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Predicting intramuscular fat content of pork using hyperspectral imaging
Journal of Food Engineering 134 (2014) 16–23
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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Predicting intramuscular fat content of pork using hyperspectral imaging L. Liu, M.O. Ngadi ⇑ Department of Bioresource Engineering, McGill University, Macdonald Campus, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec H9X 3V9, Canada
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 28 November 2013 Accepted 12 February 2014 Available online 22 February 2014 Keywords: Pork Intramuscular fat IMF content Hyperspectral imaging Wide line detector Linear regression PLS Stepwise procedure
a b s t r a c t Intramuscular fat (IMF) content is an important quality trait of pork. It influences taste, juiciness and tenderness of the meat. The aim of this study was to develop an objective, rapid, and non-destructive method for predicting the IMF content of pork using hyperspectral imaging technology. Critical wavelengths were selected using correlation analysis based on the spectral profiles of pork samples. The visual IMF flecks on both sides of pork chops were extracted using the wide line detector at the selected critical wavelengths. The proportion of IMF fleck areas (PFA) at critical wavelengths was used for modeling to predict the IMF content of pork. Both stepwise procedures and partial least squares (PLS) analysis were employed to establish the prediction models. Three different multilinear models were obtained using the stepwise procedure with different first entry variable of the initial model. A 3-component PLS model was developed for prediction of the IMF content. The PLS model outperformed the three multilinear models. The coefficients of determination (R2) of the PLS model on the calibration set and validation set were 0.94 and 0.97, respectively, and the adjusted R2 were 0.92 and 0.93, respectively. The prediction results of mutilinear models and PLS models indicated the potentials of using hyperspectral imaging to predict the IMF content of pork. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Intramuscular fat (IMF) corresponds to the amount of fat found between muscle fiber bundles within muscles. The amount of IMF, i.e. IMF content, varies between species, breeds and muscle types. IMF content plays an important role in various quality traits of pork. It is generally accepted that a higher IMF content has a positive effect on sensory quality traits of pork, for example, juiciness, tenderness, and flavor. Since it is strongly related to carcass quality, IMF content is also a useful tool to make genetic improvement in selection programs for carcass quality in the pork industry. IMF content is normally determined by chemical extraction of lipid from muscle samples (Folch et al., 1957). Chemical extraction is time-consuming, labor-intensive and destructive, which makes it not suitable for industrial application. In the pork industry, another quality trait, i.e. the marbling score, is widely used to estimate the IMF content of muscles. Marbling refers to the visible IMF of muscles. Marbling scores are visually assessed by experienced assessors by comparing marbling levels of meat with a standardized chart system (NPB, 2002). However, visual and subjective
⇑ Corresponding author. Tel.: +1 514 3987779; fax: +1 514 3988387. E-mail address: [email protected] (M.O. Ngadi). http://dx.doi.org/10.1016/j.jfoodeng.2014.02.007 0260-8774/Ó 2014 Elsevier Ltd. All rights reserved.
measurement of marbling scores can be difficult and has poor repeatability of results. This makes the estimation of IMF content unreliable. Therefore, an objective, rapid, accurate and nondestructive measurement for the IMF content would be an asset for the pork industry. Recent research efforts have shown high potential of hyperspectral imaging (HSI) in the development of objective, rapid, and non-destructive systems for assessment of food quality. Hyperspectral imaging is an emerging, cutting-edge and nondestructive analytical technology that combines spectroscopy and digital imagery to simultaneously acquire both spectral and spatial information from an object. A hyperspectral image, also called ‘hypercube’, is a three-dimensional image with two spatial dimensions and one spectral dimension (Qiao et al., 2007a,b), which contains enormous information about the analyzed object. The combination of spectral and spatial information makes hyperspectral imaging able to ascertain minor and/or subtle physical and chemical properties in an object. The advantages of hyperspectral imaging indicate that the technology has a promising future for food quality inspections. With respect to pork, hyperspectral imaging has been successfully applied for classification of pork qualities (Qiao et al., 2007a; Liu et al., 2010; Barbin et al., 2012a) and for prediction of quality traits such as color, pH, and drip loss (Qiao et al., 2007b; Barbin et al., 2012b). Hyperspectral imaging was also
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Table 1 Statistics of pork samples.
Chemical IMF content
Mean
Max
Min
Std
2.06
3.21
0.61
0.79
applied for assessment of pork marbling scores based on the image texture index measured by angular second moment (ASM) (Qiao et al., 2007a). The results showed that the sorted results using ASM were higher than that obtained by experienced assessors with an error around 1.0. In the very recent publications, an advanced image processing method, the wide line detector (WLD), was introduced to detect marblings of intact pork muscles from digital color pictures (Liu et al., 2012; Huang et al., 2013). The high prediction results at all the three RGB channels indicated the ability of the wide line detector to extract useful image features for prediction of marbling scores, i.e. the amount of the visible IMF of muscles. This strongly suggested the potential of using the WLD to predict the IMF content of pork. This paper aimed to develop advanced hyperspectral imaging techniques to predict the IMF content of pork in a non-destructive, rapid and accurate way. The specific objectives were to extract spectral features and identify the critical wavelengths for prediction of the IMF content; to detect the IMF flecks on both sides of pork chops at the critical wavelengths using the wide line detector; and to develop and validate different regression models based on detected IMF flecks to predict the IMF content of pork. 2. Materials and methods 2.1. Pork samples Four packages of pork loin center chops were bought from three different grocery stores in Montreal, Quebec, Canada. A total of 20 pork samples with thickness between 1 and 1.5 cm were used for predicting intramuscular fat content of pork.
Fig. 1. The near infrared hyperspectral imaging system used in the study.
Extraction Unit SER 148/6 (Velp Scientifica, Usmate, Italy), in accordance with Official Method 960.39 (AOAC, 2000). IMF content was determined as the ratio of the mass of extracted fat and the mass of the sample before freezing. The statistics of IMF content for all pork samples are listed in Table 1.
2.2. Near infrared hyperspectral imaging system and image acquisition A laboratory near infrared (NIR) hyperspectral imaging (HSI) system was set up to collect the hyperspectral images of the pork samples. The NIR-HSI system consisted of an InGaAs camera mounted with a line-scan spectrograph (Headwall photonics, USA, 900–1700 nm), two halogen lamps (JDR-C GU10, 120 V, 50 W) placed an angle of 45° to illuminate the camera’s field of view, a moving conveyer driven by a stepping motor with a userdefined speed (MDIP22314, Intelligent motion system Inc., USA), an anodized aluminum enclosure, and a PC, as shown in Fig. 1. Each pork sample was placed on a dark panel and double-sideimaged line by line using the NIR-HSI system with an optimal speed. The obtained hypercube (hyperspectral image with the BIL format) included 167 image planes over the range of wavelengths 900–1700 nm with the resolution of 4.8 nm. A total of 40 hypercubes were obtained for this study.
2.4. Image preprocessing All the acquired hypercubes were processed and analyzed using MATLAB 7.13.0.564 (The MathWorks, Inc., Mass., USA). Each hypercube was corrected from the dark current of the camera prior to segmenting the region of interest (ROI) of each sample. To correct the spectral images, a dark image B and a white image W were obtained by covering the lens with a cap, and by taking an image from a standard white reference (Spectralon, Labsphere,
2.3. Intramuscular fat content analysis After imaging, all pork samples were carefully trimmed to remove peripheral and intermuscular fat as well as the connective tissue and surrounding muscles. Samples were freeze-dried and ground in a coffee grinder (Bodum 5678-57; C-Mill, Bodum Inc., New York, NY, USA). A ground meat sample of known weight was used for determining the intramuscular fat (IMF) content in duplicate with petroleum ether extraction using a Solvent
Fig. 2. Corrected image planes of (a) Side 1 and (b) Side 2 of a pork sample at 1076 nm.
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North Sutton, New Hamshire, USA), respectively. The relative reflectance I of each image plane was calculated by
I¼
I0 B ; W B
ð1Þ
where I0 was the original image plane. Examples of the corrected image planes are shown in Fig. 2. The region of interest (ROI) of pork samples was the loin area without the peripheral and intermuscular fat as well as the connective tissue and the surrounding muscles. The ROI of each hypercube was obtained using the segmentation algorithm presented in Liu et al. (2012). 2.5. Spectral features and wavelengths selection The mean spectrum of the ROI (i.e. the average values of the ROI of image planes over the wavelength range) of each pork sample was used as spectral features of the hypercube. Each mean spectrum was smoothed using the Savitzky–Golay (Savitzky and Golay, 1964) filter with a window length of 11 points. Since the pork samples were double side imaged, each pork sample had two mean spectra corresponding to the two sides of the pork chop. The spectral feature of a pork sample denoted as MS was defined as the average profile of the smoothed mean spectra for both sides of the pork sample. The hyperspectral images contain high correlated data between adjacent wavelengths. It was not necessary to include all measured 167 wavebands in the application, not only because of the high correlation among the wavelengths, but also due to the purpose of developing application-specific multispectral imaging systems for real-time application. Correlation analysis, principal component analysis (PCA), and partial least squares (PLS) are representative methods for wavelength selection (Lee et al., 2008; Song et al., 2011). In this study, correlation analysis based on spectral feature (MS), 1st derivative (MS1) and 2nd derivative (MS2) of MS using the Savitzky–Golay method (Savitzky and Golay, 1964) was applied to select the critical wavelengths with rich spectral information related to the intramuscular fat (IMF) content. The Pearson’s correlation coefficients between chemical IMF content and MS (R0), MS1 (R1), MS2 (R2) were calculated, respectively, and the wavelengths that produced the highest correlation values were selected as the critical wavelengths. 2.6. Image line feature extraction at the critical wavelengths In previous work, marbling in pork was recognized as image line feature and was well detected using the wide line detector (Liu et al., 2012). Based on the detected marbling, marbling score was successfully assessed using linear regression models. Since the IMF content and marbling scores are correlated and follow a similar pattern (Faucitano et al., 2004), the image line feature were extracted at the critical wavelengths for IMF content prediction. The wide line detector presented in Liu et al. (2012) was used to extract the line features of image planes at the critical wavelengths. A simple thresholding method was also applied for the extracted line feature images to obtain the IMF flecks. A total of four parameters were involved in the wide line detector and the thresholding method: the radius of circular mask (r) determining the maximum width of marblings that can be detected, the intensity contrast threshold (t) defining the minimum visibility of marblings that can be detected, the global threshold (l) controlling the noise level in the detected marblings, and the minimum area of interest (a) determining the smallest object can be regarded as a marbling. The ratio of the IMF fleck area against the ROI area was calculated for each side of the pork samples. The proportion of IMF fleck
areas of each sample, PFA, was the average value of ratios of IMF fleck areas of both sides and defined as follows:
PFA ¼
areaðIMF 1 Þ areaðIMF 2 Þ 2; þ areaðROI1 Þ areaðROI2 Þ
ð2Þ
where area(IMFi) (i = 1, 2) is the total number of pixels of the detected IMF flecks on Side i, and area(ROIi) is the total number of pixels of the corresponding ROI. The PFA at critical wavelengths were used for modeling to predict the IMF content. 2.7. Modeling The relationship between chemical IMF content and PFA of pork samples was calculated over the critical wavelengths with Pearson’s correlation coefficients as well as the significance level p-value using the function ‘corr’ in MATLAB 7.13.0.564 (The MathWorks, Inc., Mass., USA). All pork samples (n = 20) were divided into two sets, the calibration set (n = 13) and the validation set (n = 7). In order to investigate the ability of the obtained PFA to predict the chemical IMF content of pork, both stepwise procedures and partial least squares (PLS) analysis were employed to build the prediction models. 2.7.1. Stepwise procedure and multi-linear regression Stepwise procedure, also called stepwise regression, is a systematic procedure for construction of a regression model that involves automatic selection of independent variables based on their statistical significance in the regression. The p-value of an F-statistic is used as the entrance/exit criterion of potential variables for the models after the initial model is decided. The procedure may build different models from the same set of potential variables due to various variables included in the initial model. The procedure terminates when no entrance or exit of variables improves the model. The purpose of using stepwise procedure was to find the subset of critical wavelengths where the PFA can best predict IMF content of pork. In this study, a multi-linear regression (MLR) model was selected as the initial model for the stepwise procedure, which was defined as
b ¼ a0 þ Y
X ai PFAi ;
ð3Þ
i
b is the vector of predicted IMF content, PFAi is the vector of where Y PFA at the critical wavelengths, a0 is the constant term and ai is the regression coefficient of the variable PFAi. Each potential variable was used as the first entry into the initial model to build multilinear models for predicting IMF content of pork. The qualities of multi-linear models were evaluated by the coefficient of determination between the predicted and measured IMF content of the calibration (R2c )/validation (R2v ) set, the adjusted R2c and R2v , the root mean square error of calibration (RMSEC), and the root mean square error of validation (RMSEV). A good model should have a low RMSEC and RMSEV, a high R2 /adjusted R2, and a small difference between R2 and adjusted R2 . 2.7.2. Partial least squares regression PLS regression (i.e. Partial Least Squares regression) is a statistical technique that generalizes and combines a large number of predictors from principal component analysis and multiple regression to find a new variable space based on small number of orthogonal components (latent variables) which are mutually independent linear combinations of predictors. It is particularly useful when the experimental data (PFA at the critical wavelengths) has more predictors than observations, and/or is highly correlated.
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In this study, the aim of PLS analysis is to find a mathematical relationship between a set of predictors, X matrix (N13 pork samples PFAn critical wavelengths), and the dependent variables, Y matrix (N13 pork samples 1). The PFA values at the identified critical wavelengths of the 13 pork samples were used as the predictors (X) and the values of chemical IMF content of the calibration set as the dependent variables (Y). Typically, most of the variations can be captured within the first few components/latent variables, while the remaining components describe random noise or linear dependencies between the wavelengths/predictors. The optimal number of PLS components used for prediction was determined by the accumulated percentage of variance explained in Y. The accumulated percentage of variance was a function of the number of components. The quality of the predictive model was also evaluated by the coefficient of determination R2c and R2v , the adjusted R2c and R2v , RMSEC, and RMSEV.
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Fig. 3. Region of interest (ROI) of the image planes in Fig. 2.
3. Results and discussion 3.1. Spectral features of pork samples Each hypercube was first corrected using Eq. (1) and then processed to obtain the region of interest (ROI). An example of the image planes of corrected hypercubes from both sides of a pork sample at the wavelength of 1076 nm is shown in Fig. 2 and the corresponding segmented ROI shown in Fig. 3. The mean spectrum of each ROI was calculated and smoothed, and the spectral feature MS of each sample was obtained based on the smoothed mean spectra from both sides of the sample. Fig. 4 shows the mean spectrum of the ROI in Fig. 3, as well as the MS of the corresponding pork sample. Fig. 5(b) shows the spectral profiles (i.e. mean spectrum) of different areas (marked in Fig. 5(a)) such as pure fat, marbling, and lean part of the pork sample, which are similar to the mean spectra of fat layer, lean portion, and marbling pixels reported in Barbin et al. (2012). All three different spectral profiles produced peak values around the wavelength of 1080 nm, and local maxima around 1270 nm. The spectral profile of pure fat also had another local maximum around 1635 nm, as well as the spectral profile of marbling even though its local maximum was very small. The mean spectrum of lean part was almost zero over the range of wavelengths 1300–1700 nm. Comparing the MS of the pork sample shown in Fig. 4 and the spectral profiles in Fig. 5(b), it is clear that
Fig. 4. Mean spectra of ROI for both sides of the pork sample and MS of the corresponding pork sample.
the MS of the pork sample is the integration of spectral profiles of marbling and lean part which are components of loin eye. 3.2. Selection of critical wavelengths Spectral features (MS) of all pork samples are shown in Fig. 6, as well as the first (MS1) and second (MS2) derivatives of MS obtained
Fig. 5. Spectral profiles of different areas. (a) Pork sample marked with the areas of pure fat, marbling, and lean part; (b) spectral profiles of the marked areas.
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Fig. 6. Spectral profiles of (a) spectral features (MS), (b) 1st derivative of spectral features (MS1), and (c) 2nd derivative of spectral features (MS2).
using the Savitzky–Golay method. Correlation analysis was conducted between the chemical IMF content and each of MS, MS1, and MS2, to select the critical wavelengths for the prediction of IMF content. The criterion of selecting critical wavelengths is that the critical wavelengths should produce the highest (maximal or minimal) correlation coefficients that should be statistically significant (i.e. the corresponding p-values were smaller than 0.05). The maximum and minimum of correlation coefficients between chemical IMF content and different spectral profiles were listed in Table 2, as well as the corresponding p-values and the wavelengths. According to the selection criterion of critical wavelengths, five wavelengths determined by the first and second
Table 2 Correlation analysis between chemical IMF content and spectral features. Spectral profile
Rmax/min
p-Value
Wavelength (nm)
Spectral feature (MS)
0.40 0.34 0.88 0.88 0.92 0.81
0.0800 0.1438 0.0001 0.0001 0.0001 0.0001
1143 1023 1076, 1258 1191 1210 1129
1
1st derivative of MS (MS ) 2nd derivative of MS (MS2)
derivatives of spectral features, i.e. 1076, 1129, 1191, 1210, and 1258 nm were recognized as the critical wavelengths for the prediction of IMF content. Among the five critical wavelengths, 1076 and 1258 nm were the global/local maximum of MS, 1191 nm was the local minimum of MS, 1129 and 1210 nm were the inflection points of MS where a dramatic change happened.
3.3. Extraction of image line features The wide line detector (Liu et al., 2012) was applied to extract image line features from the ROI of pork samples at the critical wavelengths. The extraction results of image line features at different critical wavelengths for the ROI in Fig. 3(b) were shown in Fig. 7 where the radius of circular mask r is 10, the intensity contrast threshold t is 4, the global threshold l is 0.3, and the minimum area of interest a is 30. The parameters were determined based on trial-and-error. The same combination of parameters was used for all pork samples. The proportion of IMF fleck areas (PFA) at different critical wavelengths was calculated for all pork samples according to Eq. (2) and the statistics of the PFA were listed in Table 3. Pearson’s correlation coefficients between the chemical IMF content and
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Fig. 7. Extraction results of image line features at (a) 1076 nm, (b) 1129 nm, (c) 1191 nm, (d) 1210 nm, and (e) 1258 nm.
Table 3 Statistics of PFA for all samples.
Table 5 Statistics of PFA for the calibration and validation sets.
Wavelengths (nm)
Mean
Max
Min
Standard deviation
1076 1129 1191 1210 1258
0.038 0.046 0.067 0.060 0.056
0.056 0.068 0.170 0.124 0.080
0.018 0.024 0.026 0.028 0.028
0.012 0.012 0.033 0.022 0.013
Wavelengths (nm)
Set
Mean
Max
Min
Standard deviation
1076
Calibration Validation Calibration Validation Calibration Validation Calibration Validation Calibration Validation
0.040 0.035 0.048 0.043 0.067 0.069 0.061 0.058 0.057 0.054
0.056 0.053 0.068 0.061 0.170 0.125 0.124 0.101 0.080 0.067
0.022 0.018 0.024 0.026 0.026 0.042 0.028 0.039 0.028 0.042
0.012 0.012 0.013 0.012 0.035 0.031 0.023 0.021 0.015 0.008
1129 1191 1210
Table 4 Correlation coefficients between chemical IMF content and PFA at critical wavelengths. Wavelengths (nm)
R
p-Value
1076 1129 1191 1210 1258
0.92 0.80 0.39 0.45 0.65
0.0001 0.0001 0.089 0.046 0.002
the PFA at different critical wavelengths were also calculated and listed in Table 4 as well as the corresponding p-value. The highest correlation (R = 0.92, P 0.0001) was obtained at the wavelength of 1076 nm where the spectral features MS produced the global maximum. The PFA had a very strong correlation (R = 0.80, P 0.0001) with the chemical IMF content at one inflection point (1129 nm) and a moderate correlation (R = 0.45, P < 0.05) at another inflection point (1210 nm). The proportion of IMF fleck areas were strongly correlated (R = 0.65, P < 0.005) with the chemical IMF content at the local maximum (1258 nm) and had a low correlation (R = 0.39, P < 0.1) at the local minimum (1191 nm). All critical wavelengths were used for modeling to predict the IMF content. 3.4. Selection of models using stepwise procedure All pork samples were divided into two sets: the calibration set and the validation set. The statistics of the calibration set (n = 13)
1258
and the validation set (n = 7) at different critical wavelengths is listed in Table 5. The PFA values of the calibration set at all critical wavelengths were used as the potential variables of the stepwise procedure. PFA at each critical wavelength was used separately as the first entry into the initial model defined by Eq. (3) to build different multilinear models for prediction of pork IMF content. Table 6 lists the regression coefficients of the multilinear models with the first entry variable at different critical wavelengths, as well as the multilinear model with no first entry variable forced into the initial model. The use of the first entry variables at the wavelengths of 1076 and 1258 nm led to the same multilinear model, MLR15, while the use of the first entry variables at the wavelengths of 1191 and 1210 nm led to another multilinear model, MLR134. When the PFA value at the wavelength 1129 nm was used as the first entry variable, the obtained multilinear model was MLR12 which included the terms at the wavelengths of 1076 nm and 1129 nm. The MLR15 model was obtained again when no variable was forced into the initial model at the beginning of the stepwise procedure. The wavelength of 1076 nm was involved in all the multilinear models no matter which critical wavelength was used as the first entry variable. This indicated that the PFA obtained from the wavelength of 1076 nm might have the most explanatory power, which was consistent with the highest correlation between the chemical IMF content and the PFA values obtained at this wavelength.
Table 6 Regression coefficients of the multilinear models from the stepwise procedure with different first entry wavelengths. Initial term
Wavelength (nm)
Models
a0
a1
a2
a3
a4
a5
1 2 3 4 5 None
1076 1129 1191 1210 1258 –
MLR15 MLR12 MLR134 MLR134 MLR15 MLR15
0.28 0.19 0.67 0.67 0.28 0.28
91.96 100.81 81.47 81.47 91.96 91.96
0 43.99 0 0 0 0
0 0 43.76 43.76 0 0
0 0 77.19 77.19 0 0
32.08 0 0 0 32.08 32.08
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Fig. 8. Measured and predicted IMF content (%) for calibration and validation sets using the multilinear model (a) MLR12 at the selected wavelengths of 1076 and 1129 nm, (b) MLR15 at 1076 and 1258 nm, and (c) MLR134 at 1076, 1191, and 1210 nm.
Fig. 8 shows the accuracies of the three multilinear models, MLR12, MLR15 and MLR134, for predicting the pork IMF content and their performances given as R2 , adjusted R2, RMSEC, and RMSEV in Table 7. The model using three critical wavelengths, MLR134 (R2c ¼ 0:93; adjusted R2c ¼ 0:91; RMSEC ¼ 0:19), produced higher prediction results on the calibration set than the two models using two critical wavelengths, MLR12 (R2c ¼ 0:86, adjusted R2c ¼ 0:84; RMSEC ¼ 0:27) and MLR15 (R2c ¼ 0:90; adjusted R2c ¼ 0:88; RMSEC ¼ 0:23), but the lower prediction on the validation set with R2v ¼ 0:82, adjusted R2v ¼ 0:64, and RMSEV ¼ 0:38. This indicates that the regression models based on two critical wavelengths are more robust than the models developed by three critical wavelengths. Comparing the two models with two critical
Table 7 Performance of the MLR models. Models
MLR12 MLR15 MLR134
Calibration R2c
Adjusted
0.86 0.90 0.93
0.84 0.88 0.91
Validation R2c
RMSEC
R2v
Adjusted R2v
RMSEV
0.27 0.23 0.19
0.92 0.88 0.82
0.89 0.83 0.64
0.24 0.27 0.38
wavelengths, the model MLR12 (R2v ¼ 0:92, adjusted R2v ¼ 0:89; RMSEV ¼ 0:24) created better prediction results on the validation set than the model MLR15 (R2v ¼ 0:88, adjusted R2v ¼ 0:83, and RMSEV ¼ 0:27). The reason might be that the correlation between the chemical IMF content and the PFA values at the wavelength of 1129 nm (R = 0.80) was higher than the correlation at the wavelength of 1258 nm (R = 0.65).
3.5. The PLS model The same calibration and validation sets were used for establishing the PLS model. In order to determine the number of components (i.e. the latent factors) for the PLS model, the PLS regression was performed with the same number of components (n = 5) as predictors X and the percentage of variance explained in the response (Y) was plotted in Fig. 9(a) as a function of the number of components. The first component explained only 32% of the variance in Y. The second and third components made significant contributions to the percentage of variance explained in the response up to nearly 95%, while very little contribution was obtained when added the last two components. So the ideal number of the PLS components in the model was 3.
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Fig. 9. Prediction of IMF content (%) using the PLS model. (a) The percentage of variance explained in the response as a function of the number of components, (b) measured and predicted IMF content (%) for calibration and validation sets using the three-component PLS model.
Table 8 Performance of the PLS model with the first 3 PLS components. Models
R2c
Adjusted R2c
RMSEC
R2v
Adjusted R2v
RMSEV
PLSR
0.94
0.92
0.17
0.97
0.93
0.17
The chemical IMF content of pork samples and the predicted values calculated using the 3-component PLS model are shown in Fig. 9(b) and Table 8 lists the performance of the PLS model. Higher accuracy was obtained using the PLS model for both calibration set (R2c ¼ 0:94; adjusted R2c ¼ 0:92; RMSEC ¼ 0:17) and validation set (R2v ¼ 0:97; adjusted R2v ¼ 0:93; RMSEV ¼ 0:17) comparing to the results based on the MLR models. This not only indicated that the PLS model might be more efficient than the MLR model for prediction of the IMF content of pork, but also showed the strong possibility of determining the IMF content in a rapid, accurate, and non-destructive way. 4. Conclusions and discussion In this study, hyperspectral imaging technology along with the advanced image processing method was applied to predict the IMF content of pork. High prediction results were obtained using different linear regression models. This shows the efficiency of the intramuscular fat detection using the wide line detector. Since only the selected critical wavelengths were used to establish the multiple linear regression models, the high prediction results also demonstrates the potentials of developing a non-destructive and realtime spectral system to predict the IMF content of pork. Although the linear model created in this study produced promising results for the prediction of pork IMF content, the non-linear criterion is still necessary to investigate for better understanding of the pork IMF distribution especially for a large population of pork samples. The pork samples used in this study were obtained from different local grocery stores and the thickness ranged between 1 and 1.5 cm. The effect of the sample thickness on the prediction
results should also be studied to understand how the results vary with different thickness of samples and what thickness (or what the range of thickness) is best for the use of hyperspectral imaging to predict IMF distribution. Therefore, our future research work on this topic will focus on establishing the non-linear criterion for pork IMF distribution and investigating the effect of the sample thickness on the prediction results. References AOAC, 2000. Official methods an analysis. Association of Official Analytical Chemist. EUA. Barbin, D., Elmasry, G., Sun, D.W., Allen, P., 2012a. Near-infrared hyperspectral imaging for grading and classification of pork. Meat Sci. 90, 259–268. Barbin, D.F., ElMasry, G., Sun, D.W., Allen, P., 2012b. Predicting quality and sensory attributes of pork using near-infrared hyperspectral imaging. Anal. Chim. Acta 719, 30–42. Faucitano, L., Rivest, J., Daigle, J.P., Levesque, J., Gariepy, C., 2004. Distribution of intramuscular fat content and marbling within the longissimus muscle of pigs. Canad. J. Animal Sci. 84, 57–61. Folch, J., Lees, M., Slone-Stanley, H.S., 1957. A simple method for the isolation and purification of lipids from animal tissues. J. Biolo. Chem. 226, 497–509. Huang, H., Liu, L., Ngadi, M.O., Gariepy, C., 2013. Prediction of pork marbling scores using pattern analysis techniques. Food Control 31 (1), 224–229. Lee, K., Kang, S., Delwiche, S., Kim, M., Noh, S., 2008. Correlation analysis of hyperspectral imagery for multispectral wavelength selection for detection of defects on apples. Sens. Instrum. Food Qual. Safe. 2, 90–96. Liu, L., Ngadi, M.O., Prasher, S.O., Gariépy, C., 2010. Categorization of pork quality using Gabor filter-based hyperspectral imaging technology. J. Food Eng. 99 (3), 284–293. Liu, L., Ngadi, M.O., Prasher, S.O., Gariepy, C., 2012. Objective determination of pork marbling scores using the wide line detector. J. Food Eng. 110 (3), 497–504. NPB (National pork board), 2002. Pork quality standards. Des Moines, IA USA. Qiao, J., Ngadi, M.O., Wang, N., Gariepy, C., Prasher, S.O., 2007a. Pork quality and marbling level assessment using a hyperspectral imaging system. J. Food Eng. 83, 10–16. Qiao, J., Wang, N., Ngadi, M.O., Gunenc, A., Monroy, M., Gariepy, C., Prasher, S.O., 2007b. Prediction of drip-loss, pH & colour for pork using a hyperspectral imaging technique. Meat Sci. 76, 1–8. Savitzky, A., Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36 (8), 1627–1639. Song, S., Gong, W., Zhu, B., Huang, X., 2011. Wavelength selection and spectral discrimination for paddy rice, with laboratory measurements of hyperspectral leaf reflectance. ISPRS J. Photogram. Remote Sens. 66, 672–682.
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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Predicting intramuscular fat content of pork using hyperspectral imaging L. Liu, M.O. Ngadi ⇑ Department of Bioresource Engineering, McGill University, Macdonald Campus, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec H9X 3V9, Canada
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 28 November 2013 Accepted 12 February 2014 Available online 22 February 2014 Keywords: Pork Intramuscular fat IMF content Hyperspectral imaging Wide line detector Linear regression PLS Stepwise procedure
a b s t r a c t Intramuscular fat (IMF) content is an important quality trait of pork. It influences taste, juiciness and tenderness of the meat. The aim of this study was to develop an objective, rapid, and non-destructive method for predicting the IMF content of pork using hyperspectral imaging technology. Critical wavelengths were selected using correlation analysis based on the spectral profiles of pork samples. The visual IMF flecks on both sides of pork chops were extracted using the wide line detector at the selected critical wavelengths. The proportion of IMF fleck areas (PFA) at critical wavelengths was used for modeling to predict the IMF content of pork. Both stepwise procedures and partial least squares (PLS) analysis were employed to establish the prediction models. Three different multilinear models were obtained using the stepwise procedure with different first entry variable of the initial model. A 3-component PLS model was developed for prediction of the IMF content. The PLS model outperformed the three multilinear models. The coefficients of determination (R2) of the PLS model on the calibration set and validation set were 0.94 and 0.97, respectively, and the adjusted R2 were 0.92 and 0.93, respectively. The prediction results of mutilinear models and PLS models indicated the potentials of using hyperspectral imaging to predict the IMF content of pork. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Intramuscular fat (IMF) corresponds to the amount of fat found between muscle fiber bundles within muscles. The amount of IMF, i.e. IMF content, varies between species, breeds and muscle types. IMF content plays an important role in various quality traits of pork. It is generally accepted that a higher IMF content has a positive effect on sensory quality traits of pork, for example, juiciness, tenderness, and flavor. Since it is strongly related to carcass quality, IMF content is also a useful tool to make genetic improvement in selection programs for carcass quality in the pork industry. IMF content is normally determined by chemical extraction of lipid from muscle samples (Folch et al., 1957). Chemical extraction is time-consuming, labor-intensive and destructive, which makes it not suitable for industrial application. In the pork industry, another quality trait, i.e. the marbling score, is widely used to estimate the IMF content of muscles. Marbling refers to the visible IMF of muscles. Marbling scores are visually assessed by experienced assessors by comparing marbling levels of meat with a standardized chart system (NPB, 2002). However, visual and subjective
⇑ Corresponding author. Tel.: +1 514 3987779; fax: +1 514 3988387. E-mail address: [email protected] (M.O. Ngadi). http://dx.doi.org/10.1016/j.jfoodeng.2014.02.007 0260-8774/Ó 2014 Elsevier Ltd. All rights reserved.
measurement of marbling scores can be difficult and has poor repeatability of results. This makes the estimation of IMF content unreliable. Therefore, an objective, rapid, accurate and nondestructive measurement for the IMF content would be an asset for the pork industry. Recent research efforts have shown high potential of hyperspectral imaging (HSI) in the development of objective, rapid, and non-destructive systems for assessment of food quality. Hyperspectral imaging is an emerging, cutting-edge and nondestructive analytical technology that combines spectroscopy and digital imagery to simultaneously acquire both spectral and spatial information from an object. A hyperspectral image, also called ‘hypercube’, is a three-dimensional image with two spatial dimensions and one spectral dimension (Qiao et al., 2007a,b), which contains enormous information about the analyzed object. The combination of spectral and spatial information makes hyperspectral imaging able to ascertain minor and/or subtle physical and chemical properties in an object. The advantages of hyperspectral imaging indicate that the technology has a promising future for food quality inspections. With respect to pork, hyperspectral imaging has been successfully applied for classification of pork qualities (Qiao et al., 2007a; Liu et al., 2010; Barbin et al., 2012a) and for prediction of quality traits such as color, pH, and drip loss (Qiao et al., 2007b; Barbin et al., 2012b). Hyperspectral imaging was also
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Table 1 Statistics of pork samples.
Chemical IMF content
Mean
Max
Min
Std
2.06
3.21
0.61
0.79
applied for assessment of pork marbling scores based on the image texture index measured by angular second moment (ASM) (Qiao et al., 2007a). The results showed that the sorted results using ASM were higher than that obtained by experienced assessors with an error around 1.0. In the very recent publications, an advanced image processing method, the wide line detector (WLD), was introduced to detect marblings of intact pork muscles from digital color pictures (Liu et al., 2012; Huang et al., 2013). The high prediction results at all the three RGB channels indicated the ability of the wide line detector to extract useful image features for prediction of marbling scores, i.e. the amount of the visible IMF of muscles. This strongly suggested the potential of using the WLD to predict the IMF content of pork. This paper aimed to develop advanced hyperspectral imaging techniques to predict the IMF content of pork in a non-destructive, rapid and accurate way. The specific objectives were to extract spectral features and identify the critical wavelengths for prediction of the IMF content; to detect the IMF flecks on both sides of pork chops at the critical wavelengths using the wide line detector; and to develop and validate different regression models based on detected IMF flecks to predict the IMF content of pork. 2. Materials and methods 2.1. Pork samples Four packages of pork loin center chops were bought from three different grocery stores in Montreal, Quebec, Canada. A total of 20 pork samples with thickness between 1 and 1.5 cm were used for predicting intramuscular fat content of pork.
Fig. 1. The near infrared hyperspectral imaging system used in the study.
Extraction Unit SER 148/6 (Velp Scientifica, Usmate, Italy), in accordance with Official Method 960.39 (AOAC, 2000). IMF content was determined as the ratio of the mass of extracted fat and the mass of the sample before freezing. The statistics of IMF content for all pork samples are listed in Table 1.
2.2. Near infrared hyperspectral imaging system and image acquisition A laboratory near infrared (NIR) hyperspectral imaging (HSI) system was set up to collect the hyperspectral images of the pork samples. The NIR-HSI system consisted of an InGaAs camera mounted with a line-scan spectrograph (Headwall photonics, USA, 900–1700 nm), two halogen lamps (JDR-C GU10, 120 V, 50 W) placed an angle of 45° to illuminate the camera’s field of view, a moving conveyer driven by a stepping motor with a userdefined speed (MDIP22314, Intelligent motion system Inc., USA), an anodized aluminum enclosure, and a PC, as shown in Fig. 1. Each pork sample was placed on a dark panel and double-sideimaged line by line using the NIR-HSI system with an optimal speed. The obtained hypercube (hyperspectral image with the BIL format) included 167 image planes over the range of wavelengths 900–1700 nm with the resolution of 4.8 nm. A total of 40 hypercubes were obtained for this study.
2.4. Image preprocessing All the acquired hypercubes were processed and analyzed using MATLAB 7.13.0.564 (The MathWorks, Inc., Mass., USA). Each hypercube was corrected from the dark current of the camera prior to segmenting the region of interest (ROI) of each sample. To correct the spectral images, a dark image B and a white image W were obtained by covering the lens with a cap, and by taking an image from a standard white reference (Spectralon, Labsphere,
2.3. Intramuscular fat content analysis After imaging, all pork samples were carefully trimmed to remove peripheral and intermuscular fat as well as the connective tissue and surrounding muscles. Samples were freeze-dried and ground in a coffee grinder (Bodum 5678-57; C-Mill, Bodum Inc., New York, NY, USA). A ground meat sample of known weight was used for determining the intramuscular fat (IMF) content in duplicate with petroleum ether extraction using a Solvent
Fig. 2. Corrected image planes of (a) Side 1 and (b) Side 2 of a pork sample at 1076 nm.
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North Sutton, New Hamshire, USA), respectively. The relative reflectance I of each image plane was calculated by
I¼
I0 B ; W B
ð1Þ
where I0 was the original image plane. Examples of the corrected image planes are shown in Fig. 2. The region of interest (ROI) of pork samples was the loin area without the peripheral and intermuscular fat as well as the connective tissue and the surrounding muscles. The ROI of each hypercube was obtained using the segmentation algorithm presented in Liu et al. (2012). 2.5. Spectral features and wavelengths selection The mean spectrum of the ROI (i.e. the average values of the ROI of image planes over the wavelength range) of each pork sample was used as spectral features of the hypercube. Each mean spectrum was smoothed using the Savitzky–Golay (Savitzky and Golay, 1964) filter with a window length of 11 points. Since the pork samples were double side imaged, each pork sample had two mean spectra corresponding to the two sides of the pork chop. The spectral feature of a pork sample denoted as MS was defined as the average profile of the smoothed mean spectra for both sides of the pork sample. The hyperspectral images contain high correlated data between adjacent wavelengths. It was not necessary to include all measured 167 wavebands in the application, not only because of the high correlation among the wavelengths, but also due to the purpose of developing application-specific multispectral imaging systems for real-time application. Correlation analysis, principal component analysis (PCA), and partial least squares (PLS) are representative methods for wavelength selection (Lee et al., 2008; Song et al., 2011). In this study, correlation analysis based on spectral feature (MS), 1st derivative (MS1) and 2nd derivative (MS2) of MS using the Savitzky–Golay method (Savitzky and Golay, 1964) was applied to select the critical wavelengths with rich spectral information related to the intramuscular fat (IMF) content. The Pearson’s correlation coefficients between chemical IMF content and MS (R0), MS1 (R1), MS2 (R2) were calculated, respectively, and the wavelengths that produced the highest correlation values were selected as the critical wavelengths. 2.6. Image line feature extraction at the critical wavelengths In previous work, marbling in pork was recognized as image line feature and was well detected using the wide line detector (Liu et al., 2012). Based on the detected marbling, marbling score was successfully assessed using linear regression models. Since the IMF content and marbling scores are correlated and follow a similar pattern (Faucitano et al., 2004), the image line feature were extracted at the critical wavelengths for IMF content prediction. The wide line detector presented in Liu et al. (2012) was used to extract the line features of image planes at the critical wavelengths. A simple thresholding method was also applied for the extracted line feature images to obtain the IMF flecks. A total of four parameters were involved in the wide line detector and the thresholding method: the radius of circular mask (r) determining the maximum width of marblings that can be detected, the intensity contrast threshold (t) defining the minimum visibility of marblings that can be detected, the global threshold (l) controlling the noise level in the detected marblings, and the minimum area of interest (a) determining the smallest object can be regarded as a marbling. The ratio of the IMF fleck area against the ROI area was calculated for each side of the pork samples. The proportion of IMF fleck
areas of each sample, PFA, was the average value of ratios of IMF fleck areas of both sides and defined as follows:
PFA ¼
areaðIMF 1 Þ areaðIMF 2 Þ 2; þ areaðROI1 Þ areaðROI2 Þ
ð2Þ
where area(IMFi) (i = 1, 2) is the total number of pixels of the detected IMF flecks on Side i, and area(ROIi) is the total number of pixels of the corresponding ROI. The PFA at critical wavelengths were used for modeling to predict the IMF content. 2.7. Modeling The relationship between chemical IMF content and PFA of pork samples was calculated over the critical wavelengths with Pearson’s correlation coefficients as well as the significance level p-value using the function ‘corr’ in MATLAB 7.13.0.564 (The MathWorks, Inc., Mass., USA). All pork samples (n = 20) were divided into two sets, the calibration set (n = 13) and the validation set (n = 7). In order to investigate the ability of the obtained PFA to predict the chemical IMF content of pork, both stepwise procedures and partial least squares (PLS) analysis were employed to build the prediction models. 2.7.1. Stepwise procedure and multi-linear regression Stepwise procedure, also called stepwise regression, is a systematic procedure for construction of a regression model that involves automatic selection of independent variables based on their statistical significance in the regression. The p-value of an F-statistic is used as the entrance/exit criterion of potential variables for the models after the initial model is decided. The procedure may build different models from the same set of potential variables due to various variables included in the initial model. The procedure terminates when no entrance or exit of variables improves the model. The purpose of using stepwise procedure was to find the subset of critical wavelengths where the PFA can best predict IMF content of pork. In this study, a multi-linear regression (MLR) model was selected as the initial model for the stepwise procedure, which was defined as
b ¼ a0 þ Y
X ai PFAi ;
ð3Þ
i
b is the vector of predicted IMF content, PFAi is the vector of where Y PFA at the critical wavelengths, a0 is the constant term and ai is the regression coefficient of the variable PFAi. Each potential variable was used as the first entry into the initial model to build multilinear models for predicting IMF content of pork. The qualities of multi-linear models were evaluated by the coefficient of determination between the predicted and measured IMF content of the calibration (R2c )/validation (R2v ) set, the adjusted R2c and R2v , the root mean square error of calibration (RMSEC), and the root mean square error of validation (RMSEV). A good model should have a low RMSEC and RMSEV, a high R2 /adjusted R2, and a small difference between R2 and adjusted R2 . 2.7.2. Partial least squares regression PLS regression (i.e. Partial Least Squares regression) is a statistical technique that generalizes and combines a large number of predictors from principal component analysis and multiple regression to find a new variable space based on small number of orthogonal components (latent variables) which are mutually independent linear combinations of predictors. It is particularly useful when the experimental data (PFA at the critical wavelengths) has more predictors than observations, and/or is highly correlated.
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In this study, the aim of PLS analysis is to find a mathematical relationship between a set of predictors, X matrix (N13 pork samples PFAn critical wavelengths), and the dependent variables, Y matrix (N13 pork samples 1). The PFA values at the identified critical wavelengths of the 13 pork samples were used as the predictors (X) and the values of chemical IMF content of the calibration set as the dependent variables (Y). Typically, most of the variations can be captured within the first few components/latent variables, while the remaining components describe random noise or linear dependencies between the wavelengths/predictors. The optimal number of PLS components used for prediction was determined by the accumulated percentage of variance explained in Y. The accumulated percentage of variance was a function of the number of components. The quality of the predictive model was also evaluated by the coefficient of determination R2c and R2v , the adjusted R2c and R2v , RMSEC, and RMSEV.
19
Fig. 3. Region of interest (ROI) of the image planes in Fig. 2.
3. Results and discussion 3.1. Spectral features of pork samples Each hypercube was first corrected using Eq. (1) and then processed to obtain the region of interest (ROI). An example of the image planes of corrected hypercubes from both sides of a pork sample at the wavelength of 1076 nm is shown in Fig. 2 and the corresponding segmented ROI shown in Fig. 3. The mean spectrum of each ROI was calculated and smoothed, and the spectral feature MS of each sample was obtained based on the smoothed mean spectra from both sides of the sample. Fig. 4 shows the mean spectrum of the ROI in Fig. 3, as well as the MS of the corresponding pork sample. Fig. 5(b) shows the spectral profiles (i.e. mean spectrum) of different areas (marked in Fig. 5(a)) such as pure fat, marbling, and lean part of the pork sample, which are similar to the mean spectra of fat layer, lean portion, and marbling pixels reported in Barbin et al. (2012). All three different spectral profiles produced peak values around the wavelength of 1080 nm, and local maxima around 1270 nm. The spectral profile of pure fat also had another local maximum around 1635 nm, as well as the spectral profile of marbling even though its local maximum was very small. The mean spectrum of lean part was almost zero over the range of wavelengths 1300–1700 nm. Comparing the MS of the pork sample shown in Fig. 4 and the spectral profiles in Fig. 5(b), it is clear that
Fig. 4. Mean spectra of ROI for both sides of the pork sample and MS of the corresponding pork sample.
the MS of the pork sample is the integration of spectral profiles of marbling and lean part which are components of loin eye. 3.2. Selection of critical wavelengths Spectral features (MS) of all pork samples are shown in Fig. 6, as well as the first (MS1) and second (MS2) derivatives of MS obtained
Fig. 5. Spectral profiles of different areas. (a) Pork sample marked with the areas of pure fat, marbling, and lean part; (b) spectral profiles of the marked areas.
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Fig. 6. Spectral profiles of (a) spectral features (MS), (b) 1st derivative of spectral features (MS1), and (c) 2nd derivative of spectral features (MS2).
using the Savitzky–Golay method. Correlation analysis was conducted between the chemical IMF content and each of MS, MS1, and MS2, to select the critical wavelengths for the prediction of IMF content. The criterion of selecting critical wavelengths is that the critical wavelengths should produce the highest (maximal or minimal) correlation coefficients that should be statistically significant (i.e. the corresponding p-values were smaller than 0.05). The maximum and minimum of correlation coefficients between chemical IMF content and different spectral profiles were listed in Table 2, as well as the corresponding p-values and the wavelengths. According to the selection criterion of critical wavelengths, five wavelengths determined by the first and second
Table 2 Correlation analysis between chemical IMF content and spectral features. Spectral profile
Rmax/min
p-Value
Wavelength (nm)
Spectral feature (MS)
0.40 0.34 0.88 0.88 0.92 0.81
0.0800 0.1438 0.0001 0.0001 0.0001 0.0001
1143 1023 1076, 1258 1191 1210 1129
1
1st derivative of MS (MS ) 2nd derivative of MS (MS2)
derivatives of spectral features, i.e. 1076, 1129, 1191, 1210, and 1258 nm were recognized as the critical wavelengths for the prediction of IMF content. Among the five critical wavelengths, 1076 and 1258 nm were the global/local maximum of MS, 1191 nm was the local minimum of MS, 1129 and 1210 nm were the inflection points of MS where a dramatic change happened.
3.3. Extraction of image line features The wide line detector (Liu et al., 2012) was applied to extract image line features from the ROI of pork samples at the critical wavelengths. The extraction results of image line features at different critical wavelengths for the ROI in Fig. 3(b) were shown in Fig. 7 where the radius of circular mask r is 10, the intensity contrast threshold t is 4, the global threshold l is 0.3, and the minimum area of interest a is 30. The parameters were determined based on trial-and-error. The same combination of parameters was used for all pork samples. The proportion of IMF fleck areas (PFA) at different critical wavelengths was calculated for all pork samples according to Eq. (2) and the statistics of the PFA were listed in Table 3. Pearson’s correlation coefficients between the chemical IMF content and
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Fig. 7. Extraction results of image line features at (a) 1076 nm, (b) 1129 nm, (c) 1191 nm, (d) 1210 nm, and (e) 1258 nm.
Table 3 Statistics of PFA for all samples.
Table 5 Statistics of PFA for the calibration and validation sets.
Wavelengths (nm)
Mean
Max
Min
Standard deviation
1076 1129 1191 1210 1258
0.038 0.046 0.067 0.060 0.056
0.056 0.068 0.170 0.124 0.080
0.018 0.024 0.026 0.028 0.028
0.012 0.012 0.033 0.022 0.013
Wavelengths (nm)
Set
Mean
Max
Min
Standard deviation
1076
Calibration Validation Calibration Validation Calibration Validation Calibration Validation Calibration Validation
0.040 0.035 0.048 0.043 0.067 0.069 0.061 0.058 0.057 0.054
0.056 0.053 0.068 0.061 0.170 0.125 0.124 0.101 0.080 0.067
0.022 0.018 0.024 0.026 0.026 0.042 0.028 0.039 0.028 0.042
0.012 0.012 0.013 0.012 0.035 0.031 0.023 0.021 0.015 0.008
1129 1191 1210
Table 4 Correlation coefficients between chemical IMF content and PFA at critical wavelengths. Wavelengths (nm)
R
p-Value
1076 1129 1191 1210 1258
0.92 0.80 0.39 0.45 0.65
0.0001 0.0001 0.089 0.046 0.002
the PFA at different critical wavelengths were also calculated and listed in Table 4 as well as the corresponding p-value. The highest correlation (R = 0.92, P 0.0001) was obtained at the wavelength of 1076 nm where the spectral features MS produced the global maximum. The PFA had a very strong correlation (R = 0.80, P 0.0001) with the chemical IMF content at one inflection point (1129 nm) and a moderate correlation (R = 0.45, P < 0.05) at another inflection point (1210 nm). The proportion of IMF fleck areas were strongly correlated (R = 0.65, P < 0.005) with the chemical IMF content at the local maximum (1258 nm) and had a low correlation (R = 0.39, P < 0.1) at the local minimum (1191 nm). All critical wavelengths were used for modeling to predict the IMF content. 3.4. Selection of models using stepwise procedure All pork samples were divided into two sets: the calibration set and the validation set. The statistics of the calibration set (n = 13)
1258
and the validation set (n = 7) at different critical wavelengths is listed in Table 5. The PFA values of the calibration set at all critical wavelengths were used as the potential variables of the stepwise procedure. PFA at each critical wavelength was used separately as the first entry into the initial model defined by Eq. (3) to build different multilinear models for prediction of pork IMF content. Table 6 lists the regression coefficients of the multilinear models with the first entry variable at different critical wavelengths, as well as the multilinear model with no first entry variable forced into the initial model. The use of the first entry variables at the wavelengths of 1076 and 1258 nm led to the same multilinear model, MLR15, while the use of the first entry variables at the wavelengths of 1191 and 1210 nm led to another multilinear model, MLR134. When the PFA value at the wavelength 1129 nm was used as the first entry variable, the obtained multilinear model was MLR12 which included the terms at the wavelengths of 1076 nm and 1129 nm. The MLR15 model was obtained again when no variable was forced into the initial model at the beginning of the stepwise procedure. The wavelength of 1076 nm was involved in all the multilinear models no matter which critical wavelength was used as the first entry variable. This indicated that the PFA obtained from the wavelength of 1076 nm might have the most explanatory power, which was consistent with the highest correlation between the chemical IMF content and the PFA values obtained at this wavelength.
Table 6 Regression coefficients of the multilinear models from the stepwise procedure with different first entry wavelengths. Initial term
Wavelength (nm)
Models
a0
a1
a2
a3
a4
a5
1 2 3 4 5 None
1076 1129 1191 1210 1258 –
MLR15 MLR12 MLR134 MLR134 MLR15 MLR15
0.28 0.19 0.67 0.67 0.28 0.28
91.96 100.81 81.47 81.47 91.96 91.96
0 43.99 0 0 0 0
0 0 43.76 43.76 0 0
0 0 77.19 77.19 0 0
32.08 0 0 0 32.08 32.08
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Fig. 8. Measured and predicted IMF content (%) for calibration and validation sets using the multilinear model (a) MLR12 at the selected wavelengths of 1076 and 1129 nm, (b) MLR15 at 1076 and 1258 nm, and (c) MLR134 at 1076, 1191, and 1210 nm.
Fig. 8 shows the accuracies of the three multilinear models, MLR12, MLR15 and MLR134, for predicting the pork IMF content and their performances given as R2 , adjusted R2, RMSEC, and RMSEV in Table 7. The model using three critical wavelengths, MLR134 (R2c ¼ 0:93; adjusted R2c ¼ 0:91; RMSEC ¼ 0:19), produced higher prediction results on the calibration set than the two models using two critical wavelengths, MLR12 (R2c ¼ 0:86, adjusted R2c ¼ 0:84; RMSEC ¼ 0:27) and MLR15 (R2c ¼ 0:90; adjusted R2c ¼ 0:88; RMSEC ¼ 0:23), but the lower prediction on the validation set with R2v ¼ 0:82, adjusted R2v ¼ 0:64, and RMSEV ¼ 0:38. This indicates that the regression models based on two critical wavelengths are more robust than the models developed by three critical wavelengths. Comparing the two models with two critical
Table 7 Performance of the MLR models. Models
MLR12 MLR15 MLR134
Calibration R2c
Adjusted
0.86 0.90 0.93
0.84 0.88 0.91
Validation R2c
RMSEC
R2v
Adjusted R2v
RMSEV
0.27 0.23 0.19
0.92 0.88 0.82
0.89 0.83 0.64
0.24 0.27 0.38
wavelengths, the model MLR12 (R2v ¼ 0:92, adjusted R2v ¼ 0:89; RMSEV ¼ 0:24) created better prediction results on the validation set than the model MLR15 (R2v ¼ 0:88, adjusted R2v ¼ 0:83, and RMSEV ¼ 0:27). The reason might be that the correlation between the chemical IMF content and the PFA values at the wavelength of 1129 nm (R = 0.80) was higher than the correlation at the wavelength of 1258 nm (R = 0.65).
3.5. The PLS model The same calibration and validation sets were used for establishing the PLS model. In order to determine the number of components (i.e. the latent factors) for the PLS model, the PLS regression was performed with the same number of components (n = 5) as predictors X and the percentage of variance explained in the response (Y) was plotted in Fig. 9(a) as a function of the number of components. The first component explained only 32% of the variance in Y. The second and third components made significant contributions to the percentage of variance explained in the response up to nearly 95%, while very little contribution was obtained when added the last two components. So the ideal number of the PLS components in the model was 3.
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Fig. 9. Prediction of IMF content (%) using the PLS model. (a) The percentage of variance explained in the response as a function of the number of components, (b) measured and predicted IMF content (%) for calibration and validation sets using the three-component PLS model.
Table 8 Performance of the PLS model with the first 3 PLS components. Models
R2c
Adjusted R2c
RMSEC
R2v
Adjusted R2v
RMSEV
PLSR
0.94
0.92
0.17
0.97
0.93
0.17
The chemical IMF content of pork samples and the predicted values calculated using the 3-component PLS model are shown in Fig. 9(b) and Table 8 lists the performance of the PLS model. Higher accuracy was obtained using the PLS model for both calibration set (R2c ¼ 0:94; adjusted R2c ¼ 0:92; RMSEC ¼ 0:17) and validation set (R2v ¼ 0:97; adjusted R2v ¼ 0:93; RMSEV ¼ 0:17) comparing to the results based on the MLR models. This not only indicated that the PLS model might be more efficient than the MLR model for prediction of the IMF content of pork, but also showed the strong possibility of determining the IMF content in a rapid, accurate, and non-destructive way. 4. Conclusions and discussion In this study, hyperspectral imaging technology along with the advanced image processing method was applied to predict the IMF content of pork. High prediction results were obtained using different linear regression models. This shows the efficiency of the intramuscular fat detection using the wide line detector. Since only the selected critical wavelengths were used to establish the multiple linear regression models, the high prediction results also demonstrates the potentials of developing a non-destructive and realtime spectral system to predict the IMF content of pork. Although the linear model created in this study produced promising results for the prediction of pork IMF content, the non-linear criterion is still necessary to investigate for better understanding of the pork IMF distribution especially for a large population of pork samples. The pork samples used in this study were obtained from different local grocery stores and the thickness ranged between 1 and 1.5 cm. The effect of the sample thickness on the prediction
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