2.2		2.4		2.5		2.0		2.4
	Back	4	1.7	1.63	1.6	1.58	1.7	1.73	1.5	1.63	2.5	2.52	2.4	2.63	2.6	2.64	2.5	2.58
		5	2.2		2.0		2.1		2.2		2.7		3.1		3.0		3.0
		6	1.3		1.4		1.4		1.3		2.3		2.4		2.4		2.3
		7	1.3		1.3		1.7		1.5		2.5		2.7		2.6		2.6
7	Front	1	2.2	2.03	2.2	1.89	2.1	1.87	2.3	2.00	2.5	2.58	2.5	2.62	2.4	2.56	2.6	2.64
		2	1.9		1.7		1.7		1.8		2.5		2.5		2.5		2.6
		3	2.0		1.7		1.8		1.9		2.7		2.8		2.8		2.8
	Back	4	2.0	1.70	2.0	1.85	1.8	1.68	2.0	1.73	2.5	2.46	2.5	2.51	2.5	2.51	2.7	2.52
		5	2.0		2.2		2.1		2.1		2.6		2.7		2.7		2.6
		6	1.3		1.5		1.3		1.4		2.3		2.3		2.4		2.5
		7	1.5		1.7		1.5		1.4		2.4		2.5		2.4		2.3
8	Front	1	1.9	1.90	1.8	1.91	1.7	1.80	1.8	1.90	2.3	2.37	2.6	2.37	2.7	2.36	2.3	2.37
		2	1.6		1.5		1.5		1.6		2.0		2.0		1.9		2.2
		3	2.2		2.4		2.2		2.3		2.8		2.5		2.4		2.6
	Back	4	1.7	1.75	1.6	1.77	1.5	1.63	1.4	1.75	2.5	2.48	2.5	2.51	2.5	2.45	2.4	2.40
		5	2.3		2.3		2.2		2.7		2.8		2.6		2.7		2.7
		6	1.5		1.4		1.3		1.2		2.3		2.4		2.4		2.2
		7	1.5		1.7		1.5		1.7		2.3		2.6		2.3		2.3
9	Front	1	1.9	1.63	1.9	1.64	1.9	1.60	2.0	1.70	3.0	2.63	2.6	2.29	2.5	2.18	2.7	2.39
		2	1.1		1.2		1.1		1.0		2.2		1.9		1.9		2.2
		3	1.9		1.9		1.8		2.1		2.8		2.4		2.2		2.4
	Back	4	1.4	1.45	1.4	1.41	1.6	1.55	1.8	1.63	2.7	2.59	2.5	2.53	2.4	2.51	2.5	2.42
		5	1.7		1.6		1.6		1.8		2.9		3.1		3.0		2.9
		6	1.2		1.2		1.3		1.4		2.4		2.4		2.3		2.1
		7	1.5		1.5		1.7		1.5		2.4		2.2		2.4		2.2
10	Front	1	2.6	1.97	2.4	1.92	2.3	1.93	2.4	1.97	2.6	2.63	2.8	2.70	2.6	2.47	2.8	2.70
		2	1.4		1.3		1.5		1.4		2.5		2.5		2.3		2.4
		3	1.9		2.0		2.0		2.1		2.9		2.8		2.5		2.9
	Back	4	1.8	1.88	1.9	1.86	1.9	1.85	2.0	1.85	2.6	2.46	2.7	2.40	2.2	2.31	2.4	2.36
		5	2.4		2.4		2.3		2.5		2.6		2.4		2.6		2.6
		6	1.6		1.4		1.7		1.4		2.2		2.2		2.1		2.1
		7	1.7		1.7		1.5		1.5		2.3		2.3		2.3		2.3
11	Front	1	1.9	1.83	1.8	1.77	1.9	1.90	1.8	1.80	2.7	2.31	2.6	2.48	2.3	2.23	2.6	2.24
		2	1.8		1.9		1.8		1.7		2.3		2.2		2.1		1.8
		3	1.8		1.7		2.0		1.9		2.0		2.6		2.3		2.3
	Back	4	1.7	1.60	1.8	1.62	1.8	1.65	2.0	1.75	2.5	2.32	2.4	2.30	2.4	2.38	2.6	2.40
		5	2.0		2.0		2.0		1.9		2.7		2.7		2.4		2.6
		6	1.2		1.2		1.2		1.5		2.1		1.9		2.5		2.3
		7	1.5		1.5		1.6		1.6		2.0		2.2		2.2		2.1
12	Front	1	2.0	2.13	2.0	2.16	2.1	2.13	2.5	2.43	2.7	2.67	2.9	2.75	2.7	2.63	2.8	2.63
		2	1.6		1.7		1.6		1.9		2.6		2.6		2.4		2.5
		3	2.8		2.8		2.7		2.9		2.8		2.8		2.8		2.5
	Back	4	2.1	2.08	2.2	2.04	2.1	2.05	2.1	2.03	2.6	2.52	2.9	2.77	2.6	2.60	2.6	2.62
		5	2.5		2.4		2.4		2.4		2.8		3.1		2.9		3.0
		6	2.1		2.0		2.1		2.0		2.2		2.6		2.3		2.5
		7	1.6		1.6		1.6		1.6		2.4		2.5		2.6		2.3
13	Front	1	1.7	1.87	2.1	1.99	2.0	2.00	1.9	1.93	2.6	2.59	2.9	2.75	2.5	2.72	2.0	2.37
		2	1.6		1.8		1.7		1.4		2.5		2.5		2.5		2.3
		3	2.3		2.1		2.3		2.5		2.8		2.9		3.2		2.8
	Back	4	1.9	2.03	1.9	1.87	1.9	2.05	2.0	1.93	3.1	2.59	2.7	2.46	2.4	2.49	2.7	2.48
		5	2.7		2.3		2.6		2.4		2.6		2.5		2.6		2.7
		6	1.8		1.5		1.9		1.7		2.4		2.4		2.4		2.3
		7	1.7		1.7		1.8		1.6		2.3		2.2		2.5		2.2
14	Front	1	2.2	2.13	2.4	2.30	2.3	2.20	2.4	2.23	2.7	2.65	2.7	2.52	2.8	2.63	2.9	2.68
		2	2.0		2.1		2.0		2.1		2.3		2.3		2.7		2.5
		3	2.2		2.4		2.3		2.2		2.9		2.6		2.4		2.7
	Back	4	1.9	1.90	1.8	1.94	1.9	1.95	1.8	2.03	2.4	2.33	2.4	2.38	2.3	2.34	2.3	2.31
		5	2.2		2.3		2.3		2.6		2.5		2.6		2.6		2.7
		6	1.7		1.7		1.8		1.7		2.2		2.3		2.2		2.2
		7	1.8		1.9		1.8		2.0		2.2		2.2		2.2		2.2
15	Front	1	1.2	1.47	1.5	1.51	1.2	1.43	1.3	1.57	2.6	2.41	2.7	2.54	2.6	2.58	2.6	2.37
		2	1.4		1.3		1.3		1.3		2.2		2.4		2.4		2.2
		3	1.8		1.7		1.8		2.1		2.5		2.6		2.7		2.3
	Back	4	1.8	1.50	2.0	1.59	1.7	1.55	1.8	1.60	2.7	2.48	2.6	2.41	2.7	2.45	2.5	2.40
		5	1.5		1.5		1.6		1.5		2.4		2.3		2.5		2.5
		6	1.5		1.5		1.5		1.7		2.4		2.2		2.5		2.4
		7	1.2		1.3		1.4		1.4		2.4		2.5		2.2		2.2