Evaluation of pH in Sausages Stuffed in a Modified Casing with Orange Extracts by Hyperspectral Imaging Coupled with Response Surface Methodology

The pH values of sausages stuffed in natural hog casings with different modifications (soy lecithin, soy oil, orange extracts (OE) from waste orange peels, lactic acid in slush salt, and treatment time) after 16-day 4 °C storage were evaluated for the first time by hyperspectral imaging (350–1100 nm) coupled with response surface methodology (RSM). A partial least squares regression (PLSR) model was developed to relate the spectra to the pH of sausages. Spectral pretreatment, including first derivative, second derivative, multiplicative scatter correction (MSC), standard normal variate (SNV), normalization, and normalization, with different combinations was employed to improve model performance. RSM showed that only soy lecithin and OE interactively affected the pH of sausages (p < 0.05). The pH value decreased when the casing was treated with a higher concentration of soy lecithin with 0.26% OE. As the first and second derivatives are commonly used to eliminate the baseline shift, the PLSR model derived from absorbance pretreated by the first derivative in the full wavelengths showed a calibration coefficient of determination (R2) of 0.73 with a root mean square error of calibration of 0.4283. Twelve feature wavelengths were selected with a comparable R2 value compared with the full wavelengths. The prediction map enables the visualization of the pH evolution of sausages stuffed in the modified casings added with OE.


Introduction
Due to their special bite and unique flavor, natural casings are widely utilized in sausage production. Nevertheless, the high bursting incidence hinders the rapid and efficient large-scale manufacture of sausages. Nature casings are required to bear the high pressures generated during stuffing or precooking without compromising sausage quality. Previous studies have proven that casings can become more porous after modification and reduce the bursting that occurs during immersion vacuum cooling [1]. Due to the change in the microstructure of modified casings, microorganism invasion and oxidation can easily occur; therefore, a food-grade antioxidative or antimicrobial reagent is required to prolong the shelf life of modified casings for better commercial utilization.
Citrus fruit peels, which possess a large amount of useful and helpful biologically active compounds for human beings, are currently either directly discarded to landfills as fertilizer, used as animal feed, or sold as dried orange peels in China, serving as one of the ingredients of Chinese herbal medicine [2]. The waste of orange peels not only causes environmental problems, but it is also highly costly to deal with waste in accordance with the Food Recycling Law in Japan [3]. As a member of the flavonoids family and rich in the peels of citrus fruits, hesperidin has been demonstrated to be effective against liver cancer and lung cancer [4], possessing antioxidant [5] and antimicrobial properties [6,7]. The latest literature also reveals that flavonoids such as hesperidin and rutin can be regarded as the starting point for therapeutics against COVID-19 [8]. If the waste of orange peels can be taken full advantage of, it can not only reduce environmental issues but also utilize value-added products and increase industrial income [9]. As modified casings require an antioxidative or antimicrobial reagent, it is meaningful to add extracts from these waste orange peels. Fernández-López (2007) studied the quality of dry-cured sausages according to different concentrations of orange fiber powder (mixture of albedo, flavedo, and pulp) with a 28-day dry-curing time of 15 ± 1 • C and relative humidity of 75% [10]. The pH values of all samples decreased during the first week and then returned to similar values after 4 weeks. Fernández-Ginés et al. (2003) observed that a lower pH value was obtained when a higher concentration of orange fiber was used [11]. The reason for using citrus fiber was that it possesses better quality than other dietary fibers due to the presence of bioactive compounds such as flavonoids, polyphenols, carotenes, and antioxidant properties [11].
Response surface methodology (RSM) is a useful statistical method that can interpret the relationship between food processing parameters and the quality attributes of food products [12][13][14][15][16][17], especially if the effects of variables on the response are unknown. As a powerful design that can greatly reduce the number of experiments compared with a full experimental design, the central composite design (CCD) has been employed in several studies by RSM with a single run of different variable combinations and replicates only at the center point [18][19][20]. Currently, however, there are no relevant studies on combining sausage casing modification and orange extracts from waste orange peels by using RSM, which merits investigating their effects on sausage quality.
Hyperspectral imaging (HSI) is more advantageous than conventional spectroscopic methods, as it can provide the spectral information and spatial distribution of a subject simultaneously [21]. Prediction maps can provide more detailed information on how many and where attributes are exactly located. The pH changes of large Japanese sausages under different storage conditions were investigated by HSI via a distribution map developed by R statistics [21]. The results showed that the pH values of samples stored at 35 • C for 1, 3, and 5 days started to decrease in the surrounding area [19]. Compared to a conventional digital pH meter that can only identify the measuring spot, distribution maps generated by HSI can elaborate on how many different pH values exist in every spot in different test samples. The Cantonese sausage grade was classified by using multiple linear regression (MLR) and partial least squares regression (PLSR), and the best classification was achieved by using a successive projections algorithm coupled with MLR, with a predictive accuracy of 100% [22]. Shi et al. (2019) employed HSI to classify colonies from food fragments (sausage, bacon, and millet fragments) in an agar plate [23]. Kamrruzzaman et al. (2022) studied the moisture of red meat and corn using six different methods to select the wavelength in terms of model performance and demonstrated that competitive adaptive reweighted sampling (CARS) in tandem with PLSR is superior to PLSR models when developing models between the moisture and spectra of red meat and corn using a full spectral range [24]. Siripatrawan and Makino (2018) evaluated the changes in physicochemical, microbiological, and sensory attributes of packaged bratwurst (a type of sausage) during 20-day storage at 4 ± 1 • C [25]. Lightness, thiobarbituric acid, total viable counts, lactic acid bacteria, odor, and overall acceptability were found to be highly correlated with reflectance [25]. All these studies accentuate an unyielding interest in the application of HSI as an emerging method to detect different types of meat products.
Although previous studies have investigated the pH [26], color [27][28][29], and triphosphate content [30] of sausages by using HSI, scarce information has been obtained on evaluating the effects of extracts from waste orange peels on the pH of sausages after addition in a modified solution by using RSM and HSI combined with the PLSR algorithm.
The novelty of the current study is: (1) The simultaneous effects of five variables (different concentrations of soy lecithin, soy oil, lactic acid, orange extracts, and treatment times) on the pH of sausages during 15 days of storage were elucidated by RSM. (2) The pH of sausages stuffed in modified casings after adding orange extracts was elaborated for the first time by HSI. The pH changes of each pixel in casings responding to different concentrations of orange extracts were clearly illustrated via prediction maps. The results can provide a better understanding of how pH reacts with orange extracts and provide useful information for future investigations. (3) The relationship between pH and spectra from the surface of cylindrical sausages with modified casings was established for the first time by PLSR.
The purpose of this study is to evaluate the effects of five variables on the pH of sausages by using RSM. Following this, a quantitative model relating spectral data to the reference pH of sausage with this new type of casing is established. Consequently, wavelengths with high predictive power are chosen, and the distribution map of pH with differently treated casings is developed using image processing algorithms.

Soxhlet Extraction
The peels of Valencia sweet orange (Citrus sinensis) were first dried at 45 • C for 7 days. The dried orange peels were finely blade-milled into powder, and an average of 40.70 ± 0.52 g of orange powder was added to a cartridge sealed with cotton for Soxhlet extraction using 250 mL of 100% methanol. The crude extracts were separated from the solvent using a rotary vacuum evaporator. The crude extracts were placed in a flow hood overnight, allowing the solvent to be fully evaporated. Subsequently, the crude extracts were washed with distilled water of twice their weights, filtered, dried, and stored in a desiccator to finally obtain the dried precipitate extracts for further usage. The efficiencies of crude extract and precipitation were calculated based on the weight ratio of crude and precipitation with orange powder. A total of 35 repetitions were conducted to obtain enough orange extracts.

Experiment Design and Casing Modification
The simultaneous effects of five treatment variables (soy lecithin (X 1 ), soy oil (X 2 ), orange extracts (X 3 ), lactic acid (X 4 ), and treatment time (X 5 )) on pH were studied using RSM. The ranges of the independent variables were defined as follows: 2.12-4.20% for X 1 , 1.18-2.39% for X 2 , 0.12-0.40% for X 3 , 18-21 mL/kg NaCl for X 4 , and 60-90 min for X 5 . The experimental plan was designed by Minitab 21.1 software with an alpha (α) of 2 (Kozo Keikaku Engineering Inc., Tokyo, Japan). A total of 32 experiment matrices, including 6 replicates of the central point, were conducted in a random order to avoid erroneous conclusions due to extraneous sources of variability [1,17]. A quadratic polynomial equation was employed to establish the relationship between Y pH and independent variables (X a ; a = 1-5).
where β, β a , β aa , and β ab are the coefficients of constant, linear, quadratic, and interaction, respective. The F test was employed to estimate the significance of the regression parameters. The surfactant solution was made by dissolving soy lecithin and soy oil with distilled water via magnetic agitation at 500 rpm and 60 • C. The orange extracts were added when the modified solution was cooled to 25 • C and mixed well with the magnetic agitation. A length of 30 cm natural hog casing (Pakumogu.com, Niigata Prefecture, Japan) section was desalted and placed in surfactant solution added with orange extracts with magnetic agitation at 500 rpm. The casings after treatment time were picked up and placed in the slush salt with lactic acid for another treatment time. The composition of the surfactant solution with orange extracts, slush salt with lactic acid, and treatment time are shown in Table 1.

Sausage Production
Sausage batter was made of lean pork (4020 g), fat (1720 g), Chinese white wine (718.6 g; ethanol content: 52%, v/v), salt (200 g), sugar (120 g), black pepper (73.9 g), coriander powder (37.6 g), spicy pepper (42.4 g), turmeric powder (16.8 g), and garam masala powder (17.5 g). The meat and fat were sterilely cut into small pieces and mixed well with spices and wine. The mixed batter was filled into the modified casings and desalted untreated natural hog casings (as a control) by using a stuffing machine (STX-4000-TB2-PD-BL, Electric Meat Grinder & Sausage Stuffer, STX International, Lincoln, NE, USA). The sausage sections after stuffing were immediately dried in a sterilized oven at 45 • C for 24 h and aged at 20 • C for another 48 h. Subsequently, the sausage sections were vacuum packaged and stored in a fridge (4 • C) for 16 days for the following post-analysis.

Hyperspectral Imaging System
A laboratory visible near-infrared HSI (NH-4-KIT, EBA Japan, Tokyo, Japan) with a spectra range of 350 nm-1100 nm was employed for push-broom line-scanning of the sausage surface. A 10-bit charged coupled device camera was used, and the flame rate was 100 fps with an exposure time of 12.47 ms. The total contiguous spectral bands were 151 with 5 nm intervals. The halogen lamp light source was fixed on three sides of the camera, and the white sheet was used to render the light source to have an even distribution. The HSI system was calibrated by a dark reference (with 0% reflectance) by completely covering the camera lens with its opaque cap and calibrated by a white reference with 100% reflectance before measuring. Imaging acquisition was conducted using a reflectance mode of HSI with a dark room temperature of 20 • C. The corrected images reflectance (R ci ) was expressed as the following equation using the software of the imaging system where R r , R d , and R w are the reflectance images of raw, dark, and white, respectively. The absorbance profiles were transformed using the following equations: A black background (low reflectance surface) was used to achieve a good contrast between the sample and the background. Control software (HSAnalyzer, version 1.2, EBA Japan, Tokyo, Japan), supported by a computer, was used to analyze and process the hyperspectral images. The hypercubes were segmented by applying a threshold criterion. In this sense, all pixels having a reflectance higher than 0.075 at band 70 (695 nm) were considered as sausage. Moreover, several spectra from each sample, each sausage was digitally divided into five regions of equal area. The average spectrum of each segment was extracted and merged in a table that also contained the reference pH value and the sample code. The segmentation, the extraction of the spectra as well as the storage of data were developed by an algorithm coded under MATLAB (MathWorks Inc., Natick, MA, USA). This table with both spectra and pH reference values was used to develop the calibration models.

pH Analysis
Ten grams of sausage slices was homogenized with 90 mL of distilled water for 1 min and measured using a digital pH meter. The method was based on Zdolec et al. (2008) [31].

Spectral Pretreatment and Model Development
In order to enhance the model performance, the pretreatments of spectra, such as multiplicative scatter correction (MSC), standard normal variate (SNV), normalization, the first and the second derivatives, were conducted before multivariate analysis. Partial least square regression (PLSR), as one of the important regression algorithms, was employed to connect the pH parameter and the spectra of the sausages stuffed with different treated modified casings. Two-thirds of the samples were used for the calibration group, while the left one-third was used for the prediction group.
The predictive ability was estimated by the determination coefficient in calibration (R c 2 ), prediction (R p 2 ), cross-validation (R cv 2 ), the root mean square errors of calibration (RMSEC), prediction (RMSEP), and cross-validation (RMSECV). These parameters were determined as follows: where y i is the measured pH of the ith sample, and n is the number of samples. A good PLSR model is commonly believed to have a high R 2 with a low RMSE with a small absolute difference between RMSEC and RMSECV.

Feature Wavelengths Selection
The feather wavelengths (FWs) for pH were selected based on the weighted regression coefficient from the developed calibration model, to simplify the full model and reduce noise and redundancy information and so enhance the model accuracy. Wavelengths that contained large regression coefficients (irrespective of the sign) were selected as the FWs, and a new simplified model was created using those FWs. If the predictive performance of the new model is comparable to that with full spectra, it could be of practical use to design a simple cost-effective multispectral system and applicable to commercialization.

Visualization of pH Distribution
The pH prediction maps for sausages with different modified casings were produced according to calibration models with FWs. As HSI possesses a 3D matrix that contains a large amount of spatial and spectral information, it is required to unfold into a 2D matrix at the FWs. The purpose of this is to render each row standing for the spectrum of a pixel, and the columns represented the selected feather wavelengths. The matrix was then multiplied by the corresponding regression coefficient. In this way, the vector could be refolded back to generate a 2D color image, and consequently, the color heterogeneity of the sausages with a linear color scale (i.e., distribution map) could be shown. All these procedures were computed with MATLAB software (R2017b; MathWorks Inc., Natick, MA, USA). The graphical scheme of the main steps of building the prediction map is illustrated in Figure 1.
where yi is the measured pH of the ith sample, and n is the number of samples. A good PLSR model is commonly believed to have a high R 2 with a low RMSE with a small absolute difference between RMSEC and RMSECV.

Feature Wavelengths Selection
The feather wavelengths (FWs) for pH were selected based on the weighted regression coefficient from the developed calibration model, to simplify the full model and reduce noise and redundancy information and so enhance the model accuracy. Wavelengths that contained large regression coefficients (irrespective of the sign) were selected as the FWs, and a new simplified model was created using those FWs. If the predictive performance of the new model is comparable to that with full spectra, it could be of practical use to design a simple cost-effective multispectral system and applicable to commercialization.

Visualization of pH Distribution
The pH prediction maps for sausages with different modified casings were produced according to calibration models with FWs. As HSI possesses a 3D matrix that contains a large amount of spatial and spectral information, it is required to unfold into a 2D matrix at the FWs. The purpose of this is to render each row standing for the spectrum of a pixel, and the columns represented the selected feather wavelengths. The matrix was then multiplied by the corresponding regression coefficient. In this way, the vector could be refolded back to generate a 2D color image, and consequently, the color heterogeneity of the sausages with a linear color scale (i.e., distribution map) could be shown. All these procedures were computed with MATLAB software (R2017b; MathWorks Inc., Natick, MA, USA). The graphical scheme of the main steps of building the prediction map is illustrated in Figure 1.

Results and Discussion
3.1. Spectral Characteristics and Simultaneous Effects on pH Analyzed by RSM 3.1.1. Spectra Overview As illustrated in Figure 2, the average reflectance of sausages stuffed in the modified casing with Treatment 30 was higher than that with Treatment 25 and the control group, especially for the wavelengths range of 645 nm to 670 nm and 865 nm to 890 nm. The pH values for Treatments 30, 25, and control were 4.44, 6.32, and 6.24, respectively. It is well known that the NIR hyperspectral system recorded the different absorbance patterns according to the interior structural changes or intermolecular forces changes in the meat with different pH levels [32]. It was also reported that oxymyoglobin (MbO 2 ) has a large absorption coefficient at 544 nm and 582 nm, while oxyhemoglobin (HbO 2 ) possesses three absorption bands at 418 nm, 543 nm, and 574 nm, representing soret, α, and β bands [33]. The absorption bands at 780 and 980 nm were related to moisture absorption, corresponding to the third and second overtones of O-H stretching, respectively [34].

Spectra Overview
As illustrated in Figure 2, the average reflectance of sausages stuffed in the modified casing with Treatment 30 was higher than that with Treatment 25 and the control group, especially for the wavelengths range of 645 nm to 670 nm and 865 nm to 890 nm. The pH values for Treatments 30, 25, and control were 4.44, 6.32, and 6.24, respectively. It is well known that the NIR hyperspectral system recorded the different absorbance patterns according to the interior structural changes or intermolecular forces changes in the meat with different pH levels [32]. It was also reported that oxymyoglobin (MbO2) has a large absorption coefficient at 544 nm and 582 nm, while oxyhemoglobin (HbO2) possesses three absorption bands at 418 nm, 543 nm, and 574 nm, representing soret, α, and β bands [33]. The absorption bands at 780 and 980 nm were related to moisture absorption, corresponding to the third and second overtones of O-H stretching, respectively [34].  Figure 3 shows that the pH value varied from 4.44 (Treatments 19 and 30) to 6.46 (Treatment 22). Different casing treatments may have affected pH evaluation during the 16 days of storage under 4 • C. The R 2 value of the regression model developed for pH was 67.13% with a nonsignificant lack of fit (p > 0.05). Only soy lecithin and orange extracts (X 1 × X 3 ) were observed to have interactively affected the pH of sausage at a 5% significance level ( Table 2). The predicted quadratic polynomial regression equation for pH as a function of soy lecithin (X 1 ), soy oil (X 2 ), orange extracts (X 3 ), lactic acid (X 4 ), and treatment time (X 5 ) in the uncoded units are shown as follows: Y pH = 59.0000 + 1.5200 X 1 − 9.0700 X 2 − 8.4000 X 3 − 3.8400 X 4 − 0.2520 X 5 − 0.0520 X 2 1 +0.4260 X 2 2 +7.8200 X 2 3 +0.0635 X 2 4 + 0.0007 X 2 5 + 0.0110 X 1 X 2 − 3.2700 X 1 X 3 − 0.0160 X 1 X 4 − 0.0035 X 1 X 5 + 2.0700 X 2 X3 +0.2720 X 2 X 4 + 0.0216 X 2 X 5 + 1.0000 X 3 X 4 − 0.1109 X 3 X 5 + 0.0086 X 4 X 5 (6)   The value of the corresponding coefficient for orange extracts (X3, −8.4000) indicates that it exerts an important impact on casing modification and so influenced sausage pH during the 16-day storage. Further investigation shows that pH decreased when casings were treated with a higher concentration of soy lecithin with orange extracts at approximately 0.26% [ Figure 4 (a)]. According to the 2D contour plot [ Figure 4 (b)], the pH value  The value of the corresponding coefficient for orange extracts (X 3 , −8.4000) indicates that it exerts an important impact on casing modification and so influenced sausage pH during the 16-day storage. Further investigation shows that pH decreased when casings were treated with a higher concentration of soy lecithin with orange extracts at approximately 0.26% [ Figure 4a]. According to the 2D contour plot [ Figure 4b], the pH value is over 6.0 when a lower soy lecithin concentration was combined with higher orange extracts. The increased pH may be explained by the nitrogen compounds generated by proteolysis [35]. Yao et al. reported that protein enzymes, produced by microorganisms, led to the decomposition of meat protein, generating ammonia, biogenic amine, and skatole [33]. The contents of MbO 2 and HbO 2 were decreased with the decomposition of protein, which indirectly affected the change of spectra at 540 and 582 nm (related to MbO 2 ), and 418, 543, and 574 nm (related to HbO 2 ) in comparison with the control (pH = 6.24) and sample with Treatment 22 (pH = 6.46) (Figure 2). A lower soy lecithin level was reported to render the casings to be more porous [1]. Orange extracts were reported to possess certain contents of hesperidin [9,17,[36][37][38], which has a potent antioxidant effect and is an anti-microorganism.

PEER REVIEW 9 of 15
which indirectly affected the change of spectra at 540 and 582 nm (related to MbO2), and 418, 543, and 574 nm (related to HbO2) in comparison with the control (pH = 6.24) and sample with Treatment 22 (pH = 6.46) (Figure 2). A lower soy lecithin level was reported to render the casings to be more porous [1]. Orange extracts were reported to possess certain contents of hesperidin [9,17,[36][37][38], which has a potent antioxidant effect and is an anti-microorganism.

Calibration Models with Full Wavelengths
The PLSR model was employed to predict the pH values of the sausages using different modified casings from both reflectance and absorbance spectral data over the full spectral range of 350-1100 nm. Using the reflectance spectra, the Rp 2 value of data pretreated by normalization shows some improvement to 0.6855 when compared with the raw data of 0.6485, with a small decrease in RMSEP (Table 3). It is reported that normalization can improve the spectral features, making the spectra have an equal area under the curve to allow for easy comparison of spectral features in the same plot [39]. Proper normalization of hyperspectral spectra data enables a better signal-to-noise ratio, compared to the conventional spectrophotometer method [40] A-PLSR model derived from the spectra preprocessed by the first derivative presented the highest Rc 2 of 0.7300, the lowest RMSEC of 0.4283%, and Rp 2 of 0.6789 and RMSEP of 0.4501% (Table 3), with a low absolute difference between RMSEC and RMSECV, compared with raw and other pretreatments. The function of first derivatives is to remove background noise and baseline drift, as well as to improve small spectral features [41]. Regarding a similar study, the Rp 2 values for predicting pH in salted meat [42], freeze-thawed pork [43], fresh pork [44], and large Japanese sausages [19] were 0.797, 0.845, 0.55, and 0.882, respectively. The comparable low Rp 2 in the current study may be due to the factor where the pH value was only concentrated either near 4.66 or 6.32 (Figure 3), leading to a narrow pH distribution for analysis. Table 3. Statistical parameters of PLSR with raw and preprocessing spectra based on full wavelengths.

Calibration Models with Full Wavelengths
The PLSR model was employed to predict the pH values of the sausages using different modified casings from both reflectance and absorbance spectral data over the full spectral range of 350-1100 nm. Using the reflectance spectra, the R p 2 value of data pretreated by normalization shows some improvement to 0.6855 when compared with the raw data of 0.6485, with a small decrease in RMSEP (Table 3). It is reported that normalization can improve the spectral features, making the spectra have an equal area under the curve to allow for easy comparison of spectral features in the same plot [39]. Proper normalization of hyperspectral spectra data enables a better signal-to-noise ratio, compared to the conventional spectrophotometer method [40] A-PLSR model derived from the spectra preprocessed by the first derivative presented the highest R c 2 of 0.7300, the lowest RMSEC of 0.4283%, and R p 2 of 0.6789 and RMSEP of 0.4501% (Table 3), with a low absolute difference between RMSEC and RMSECV, compared with raw and other pretreatments. The function of first derivatives is to remove background noise and baseline drift, as well as to improve small spectral features [41]. Regarding a similar study, the R p 2 values for predicting pH in salted meat [42], freeze-thawed pork [43], fresh pork [44], and large Japanese sausages [19] were 0.797, 0.845, 0.55, and 0.882, respectively. The comparable low R p 2 in the current study may be due to the factor where the pH value was only concentrated either near 4.66 or 6.32 (Figure 3), leading to a narrow pH distribution for analysis.

Calibration Models with Selected Feature Wavelengths
Hyperspectral data display a high degree of interband correction with high dimensions. It is thus meaningful to select feature wavelengths to represent the full wavelengths. In this way, the model can be simplified, and data redundancy can be eliminated. Furthermore, the algorithms' efficacies can be enhanced, accelerating the classification of sausages based on the pH for industrial machine-vision systems. According to the weighted regression coefficients from the PLSR model ( Figure 5), the feature wavelengths were selected based on the peaks and valleys (i.e., indicating the important information and large contribution to the productivity of the model) in the wavelengths. To this end, twelve wavelengths (365,  385, 405, 475, 525, 580, 640, 725, 875, 915, 1005, and 1060 nm) were selected as the feature wavelengths. Table 4 elaborates on the predictive ability of the simplified model, with an R p 2 of 0.6896 and an RMSEP of 0.4426%, using data pretreated by normalization. A new PLSR with those feature wavelengths was established as follows: Y' pH = 5.335 + 7.243λ 365 − 0.060λ 385 + 7.461λ 405 − 4.098λ 475 + 3.594λ 525 + 4.443λ 580 − 5.920λ 640 − 4.083λ 725 − 3.246λ 875 + 4.495λ 915 + 3.520λ 1005 − 9.730λ 1060 (7) where λ xnm is the reflectance spectra at the wavelength of x nm, and Y' pH is the predicted pH value. Generally, the R 2 values of prediction in the reduced model were comparable to that of the model using full wavelengths, and approximately 92% of wavelengths were reduced from the full wavelengths. There were even some cases where the prediction accuracy of the model using the feature wavelengths was higher than that using the full wavelengths (e.g., R p = 0.6835 for A-1st Derivative-PLSR using feature wavelength vs. R p = 0.6789 for A-1st Derivative-PLSR using full wavelength). This may be elucidated by removing the noise and pixel outliers, resulting in the improvement of robustness and reliability of the PLSR model [44][45][46][47]. It was mentioned that the R 2 value between 0.66 and 0.81 is allowed for approximate prediction, an R 2 value between 0.82 and 0.90 is regarded as a good prediction, while an R 2 higher than 0.91 is demonstrated to be an excellent prediction [48]. The selected feature wavelengths were applied to creating prediction maps in the following step. regression coefficients from the PLSR model ( Figure 5), the feature wavelengths were selected based on the peaks and valleys (i.e., indicating the important information and large contribution to the productivity of the model) in the wavelengths. To this end, twelve wavelengths (365,385,405,475,525,580,640,725,875,915,1005, and 1060 nm) were selected as the feature wavelengths. Table 4 elaborates on the predictive ability of the simplified model, with an Rp 2 of 0.6896 and an RMSEP of 0.4426%, using data pretreated by normalization. A new PLSR with those feature wavelengths was established as follows: Figure 5. Feature wavelength selection from the PLSR model. Figure 5. Feature wavelength selection from the PLSR model.

Visual Representation of Sausage pH Distribution
As the main advantage of hyperspectral imaging technology, a prediction map (or distribution map) can illustrate where and how many different reference parameters (pH in the current study) are located from spot to spot in different detected samples. Figure 6 elaborates how pH changes in response to the different treated modified casings used for the sausages stored on Day 16. Four samples, the sample with the highest pH value (treatment 22, pH = 6.46), middle pH (Treatment 20, pH = 6.17), lowest pH (Treatment 30, pH = 4.44), and control group, were selected for representation. It is difficult to distinguish the differences in the RGB images with the naked eyes ( Figure 6). Nevertheless, the prediction maps clearly show how much different pH values were located from pixel to pixel, which is superior to the conventional pH measurement, which is time-consuming and difficult to obtain the data like this. It is meaningful to monitor and understand the spatial change, which could provide useful information on how intrinsic properties such as the composition and biochemical attributes of samples react to different modified casings. To this point, it could serve as a good reference before those types of modified casings are commercially utilized.
in the current study) are located from spot to spot in different detected samples. Figure 6 elaborates how pH changes in response to the different treated modified casings used for the sausages stored on Day 16. Four samples, the sample with the highest pH value (treatment 22, pH = 6.46), middle pH (Treatment 20, pH = 6.17), lowest pH (Treatment 30, pH = 4.44), and control group, were selected for representation. It is difficult to distinguish the differences in the RGB images with the naked eyes ( Figure 6). Nevertheless, the prediction maps clearly show how much different pH values were located from pixel to pixel, which is superior to the conventional pH measurement, which is time-consuming and difficult to obtain the data like this. It is meaningful to monitor and understand the spatial change, which could provide useful information on how intrinsic properties such as the composition and biochemical attributes of samples react to different modified casings. To this point, it could serve as a good reference before those types of modified casings are commercially utilized.

Conclusions
The present study investigated the feasibility of employing HSI for rapidly and nondestructively predicting pH values in sausages stuffed in modified casings added with orange extracts from waste orange peels. RSM was used to explain the relationship between different modified factors and sausage pH. The R 2 value of the polynomial regression model was 67.13% with a nonsignificant lack of fit (p > 0.05). When using full wavelengths, the A-PLSR model derived from the spectra preprocessed by the first derivative presented the highest Rc 2 of 0.7300, while R-PLSR derived from normalization achieved the highest Rp 2 of 0.6855. Twelve feature wavelengths (365, 385, 405, 475, 525, 580, 640, 725, 875, 915, 1005, and 1060 nm) were selected to develop a simplified model. This reduced model achieved a comparable R 2 value in comparison with that using full wavelengths, which means it can be applied to a simple, cost-effective, multispectral system establishment or for online industrial applications. For the first time, the prediction map developed in this study clearly displayed sausage pH evolution according to different modified casings.

Conclusions
The present study investigated the feasibility of employing HSI for rapidly and nondestructively predicting pH values in sausages stuffed in modified casings added with orange extracts from waste orange peels. RSM was used to explain the relationship between different modified factors and sausage pH. The R 2 value of the polynomial regression model was 67.13% with a nonsignificant lack of fit (p > 0.05). When using full wavelengths, the A-PLSR model derived from the spectra preprocessed by the first derivative presented the highest R c 2 of 0.7300, while R-PLSR derived from normalization achieved the highest R p 2 of 0.6855. Twelve feature wavelengths (365, 385, 405, 475, 525, 580, 640, 725, 875, 915, 1005, and 1060 nm) were selected to develop a simplified model. This reduced model achieved a comparable R 2 value in comparison with that using full wavelengths, which means it can be applied to a simple, cost-effective, multispectral system establishment or for online industrial applications. For the first time, the prediction map developed in this study clearly displayed sausage pH evolution according to different modified casings.