- Email: [email protected]
Fresh-sliced tissue inspection: Characterization of pork and salmon composition based on fractal analytics
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Contents lists available at ScienceDirect
Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp
Fresh-sliced tissue inspection: Characterization of pork and salmon composition based on fractal analytics Samuel Verdú ∗ , José M. Barat, Raúl Grau Departamento de Tecnología de Alimentos, Universitat Politècnica de València, Spain
a r t i c l e
i n f o
a b s t r a c t
Article history:
The capability of fractal analytics of digital images for characterizing sliced tissue was tested
Received 11 January 2019
in fat and water fractions terms. The study was based on three factors: tissue type (pork loin
Received in revised form 21 March
and salmon); fractal parameter (fractal dimension and lacunarity); image type in color terms
2019
(grayscale and RGB channels). After capturing images of tissue samples, the water and fat
Accepted 20 April 2019
fractions were analyzed from each one. The fractal information was expressed as specific
Available online 28 April 2019
spectra from each image type, which were related with composition properties. The rela-
Keywords:
reported that fractal information collected the variability due to both composition and tis-
tionship between both data blocks was tested by multivariate regression assays. The results Fresh sliced tissues
sue morphology. Both fractal parameters and all the image types successfully reported the
Inspection
results. The two fractal parameters displayed a strong dependency on components, and both
Fractal analytics
characterized sample properties. No considerable differences were found in the results for
Image
image type. However, the inclusion of the entire color spectra increased the observed coef-
Characterization
ficients. The idea presented here could be a simple rapid non destructive technique for
Composition
characterizing tissue composition. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
The yield increment necessity in industrial processes, and the sophistication of the operations involved in production chains specifically for the food industry, generate the requirements of new developments, which keep the system under control and reduce costs to a minimum (Lim and Antony, 2016). When a given food sector requires exceptional control measures for hygienic parameters, e.g., those to produce fresh and raw materials (meat, fish, dairy, etc.), the development of fast simple non destructive inspection techniques offers notable advantages for the entire production system (Chen et al., 2013a, b; Ropodi et al., 2015). The main advantage of non destructive inspection techniques is the increased velocity of a given operation, and a high rate of analyzed samples is achieved per time unit to collect information from entire lots sample by sample. The ability to obtain information continuously from each sample allows accuracy in inspection operations to improve auto-
matic works, like classification, slicing, packaging, labeling, storage, etc. (Arendse et al., 2017). Indeed one of the most productive areas in the control and monitoring of non destructive fresh products is image analysis in several categories. Some of these categories are visible 2D images, spectral imaging, X-ray imaging, among others (Jackman et al., 2011). Applications like classifying pork hams, assessing the tenderness of beef carcasses, controlling the freshness of gilthead sea bream based on gill and eye color changes, automatic fishbone detection, etc. (Dowlati et al., 2013; Ivorra et al., 2016a, b; Jackman et al., 2012; Konda Naganathan et al., 2015; Mery et al., 2011), have been previously reported, and have proven the potential of these technology groups that operate for such purposes. A visible image analysis is one of the most accessible techniques from which many studies have offered successful results in diverse research areas about versatility and reduced cost possibilities. This technique includes the fractal analysis of digital images. The fractal analysis is a group of calculated algorithms used to study and characterize highly complex systems with chaotic structures to
∗ Corresponding author at: Edificio 8E - Acceso F — Planta 0, Ciudad Politécnica de la Innovación, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain. E-mail address: [email protected] (S. Verdú). https://doi.org/10.1016/j.fbp.2019.04.008 0960-3085/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
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detect measurable patterns which can offer valuable information from a given sample. An example of such is biological structures. Indeed biological systems have been studied mainly using the fractal analytics of digital images in biomedical and histological research areas to report useful applications for characterizing and diagnosing organic structure features. Some of these applications have been applied to study neurophysiology systems, organ malformations or glucose fluc´ 2016; tuation kinetics, among others (Akar et al., 2015; Kesic´ and Spasic, Weissman and Binah, 2014). Fractal information has also been used to develop applications for characterizing geological structures and their properties. Some examples include the use of fractal dimensions to characterize the urban nucleus (Ge and Lin, 2009; Zhang et al., 2008), to model the spatio-temporal behavior of fluvial landform evolution (Pelletier, 2007), and to quantify the properties of river deltas and their channel networks (Edmonds et al., 2011). Therefore, the application of this technique to the food industry offers real potential to be exploited. Some recent studies have applied the fractal analysis to characterize different types of fresh food tissues and processing types with both fresh meat and fish products. The influence of certain factors, such as origin, freshness and processing of tissue, is characterized and successfully modeled by processing fractal information. Some examples are the characterization of fatty infiltration in Iberian and white pork sirloins, color changes on the surface of fresh cut meat, evaluations of the effects of frozen storage on the tilapia microstructure (He et al., 2015; Quevedo et al., 2013; Serrano et al., 2013), and the evaluation of antioxidants in juices, bruising in red bayberries, browning in avocado, acrylamide in biscuits, the characterization of low-fat yogurts, etc. (Zheng et al., 2011). Although these studies have shown the effectiveness of fractals, fractal analytics has been used mainly as a tool to classify and characterize the composition of some products from a qualitative point of view. The development of non invasive tools to fulfill this aim, mainly with quantification capacity, is in accordance with the tendency of recent food regulations like (UE)
Fig. 1 – Experiment procedure scheme. Xw: water fraction; Xf: fat fraction; R, G and B: red, green and blue color image channels, respectively; Fd: fractal dimension; L: lacunarity; R: red; G: green; B: blue (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
2.2.
Preparing fresh-sliced samples
no. 1169/2011 of the European Parliament about food information sup-
2.
Material and methods
Two types of fresh-sliced tissues were used: pork loin and salmon. Both represent edible tissues from different origins that are often sliced, packaged and labeled automatically to be sold. Twenty-six slices of fresh pork loin from five different lots (26 × 5/130 samples) and 20 slices of fresh salmon from four different lots (20 × 5/100 samples) were bought from a local provider. The sizes of all the slices were 1 ± 0.5 cm thick and 15 ± 2.1 cm long. This range of sizes was that which the samples from the commercialized product originally had, which was not modified to maintain the morphological features from which they were originally processed (Step 1 in Fig. 1).
2.1.
Experiment procedure
2.3.
plied to consumers, which obliges food producers to include nutritional labeling on most processed food products. Hence this work aimed to evaluate the fractal analytics of digital images as a non destructive inspecting tool to evaluate the morphology and composition in the fat and water fraction terms of fresh sliced pork loin and salmon tissues by studying different fractal parameters such as spectral data within color spaces.
The experiment tested the capability of the fractal analytics of images to characterize sliced tissues in fat and water composition terms (Fig. 1). The objective of this procedure was to non destructively collect information about the pork loin and salmon that come in commonly processed and commercialized formats. The study was based on three factors: tissue type (pork loin and salmon), fractal parameter (fractal dimension and lacunarity) and image type (grayscale and RGB). The first step was to prepare the pork and loin samples. Next images of samples were taken (Step 2 in Fig. 1) and processed to obtain the grayscale and their R, G and B versions (Step 3 in Fig. 1). Then fractal parameters were extracted from these images (Step 4 in Fig. 1). After image processing, the fat and water fractions were analyzed from each sample (Step 5 in Fig. 1). The last step involved testing the dependency of both the compositional data (fat and water fractions) and the multivariable fractal data blocks (the spectra of the fractal parameters from grayscale, and the R, G, B and RGB images).
Image capturing
Images were obtained by a standard device that can be easily implemented into an online inspection in the production chain. The single images of one surface of each slice were obtained via a HD webcam C615 (CCD, 8 megapixels, Logitech International S.A., Switzerland) vertically fixed to a rigid structure 20 cm over the sample. The device was fitted inside a chamber to protect it from external lighting. The lighting source was a LED IP20 5 W lamp. The camera was connected to a laptop equipped with the control software. On the camera capture scene, a black matte material was placed to reduce reflections on the camera. The camera took pictures of 3264 × 2448 pixels in the JPEG format, which gave a pixel size of 0.05 mm/pixel (Step 2 in Fig. 1).
2.4.
Compositional characterization of samples
The composition in the moisture fraction (Xw) and fat fraction (Xf) terms of both sample types was analyzed. Moisture was determined by oven drying to constant weight at 100 ◦ C (ISO
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Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Norm R-1442, 1979) and fat was in accordance with ISO Norm R-1443 (1973) using a FOSS Soxtec System 2055 Tecator. All the parameters were expressed on a wet basis and analyzed in triplicate per slice (Step 3 in Fig. 1).
2.5. Image processing and acquiring fractal information In order to obtain the multivariable data matrices of the fractal information, images were processed by the method according to Zheng et al. (2011) with modifications (Steps 3 and 4 in Fig. 1). The basic procedures were: 1. Adapting images: the capturing of each sample was done in the RGB format and derived into four different images based on color format: grayscale, red (R), green (G) and blue (B). 2. Image segmentation: each image obtained in the previous step was segmented for each color value: grayscale: from black (0) to white (255); R channel: from black (0) to red (255); G channel: from black (0) to green (255); B channel: from black (0) to blue (255). This step provided 1024 segmented images from each image (256 × 4). 3. Extracting parameters: both the fractal parameters, namely fractal dimension (Fd) and lacunarity (L), were calculated for each segmented image from Step 2. Both fractal parameters were selected for their simple calculation. They essentially consider the relationship between the scale of a square (called box) and the number of this square required to scan the objects contained in a given image (i.e. contours, areas, etc.) in the image (Fig. 2B and C show two examples of the scales of box grids), although each one presents different approaches: 4. The fractal dimension (Fd) was obtained by the boxcounting method. Images were divided into boxes with a variable size denoted as box scale (ε). ε went from 1% to 15% of the entire image width. Thus the number of boxes containing pixels was counted for each ε, and called Nε. The loin sample included in Fig. 2B and C shows as example of two different box scale grids and the number of the boxes required to complete the segmented image. The relationship between ε and Nε can be described by the following equation: Fd = −lim
n→0
logNε logε
(1)
where Fd is the fractal dimension, Nε is the number of boxes containing pixels on a given box scale and ε is the box scale. Then Fd is the slope of the regression line for the log–log plot of ε and Nε. Fig. 2D shows this type of plot according to the loin example, where the determination coefficient was tested and the regression equation was calculated to obtain the absolute slope value. - Lacunarity (L) is based on quantifying the variation in pixel density at different ε by linear scanning across images. Scanning was done from left to right, and by descending row by row once this had finished. In this case, ε went from 1% to 50% of the entire image width. Eq. 2 represents L to be calculated on each box scale: Lε =
2
(2)
where Lε is lacunarity on a given box scale, is the standard deviation of the pixels in the boxes of that scale, and is the average of the pixels in the boxes on that scale. Thus the L of the entire scan was calculated as the average of the Lε values from all the tested ε. The salmon sample in Fig. 2B and C shows, by way of example, two different box scales, the starting point and direction of the linear scanning across the segmented image (black arrows), and the type of plot obtained during this process. Both parameters were calculated in 15 different grid positions for each image to avoid the effect of sample position in the capturing area. All 15 results were taken as the single replica data of each image. Data were obtained using FracLac for ImageJ created by Karperien (2013). 1. Obtaining spectra: the data acquired from each image by the above-explained processes were organized into spectra. These spectra were expressed as fractal parameter vs. color value for each image. Four spectra (one from each image type) of each fractal parameter were obtained per sample, from which a multivariate data block was created.
2.6.
Quantifying data block dependency
The dependency of both the compositional data (fat and water fractions) and the multivariable fractal data blocks (the spectra of the fractal parameters from the grayscale, and the R, G, B and RGB images) was tested by the non linear regression method Support Vector Machines (SVM) (Step 6 in Fig. 1). SVM is a powerful supervised learning methodology based on the statistical learning theory, which is commonly used for multivariable data analyses (Boser, Guyon, & Vapnik, 1992). The used version was epsilon-support vector regression (-SVM) and the radial basis function was kernel (RBF kernel). The dependencies of the water and fat fractions of both the fractal parameters spectra (Fd and L) and image information type were tested by this method. The results were evaluated in terms of calibration (Cal) and cross validation (CV) coefficients following (Ropodi et al., 2016). The method used for the cross validation process was “venetian blinds”. There were three data splits. Then 70% of the samples were taken as training data and 30% as testing data in three different iterations. The results were also evaluated by the root mean square error (RMSE), Eq. (3), which is a measure of the differences between the values predicted by the model and the observed values being modeled. These individual differences are also called residuals, and RMSE represents an aggregate of them all in a single measure.
RMSE =
n (X − X ˙i=1 o,i m,i )
2
n
(3)
where Xo is the observed values and Xm is the modeled values at place i. Procedures were performed with the PLS Toolbox, 6.3 (Eigenvector Research Inc., Wenatchee, Washington, USA), a toolbox extension in the Matlab 7.6 computational environment (The Mathworks, Natick, Massachusetts, USA).
3.
Results and discussion
3.1.
Acquiring fractal information (Fd and L)
The relationship between fractal information variation and the complexity of the taken images was tested to observe the evidence of the influence by the tissue components mor-
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
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Fig. 2 – Scheme of the fractal information obtained. Left: Fractal dimension (Fd); Right: Lacunarity (L). A: originally taken images of pork loin and salmon samples; B: example of the binary thresholded images with a large box size grid. C: The same images with the small box size grid. D: Performance plots and results of both fractal parameters; left: fractal dimension is the slope of log Nε vs. log ε plot (red square), where Nε is the box count and is the box scale; right: lacunarity values from the image scan across the box scale. Black arrows indicate the start position and directionality of the scan (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). phology. It was assumed that the fractal information in the spectra depended mainly on the complexity of the analyzed shapes because of the frequency and distribution of pixels in a given color value. In this case, however, a high load of the collected complexity in the images was verified to come from the combination of the different components of sliced samples (fat and muscle tissues). The evolution of both fractal parameters across the color values from each image type was observed. Fig. 3 illustrates the evolution of both fractal parameters across the grayscale of a pork loin sample as an example. Spectra denote a non constant evolution across color values, and peaks formed mainly around values 30–40. This behavior indicated real variation following the color values, where an inverse tendency between Fd and L was observed, but the main peak took place in the same zone. These peaks were
according to image type, with variations observed compared to spectra R, G and B (Fig. 5). Moreover, although both parameters were based on different calculation procedures, they reported the equivalent information of image complexity in this case. In spite of proving the variability of the fractal parameters, it was necessary to attach the real processed images from which the data set was obtained as spectra evolutions were easily interpreted. The evolution of the processed images on the grayscale of the pork loin example is shown at the bottom of Fig. 3. From value 0 (black), an increment in complexity was observed in the images because many pixels (frequency) in these color values produced the maximum complexity precisely where the fractal parameters generated the abovementioned peaks, from which complexity reduced following
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Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Fig. 3 – Example of the evolution of fractal parameters Fractal dimension (Fd) and Lacunarity (L) across the grayscale for a pork loin sample. The left axis represents Fractal dimension (red lines) and the right axis denotes Lacunarity (black lines). The bottom zone corresponds to the obtained segmented images following gray values. The range between the discontinued lines marks tones with the images that present a maximum complex shape (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4 – The 3D scatterplot of Fd (left) and L (right) for value 70 on the grayscale (Z-axis) vs. the fat and water fraction (Xf and Xw, respectively) from all the pork loin (green dots) and salmon (orange dots) examples. Letters P and S are an example of the pork loin sample and the salmon sample, respectively, with the same amount of Xf, but different fractal values (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). the reduction in the number of pixels, as visually observed. Indeed the shapes described by the pixels in each value corresponded principally to the variability in the fat and muscle tissue distributions. Therefore, it is noteworthy that most of the complexity collected by the fractal parameters was due to the morphology of both tissue types. This fact was crucial to assume the possibility of measuring the differences in not only the amount of fat, but also in the morphologies between the pork and salmon tissues.
3.2.
Results of the dependency of data blocks
A single relationship between tissue characteristics and fractal information was observed. However to further characterize samples, this variability had to be related first to the amount of each fatty and lean tissue, and then to composition. Fig. 4
shows an exploratory scatterplot by way of example, which represents Fd (left) and L (right) vs. the fat fraction (Xf) and the water fraction (Xw) for some samples of value 70 on the grayscale, which was taken as the average value of the complete spectra (Fig. 3). Here we see how the fractal parameters covariated with both Xf and Xw inversely, and two distributions can be described with marked tendencies, but with clear differences between pork loin and salmon. Fd increased with the fat fraction and decreased with the water fraction. L presented inverse behavior, which was already observed in the spectra of Fig. 3. This phenomenon depended on the features of the mathematical approach of both parameters. Although both displayed differences, high complementarity and parallelism were also observed. This behavior matched that indicated in previous studies, where applying these parameters to model the fat distribution in
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Fig. 5 – The spectra of Fd across the grayscale, channels R, G and B from the pork loin (green) and salmon (orange) samples with the same fat fraction (0.17 ± 0.8). The raw spectra from all 15 grid positions in each image were included. A: the Fd spectra of the grayscale; B: the Fd spectra of the red scale; C: the Fd spectra of the green scale; D: the Fd scale of the blue scale (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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beef samples was worked. Chen et al. (2013) a, b and Chen et al. (2012) reported the positive relationship between Fd and fatty infiltrations. In these studies, the Fd values, obtained by several methods, rose with increased beef marbling levels by augmenting the new areas with color differences in the pure lean color. This effect was applicable to both sample types, but their distributions presented some differences. These differences apparently occurred because salmon presented higher Fd values and lower L ones than the pork loin at a given fat fraction (points S and P in Fig. 4) for this explored gray value (70). This feature can be explained by the differences in fatty tissue distributions within slices. However, observing only one grayscale value was not enough to assume and understand this fact. Thus the complete Fd spectra from the grayscale, and channels R, G and B from a salmon sample and a pork loin sample with the same fat fraction (0.17 ± 0.8) (points P and S in Fig. 4), were plotted to explore these behaviors (Fig. 5). Fig. 5 shows the Fd spectra from the salmon (orange) and pork loin (green) for all image types. The former was the grayscale (Fig. 5-A), which collected the whole color variation transformed into gray values. The spectra presented a maximum around the 30–50 values for both sample types. Until that zone, pork loin obtained higher values than salmon. Salmon gave higher values from value 70 to the last one according to the scatterplot in Fig. 4, which meant most of the scale. This was interpreted as the salmon images presenting greater complexity toward light values than pork loin, which instead had high values toward dark values. This result falls in line with the fact that most of the pork loin color was formed by intense red values. Although the grayscale collects information from color features, the spectra from each RGB channel could report more specific information to characterize the samples. Fig. 5B, C and D respectively show the spectra from channels R, G and B. The spectra on the R scale better indicated the differences in the dark red values, where pork loin appeared with higher Fd values than salmon. This behavior was inversed around value 50 where, once again, salmon presented more complexity for the light values. Scale G presented marked differences for salmon in the light values. In the same way as for Scale B, salmon obtained high values for the light values. However, pork loin presented the maximum values across most of the spectrum toward the dark values. The predominant salmon colors were orange values, formed mainly by combinations of red and green values, which would explain the high values in the light values of G and for most of the R spectrum. The accentuated pork loin complexity as regards the dark values of channels R and B was also explained by the combination of the blue and red values producing intense red-magenta colors, which are typical of this meat tissue type. These results revealed the importance of the color dimension for the capability of Fd and L to collect morphological information from both the sample type and the amount of fat, which demonstrates that these fractal parameters could be insufficient if only one color threshold was taken into account due to their monofractal approach. In order to report the capacity of the fractal information to characterize the relationship with both composition and morphology, the last step involved studying and quantifying the fractal information dependency on the fat and water fractions to develop a plausible quantifier application. The study was done by taking the spectra of Fd and L from each image type and channel as the multivariable data block: grayscale, R,
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Table 1 – Fractal information and composition data blocks’ dependency study. Pork-loin
Fd
Complete spectra
L
Rcal RMSEcal Xw Rval RMSEcv Rcal RMSEcal Xf Rval RMSEcv Rcal RMSEcal Xw Rval RMSEcv Rcal RMSEcal Xf Rval RMSEcv
Salmon
grayscale
R
G
B
RGB
grayscale
R
G
B
RGB
0.99 5E-04 0.96 3E-03 0.98 4E-04 0.95 2E-03 0.98 5E-04 0.94 2E-03 0.98 4E-04 0.93 2E-03
0.97 6E-04 0.95 1E-03 0.98 4E-04 0.95 1E-03 0.97 5E-04 0.94 1E-03 0.98 3E-04 0.93 2E-03
0.94 8E-04 0.91 3E-03 0.97 7E-04 0.95 2E-03 0.95 8E-04 0.95 3E-03 0.96 7E-04 0.94 2E-03
0.95 6E-04 0.92 1E-03 0.95 6E-04 0.93 5E-04 0.95 6E-04 0.95 8E-03 0.95 5E-04 0.94 2E-03
0.99 6E-04 0.98 1E-03 0.98 5E-04 0.95 4E-03 0.98 6E-04 0.94 5E-03 0.98 5E-04 0.93 4E-03
0.99 5E-04 0.95 4E-03 0.98 4E-04 0.94 3E-03 0.98 5E-04 0.93 4E-03 0.98 4E-04 0.92 3E-03
0.98 8E-04 0.95 3E-03 0.98 8E-04 0.94 3E-03 0.98 8E-04 0.935 3E-03 0.98 7E-04 0.92 2E-03
0.98 7E-04 0.92 2E-03 0.98 6E-04 0.94 1E-03 0.98 7E-04 0.94 2E-03 0.98 6E-04 0.93 5E-03
0.85 9E-03 0.75 9E-02 0.63 1E-01 0.60 1E-03 0.74 9E-02 0.65 9E-01 0.78 9E-02 0.63 9E-01
0.99 6E-04 0.95 1E-03 0.99 5E-04 0.94 1E-03 0.98 6E-04 0.935 5E-03 0.98 5E-04 0.92 4E-03
Fd: fractal dimension; L: lacunarity; Xw: water fraction; Xf: fat fraction; R2 Cal: calibration coefficient; RMSEC: root mean square error of calibration; R2 CV: cross validation coefficient; RMSECV: root mean square error of cross validation; R: red channel of images; G: red channel of images; B: red channel of images; RGB: complete color information of images.
G and B, and RGB as a single block. The results of the non linear regressions carried out for each data block combination are offered in Table 1. The results report high coefficients for most combinations of data blocks for both calibration and cross validation. No differences were observed between Xf and Xw, and both parameters presented high coefficients for the two fractal parameters. Image type and channel had coefficients up to 0.95, except for channel B for salmon, which presented 0.85 as the maximum and 0.63 as the minimum. The separate color channels showed slightly lower coefficients in general, and tended to reach high values for the grayscale and RGB. This meant that each image channel collected singly specific information which, when combined, presented a better fit. Therefore, the separation of the color channel might not be recommendable in these cases. Thus after learning the impact of data reduction on the regression coefficients, the number of values of the spectrum used in the prediction was also evaluated to know how reducing the volume of the spectral data would influence accuracy. The study was redone from one color value, as in the common image segmenting procedure, to complete the spectrum. The data employed for each calculation were obtained by isolating the fractal information from the values with the highest fractality (peaks in the fractal spectra) from the grayscale and RGB. The improvement in the coefficients, achieved by gradually including the contiguous color values, was evaluated (10 contiguous values were included in each step). Fig. 6 offers an example of the evolution of R2 Cal and R2 CV between Fd and Xf by progressively including values in the dependency analysis for both the grayscale (Fig. 6A and C) and RGB (Fig. 6B and D). The results describe how including color values notably improved the coefficients and lowered the root mean square error (RMSE). This effect was common for pork loin (Fig. 6A and B) and salmon (Fig. 6C and D). Moreover, RGB presented fewer differences between the obtained coefficients using only one color value and all the values compared to the grayscale. This effect came about because RGB started with three values from the R, G, and B spectra peaks (one per channel), while the grayscale had only one. These observations revealed that
although the spectra value that formed the peak collected the maximum information about the sample morphology, the other spectra represented fundamental information to complete and explain the variability produced by the samples’ properties. Therefore, including fractal information from the complete color variability (grayscale and RGB) in this study gave better results than each separate color channel (R, G and B). However the predominance of the red values, which are typical of these samples, allowed us to obtain a high coefficient tendency for the R isolated channel. It is well-known that Xf and Xw are strongly and inversely related in tissue systems like those studied herein (Grau et al., 2011). This feature also contributed to obtain these high coefficients, and proved that such sliced products are susceptible to be inspected based on this type of non destructive tools. By way of conclusion, the fractal information based on both different parameters (Fd and L) and image types denoted a strong dependency of not only tissue features and natural morphology, but also of their composition in terms of fat and water fractions. These results match previous works, in which tissue morphologies have also been successfully characterized by fractal information in fat content terms by varying certain factors, such as the color space, fractal parameter and segmentation protocol. Mendoza et al. (2009) reported the possibility of using the fractal dimension to classify different cooked meat products, including pork. In this case, good classification results were obtained by including color spaces L*a* b* and HSV, but using only one gray value to extract tissue features. Serrano et al. (2019) also used fractal procedures (a multifractal analysis in this case) to successfully characterize Iberian and white pork loins in the morphology terms of fatty infiltration. These authors demonstrated that lots of information can be collected by the multifractal analysis from images also segmented from a single gray value. Indeed good results have been reported by using different features to fractal parameters, such as the quantification of fatty tissue based on counting pixels in a given area (Liu et al., 2018). This approach is less complicated on advantage, but has its limitations for collecting morphology features.
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Fig. 6 – Evolution of the regression coefficients between Fd (from the grayscale and RGB data blocks) and Xf with the number of values included in study. Circumference: calibration; Dot: cross validation; Black line: R2 ; Dotted line: RMSE; A: Salmon grayscale; B: Salmon RGB; C: Pork loin grayscale; D: Pork loin RGB.
Regarding the reported results, the feasibility of these imaging techniques could be compared to other more sophisticated ones. Some examples are hyperspectral and NIR imaging, computerized tomography imaging, etc. NIR images have been successfully used to predict fat attributes and marbling both pork and salmon (Huang et al., 2016; Ivorra et al., 2016a). Those attributes have been used to predict the content of fatty tissue and morphology, and to also study the shelf life and generation of degradation compounds. This is possible due to the chemometric capacity of such image types within the infrared zone of spectra. Indeed computerized tomography also allows the collection of both compositional and morphological information from fat tissues of this sample type, as reported by Font-i-Furnols et al. (2013), but presents long processing times. As regards statistical methods to model information from any imaging type with composition properties, both linear and non linear methods have reported good results. Some are stepwise regression, multilinear regression (MLR), partial least square (PLS), support vector machine (SVM), etc., and depends on the data structure, the studied features and the imaging technique. In our case, after previous studies SVM was the method that best fitted the necessities related to the amount of analyzed data per sample.
4.
Conclusions
The capacity of fractal analytics of digital images gave satisfactory results to characterize the two different analyzed tissues. The fractal information collected the generated variability because of the differences caused by the composition in fat and water fraction terms for both pork loin and salmon. Likewise, the variability between pork loin and salmon was also characterized because of differences in tissue morphology, mainly the fat distribution in the system, and even in those samples with no fat fraction differences. The two tested fractal parameters (fractal dimension and lacunarity) displayed a strong dependency on fat and water fraction evolution, and both were able to characterize these sample properties. The channel of the image did not show any considerable differences in the results, and the feasible use of their collected information was the main conclusion drawn. However, it was demonstrated that including the entire color spectra and all the channels reduced errors. Overall, the experiment results showed how using the fractal information of images as spectral data could represent a simple, accessible non destructive technique for characterizing the differences in both the composition and morphologies of these tissue types. This approach could be
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used both directly and to complement inspection processes to help improve classification and selection operations in food production chains. However, the variability intrinsically presented by these products has to be taken into account because it could generate alterations that should be considered to maintain accuracy.
Acknowledgment This study was supported by the Universidad Politécnica de Valencia by program “Ayudas para la Contratación de Doctores ˜ para el Acceso al Sistema Espanol de Ciencia, Tecnología e Innovación, en Estructuras de Investigación de la UPV (PAID10-17)”
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Contents lists available at ScienceDirect
Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp
Fresh-sliced tissue inspection: Characterization of pork and salmon composition based on fractal analytics Samuel Verdú ∗ , José M. Barat, Raúl Grau Departamento de Tecnología de Alimentos, Universitat Politècnica de València, Spain
a r t i c l e
i n f o
a b s t r a c t
Article history:
The capability of fractal analytics of digital images for characterizing sliced tissue was tested
Received 11 January 2019
in fat and water fractions terms. The study was based on three factors: tissue type (pork loin
Received in revised form 21 March
and salmon); fractal parameter (fractal dimension and lacunarity); image type in color terms
2019
(grayscale and RGB channels). After capturing images of tissue samples, the water and fat
Accepted 20 April 2019
fractions were analyzed from each one. The fractal information was expressed as specific
Available online 28 April 2019
spectra from each image type, which were related with composition properties. The rela-
Keywords:
reported that fractal information collected the variability due to both composition and tis-
tionship between both data blocks was tested by multivariate regression assays. The results Fresh sliced tissues
sue morphology. Both fractal parameters and all the image types successfully reported the
Inspection
results. The two fractal parameters displayed a strong dependency on components, and both
Fractal analytics
characterized sample properties. No considerable differences were found in the results for
Image
image type. However, the inclusion of the entire color spectra increased the observed coef-
Characterization
ficients. The idea presented here could be a simple rapid non destructive technique for
Composition
characterizing tissue composition. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
The yield increment necessity in industrial processes, and the sophistication of the operations involved in production chains specifically for the food industry, generate the requirements of new developments, which keep the system under control and reduce costs to a minimum (Lim and Antony, 2016). When a given food sector requires exceptional control measures for hygienic parameters, e.g., those to produce fresh and raw materials (meat, fish, dairy, etc.), the development of fast simple non destructive inspection techniques offers notable advantages for the entire production system (Chen et al., 2013a, b; Ropodi et al., 2015). The main advantage of non destructive inspection techniques is the increased velocity of a given operation, and a high rate of analyzed samples is achieved per time unit to collect information from entire lots sample by sample. The ability to obtain information continuously from each sample allows accuracy in inspection operations to improve auto-
matic works, like classification, slicing, packaging, labeling, storage, etc. (Arendse et al., 2017). Indeed one of the most productive areas in the control and monitoring of non destructive fresh products is image analysis in several categories. Some of these categories are visible 2D images, spectral imaging, X-ray imaging, among others (Jackman et al., 2011). Applications like classifying pork hams, assessing the tenderness of beef carcasses, controlling the freshness of gilthead sea bream based on gill and eye color changes, automatic fishbone detection, etc. (Dowlati et al., 2013; Ivorra et al., 2016a, b; Jackman et al., 2012; Konda Naganathan et al., 2015; Mery et al., 2011), have been previously reported, and have proven the potential of these technology groups that operate for such purposes. A visible image analysis is one of the most accessible techniques from which many studies have offered successful results in diverse research areas about versatility and reduced cost possibilities. This technique includes the fractal analysis of digital images. The fractal analysis is a group of calculated algorithms used to study and characterize highly complex systems with chaotic structures to
∗ Corresponding author at: Edificio 8E - Acceso F — Planta 0, Ciudad Politécnica de la Innovación, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain. E-mail address: [email protected] (S. Verdú). https://doi.org/10.1016/j.fbp.2019.04.008 0960-3085/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
21
detect measurable patterns which can offer valuable information from a given sample. An example of such is biological structures. Indeed biological systems have been studied mainly using the fractal analytics of digital images in biomedical and histological research areas to report useful applications for characterizing and diagnosing organic structure features. Some of these applications have been applied to study neurophysiology systems, organ malformations or glucose fluc´ 2016; tuation kinetics, among others (Akar et al., 2015; Kesic´ and Spasic, Weissman and Binah, 2014). Fractal information has also been used to develop applications for characterizing geological structures and their properties. Some examples include the use of fractal dimensions to characterize the urban nucleus (Ge and Lin, 2009; Zhang et al., 2008), to model the spatio-temporal behavior of fluvial landform evolution (Pelletier, 2007), and to quantify the properties of river deltas and their channel networks (Edmonds et al., 2011). Therefore, the application of this technique to the food industry offers real potential to be exploited. Some recent studies have applied the fractal analysis to characterize different types of fresh food tissues and processing types with both fresh meat and fish products. The influence of certain factors, such as origin, freshness and processing of tissue, is characterized and successfully modeled by processing fractal information. Some examples are the characterization of fatty infiltration in Iberian and white pork sirloins, color changes on the surface of fresh cut meat, evaluations of the effects of frozen storage on the tilapia microstructure (He et al., 2015; Quevedo et al., 2013; Serrano et al., 2013), and the evaluation of antioxidants in juices, bruising in red bayberries, browning in avocado, acrylamide in biscuits, the characterization of low-fat yogurts, etc. (Zheng et al., 2011). Although these studies have shown the effectiveness of fractals, fractal analytics has been used mainly as a tool to classify and characterize the composition of some products from a qualitative point of view. The development of non invasive tools to fulfill this aim, mainly with quantification capacity, is in accordance with the tendency of recent food regulations like (UE)
Fig. 1 – Experiment procedure scheme. Xw: water fraction; Xf: fat fraction; R, G and B: red, green and blue color image channels, respectively; Fd: fractal dimension; L: lacunarity; R: red; G: green; B: blue (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
2.2.
Preparing fresh-sliced samples
no. 1169/2011 of the European Parliament about food information sup-
2.
Material and methods
Two types of fresh-sliced tissues were used: pork loin and salmon. Both represent edible tissues from different origins that are often sliced, packaged and labeled automatically to be sold. Twenty-six slices of fresh pork loin from five different lots (26 × 5/130 samples) and 20 slices of fresh salmon from four different lots (20 × 5/100 samples) were bought from a local provider. The sizes of all the slices were 1 ± 0.5 cm thick and 15 ± 2.1 cm long. This range of sizes was that which the samples from the commercialized product originally had, which was not modified to maintain the morphological features from which they were originally processed (Step 1 in Fig. 1).
2.1.
Experiment procedure
2.3.
plied to consumers, which obliges food producers to include nutritional labeling on most processed food products. Hence this work aimed to evaluate the fractal analytics of digital images as a non destructive inspecting tool to evaluate the morphology and composition in the fat and water fraction terms of fresh sliced pork loin and salmon tissues by studying different fractal parameters such as spectral data within color spaces.
The experiment tested the capability of the fractal analytics of images to characterize sliced tissues in fat and water composition terms (Fig. 1). The objective of this procedure was to non destructively collect information about the pork loin and salmon that come in commonly processed and commercialized formats. The study was based on three factors: tissue type (pork loin and salmon), fractal parameter (fractal dimension and lacunarity) and image type (grayscale and RGB). The first step was to prepare the pork and loin samples. Next images of samples were taken (Step 2 in Fig. 1) and processed to obtain the grayscale and their R, G and B versions (Step 3 in Fig. 1). Then fractal parameters were extracted from these images (Step 4 in Fig. 1). After image processing, the fat and water fractions were analyzed from each sample (Step 5 in Fig. 1). The last step involved testing the dependency of both the compositional data (fat and water fractions) and the multivariable fractal data blocks (the spectra of the fractal parameters from grayscale, and the R, G, B and RGB images).
Image capturing
Images were obtained by a standard device that can be easily implemented into an online inspection in the production chain. The single images of one surface of each slice were obtained via a HD webcam C615 (CCD, 8 megapixels, Logitech International S.A., Switzerland) vertically fixed to a rigid structure 20 cm over the sample. The device was fitted inside a chamber to protect it from external lighting. The lighting source was a LED IP20 5 W lamp. The camera was connected to a laptop equipped with the control software. On the camera capture scene, a black matte material was placed to reduce reflections on the camera. The camera took pictures of 3264 × 2448 pixels in the JPEG format, which gave a pixel size of 0.05 mm/pixel (Step 2 in Fig. 1).
2.4.
Compositional characterization of samples
The composition in the moisture fraction (Xw) and fat fraction (Xf) terms of both sample types was analyzed. Moisture was determined by oven drying to constant weight at 100 ◦ C (ISO
22
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Norm R-1442, 1979) and fat was in accordance with ISO Norm R-1443 (1973) using a FOSS Soxtec System 2055 Tecator. All the parameters were expressed on a wet basis and analyzed in triplicate per slice (Step 3 in Fig. 1).
2.5. Image processing and acquiring fractal information In order to obtain the multivariable data matrices of the fractal information, images were processed by the method according to Zheng et al. (2011) with modifications (Steps 3 and 4 in Fig. 1). The basic procedures were: 1. Adapting images: the capturing of each sample was done in the RGB format and derived into four different images based on color format: grayscale, red (R), green (G) and blue (B). 2. Image segmentation: each image obtained in the previous step was segmented for each color value: grayscale: from black (0) to white (255); R channel: from black (0) to red (255); G channel: from black (0) to green (255); B channel: from black (0) to blue (255). This step provided 1024 segmented images from each image (256 × 4). 3. Extracting parameters: both the fractal parameters, namely fractal dimension (Fd) and lacunarity (L), were calculated for each segmented image from Step 2. Both fractal parameters were selected for their simple calculation. They essentially consider the relationship between the scale of a square (called box) and the number of this square required to scan the objects contained in a given image (i.e. contours, areas, etc.) in the image (Fig. 2B and C show two examples of the scales of box grids), although each one presents different approaches: 4. The fractal dimension (Fd) was obtained by the boxcounting method. Images were divided into boxes with a variable size denoted as box scale (ε). ε went from 1% to 15% of the entire image width. Thus the number of boxes containing pixels was counted for each ε, and called Nε. The loin sample included in Fig. 2B and C shows as example of two different box scale grids and the number of the boxes required to complete the segmented image. The relationship between ε and Nε can be described by the following equation: Fd = −lim
n→0
logNε logε
(1)
where Fd is the fractal dimension, Nε is the number of boxes containing pixels on a given box scale and ε is the box scale. Then Fd is the slope of the regression line for the log–log plot of ε and Nε. Fig. 2D shows this type of plot according to the loin example, where the determination coefficient was tested and the regression equation was calculated to obtain the absolute slope value. - Lacunarity (L) is based on quantifying the variation in pixel density at different ε by linear scanning across images. Scanning was done from left to right, and by descending row by row once this had finished. In this case, ε went from 1% to 50% of the entire image width. Eq. 2 represents L to be calculated on each box scale: Lε =
2
(2)
where Lε is lacunarity on a given box scale, is the standard deviation of the pixels in the boxes of that scale, and is the average of the pixels in the boxes on that scale. Thus the L of the entire scan was calculated as the average of the Lε values from all the tested ε. The salmon sample in Fig. 2B and C shows, by way of example, two different box scales, the starting point and direction of the linear scanning across the segmented image (black arrows), and the type of plot obtained during this process. Both parameters were calculated in 15 different grid positions for each image to avoid the effect of sample position in the capturing area. All 15 results were taken as the single replica data of each image. Data were obtained using FracLac for ImageJ created by Karperien (2013). 1. Obtaining spectra: the data acquired from each image by the above-explained processes were organized into spectra. These spectra were expressed as fractal parameter vs. color value for each image. Four spectra (one from each image type) of each fractal parameter were obtained per sample, from which a multivariate data block was created.
2.6.
Quantifying data block dependency
The dependency of both the compositional data (fat and water fractions) and the multivariable fractal data blocks (the spectra of the fractal parameters from the grayscale, and the R, G, B and RGB images) was tested by the non linear regression method Support Vector Machines (SVM) (Step 6 in Fig. 1). SVM is a powerful supervised learning methodology based on the statistical learning theory, which is commonly used for multivariable data analyses (Boser, Guyon, & Vapnik, 1992). The used version was epsilon-support vector regression (-SVM) and the radial basis function was kernel (RBF kernel). The dependencies of the water and fat fractions of both the fractal parameters spectra (Fd and L) and image information type were tested by this method. The results were evaluated in terms of calibration (Cal) and cross validation (CV) coefficients following (Ropodi et al., 2016). The method used for the cross validation process was “venetian blinds”. There were three data splits. Then 70% of the samples were taken as training data and 30% as testing data in three different iterations. The results were also evaluated by the root mean square error (RMSE), Eq. (3), which is a measure of the differences between the values predicted by the model and the observed values being modeled. These individual differences are also called residuals, and RMSE represents an aggregate of them all in a single measure.
RMSE =
n (X − X ˙i=1 o,i m,i )
2
n
(3)
where Xo is the observed values and Xm is the modeled values at place i. Procedures were performed with the PLS Toolbox, 6.3 (Eigenvector Research Inc., Wenatchee, Washington, USA), a toolbox extension in the Matlab 7.6 computational environment (The Mathworks, Natick, Massachusetts, USA).
3.
Results and discussion
3.1.
Acquiring fractal information (Fd and L)
The relationship between fractal information variation and the complexity of the taken images was tested to observe the evidence of the influence by the tissue components mor-
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
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Fig. 2 – Scheme of the fractal information obtained. Left: Fractal dimension (Fd); Right: Lacunarity (L). A: originally taken images of pork loin and salmon samples; B: example of the binary thresholded images with a large box size grid. C: The same images with the small box size grid. D: Performance plots and results of both fractal parameters; left: fractal dimension is the slope of log Nε vs. log ε plot (red square), where Nε is the box count and is the box scale; right: lacunarity values from the image scan across the box scale. Black arrows indicate the start position and directionality of the scan (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). phology. It was assumed that the fractal information in the spectra depended mainly on the complexity of the analyzed shapes because of the frequency and distribution of pixels in a given color value. In this case, however, a high load of the collected complexity in the images was verified to come from the combination of the different components of sliced samples (fat and muscle tissues). The evolution of both fractal parameters across the color values from each image type was observed. Fig. 3 illustrates the evolution of both fractal parameters across the grayscale of a pork loin sample as an example. Spectra denote a non constant evolution across color values, and peaks formed mainly around values 30–40. This behavior indicated real variation following the color values, where an inverse tendency between Fd and L was observed, but the main peak took place in the same zone. These peaks were
according to image type, with variations observed compared to spectra R, G and B (Fig. 5). Moreover, although both parameters were based on different calculation procedures, they reported the equivalent information of image complexity in this case. In spite of proving the variability of the fractal parameters, it was necessary to attach the real processed images from which the data set was obtained as spectra evolutions were easily interpreted. The evolution of the processed images on the grayscale of the pork loin example is shown at the bottom of Fig. 3. From value 0 (black), an increment in complexity was observed in the images because many pixels (frequency) in these color values produced the maximum complexity precisely where the fractal parameters generated the abovementioned peaks, from which complexity reduced following
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Fig. 3 – Example of the evolution of fractal parameters Fractal dimension (Fd) and Lacunarity (L) across the grayscale for a pork loin sample. The left axis represents Fractal dimension (red lines) and the right axis denotes Lacunarity (black lines). The bottom zone corresponds to the obtained segmented images following gray values. The range between the discontinued lines marks tones with the images that present a maximum complex shape (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4 – The 3D scatterplot of Fd (left) and L (right) for value 70 on the grayscale (Z-axis) vs. the fat and water fraction (Xf and Xw, respectively) from all the pork loin (green dots) and salmon (orange dots) examples. Letters P and S are an example of the pork loin sample and the salmon sample, respectively, with the same amount of Xf, but different fractal values (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). the reduction in the number of pixels, as visually observed. Indeed the shapes described by the pixels in each value corresponded principally to the variability in the fat and muscle tissue distributions. Therefore, it is noteworthy that most of the complexity collected by the fractal parameters was due to the morphology of both tissue types. This fact was crucial to assume the possibility of measuring the differences in not only the amount of fat, but also in the morphologies between the pork and salmon tissues.
3.2.
Results of the dependency of data blocks
A single relationship between tissue characteristics and fractal information was observed. However to further characterize samples, this variability had to be related first to the amount of each fatty and lean tissue, and then to composition. Fig. 4
shows an exploratory scatterplot by way of example, which represents Fd (left) and L (right) vs. the fat fraction (Xf) and the water fraction (Xw) for some samples of value 70 on the grayscale, which was taken as the average value of the complete spectra (Fig. 3). Here we see how the fractal parameters covariated with both Xf and Xw inversely, and two distributions can be described with marked tendencies, but with clear differences between pork loin and salmon. Fd increased with the fat fraction and decreased with the water fraction. L presented inverse behavior, which was already observed in the spectra of Fig. 3. This phenomenon depended on the features of the mathematical approach of both parameters. Although both displayed differences, high complementarity and parallelism were also observed. This behavior matched that indicated in previous studies, where applying these parameters to model the fat distribution in
Food and Bioproducts Processing 1 1 6 ( 2 0 1 9 ) 20–29
Fig. 5 – The spectra of Fd across the grayscale, channels R, G and B from the pork loin (green) and salmon (orange) samples with the same fat fraction (0.17 ± 0.8). The raw spectra from all 15 grid positions in each image were included. A: the Fd spectra of the grayscale; B: the Fd spectra of the red scale; C: the Fd spectra of the green scale; D: the Fd scale of the blue scale (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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beef samples was worked. Chen et al. (2013) a, b and Chen et al. (2012) reported the positive relationship between Fd and fatty infiltrations. In these studies, the Fd values, obtained by several methods, rose with increased beef marbling levels by augmenting the new areas with color differences in the pure lean color. This effect was applicable to both sample types, but their distributions presented some differences. These differences apparently occurred because salmon presented higher Fd values and lower L ones than the pork loin at a given fat fraction (points S and P in Fig. 4) for this explored gray value (70). This feature can be explained by the differences in fatty tissue distributions within slices. However, observing only one grayscale value was not enough to assume and understand this fact. Thus the complete Fd spectra from the grayscale, and channels R, G and B from a salmon sample and a pork loin sample with the same fat fraction (0.17 ± 0.8) (points P and S in Fig. 4), were plotted to explore these behaviors (Fig. 5). Fig. 5 shows the Fd spectra from the salmon (orange) and pork loin (green) for all image types. The former was the grayscale (Fig. 5-A), which collected the whole color variation transformed into gray values. The spectra presented a maximum around the 30–50 values for both sample types. Until that zone, pork loin obtained higher values than salmon. Salmon gave higher values from value 70 to the last one according to the scatterplot in Fig. 4, which meant most of the scale. This was interpreted as the salmon images presenting greater complexity toward light values than pork loin, which instead had high values toward dark values. This result falls in line with the fact that most of the pork loin color was formed by intense red values. Although the grayscale collects information from color features, the spectra from each RGB channel could report more specific information to characterize the samples. Fig. 5B, C and D respectively show the spectra from channels R, G and B. The spectra on the R scale better indicated the differences in the dark red values, where pork loin appeared with higher Fd values than salmon. This behavior was inversed around value 50 where, once again, salmon presented more complexity for the light values. Scale G presented marked differences for salmon in the light values. In the same way as for Scale B, salmon obtained high values for the light values. However, pork loin presented the maximum values across most of the spectrum toward the dark values. The predominant salmon colors were orange values, formed mainly by combinations of red and green values, which would explain the high values in the light values of G and for most of the R spectrum. The accentuated pork loin complexity as regards the dark values of channels R and B was also explained by the combination of the blue and red values producing intense red-magenta colors, which are typical of this meat tissue type. These results revealed the importance of the color dimension for the capability of Fd and L to collect morphological information from both the sample type and the amount of fat, which demonstrates that these fractal parameters could be insufficient if only one color threshold was taken into account due to their monofractal approach. In order to report the capacity of the fractal information to characterize the relationship with both composition and morphology, the last step involved studying and quantifying the fractal information dependency on the fat and water fractions to develop a plausible quantifier application. The study was done by taking the spectra of Fd and L from each image type and channel as the multivariable data block: grayscale, R,
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Table 1 – Fractal information and composition data blocks’ dependency study. Pork-loin
Fd
Complete spectra
L
Rcal RMSEcal Xw Rval RMSEcv Rcal RMSEcal Xf Rval RMSEcv Rcal RMSEcal Xw Rval RMSEcv Rcal RMSEcal Xf Rval RMSEcv
Salmon
grayscale
R
G
B
RGB
grayscale
R
G
B
RGB
0.99 5E-04 0.96 3E-03 0.98 4E-04 0.95 2E-03 0.98 5E-04 0.94 2E-03 0.98 4E-04 0.93 2E-03
0.97 6E-04 0.95 1E-03 0.98 4E-04 0.95 1E-03 0.97 5E-04 0.94 1E-03 0.98 3E-04 0.93 2E-03
0.94 8E-04 0.91 3E-03 0.97 7E-04 0.95 2E-03 0.95 8E-04 0.95 3E-03 0.96 7E-04 0.94 2E-03
0.95 6E-04 0.92 1E-03 0.95 6E-04 0.93 5E-04 0.95 6E-04 0.95 8E-03 0.95 5E-04 0.94 2E-03
0.99 6E-04 0.98 1E-03 0.98 5E-04 0.95 4E-03 0.98 6E-04 0.94 5E-03 0.98 5E-04 0.93 4E-03
0.99 5E-04 0.95 4E-03 0.98 4E-04 0.94 3E-03 0.98 5E-04 0.93 4E-03 0.98 4E-04 0.92 3E-03
0.98 8E-04 0.95 3E-03 0.98 8E-04 0.94 3E-03 0.98 8E-04 0.935 3E-03 0.98 7E-04 0.92 2E-03
0.98 7E-04 0.92 2E-03 0.98 6E-04 0.94 1E-03 0.98 7E-04 0.94 2E-03 0.98 6E-04 0.93 5E-03
0.85 9E-03 0.75 9E-02 0.63 1E-01 0.60 1E-03 0.74 9E-02 0.65 9E-01 0.78 9E-02 0.63 9E-01
0.99 6E-04 0.95 1E-03 0.99 5E-04 0.94 1E-03 0.98 6E-04 0.935 5E-03 0.98 5E-04 0.92 4E-03
Fd: fractal dimension; L: lacunarity; Xw: water fraction; Xf: fat fraction; R2 Cal: calibration coefficient; RMSEC: root mean square error of calibration; R2 CV: cross validation coefficient; RMSECV: root mean square error of cross validation; R: red channel of images; G: red channel of images; B: red channel of images; RGB: complete color information of images.
G and B, and RGB as a single block. The results of the non linear regressions carried out for each data block combination are offered in Table 1. The results report high coefficients for most combinations of data blocks for both calibration and cross validation. No differences were observed between Xf and Xw, and both parameters presented high coefficients for the two fractal parameters. Image type and channel had coefficients up to 0.95, except for channel B for salmon, which presented 0.85 as the maximum and 0.63 as the minimum. The separate color channels showed slightly lower coefficients in general, and tended to reach high values for the grayscale and RGB. This meant that each image channel collected singly specific information which, when combined, presented a better fit. Therefore, the separation of the color channel might not be recommendable in these cases. Thus after learning the impact of data reduction on the regression coefficients, the number of values of the spectrum used in the prediction was also evaluated to know how reducing the volume of the spectral data would influence accuracy. The study was redone from one color value, as in the common image segmenting procedure, to complete the spectrum. The data employed for each calculation were obtained by isolating the fractal information from the values with the highest fractality (peaks in the fractal spectra) from the grayscale and RGB. The improvement in the coefficients, achieved by gradually including the contiguous color values, was evaluated (10 contiguous values were included in each step). Fig. 6 offers an example of the evolution of R2 Cal and R2 CV between Fd and Xf by progressively including values in the dependency analysis for both the grayscale (Fig. 6A and C) and RGB (Fig. 6B and D). The results describe how including color values notably improved the coefficients and lowered the root mean square error (RMSE). This effect was common for pork loin (Fig. 6A and B) and salmon (Fig. 6C and D). Moreover, RGB presented fewer differences between the obtained coefficients using only one color value and all the values compared to the grayscale. This effect came about because RGB started with three values from the R, G, and B spectra peaks (one per channel), while the grayscale had only one. These observations revealed that
although the spectra value that formed the peak collected the maximum information about the sample morphology, the other spectra represented fundamental information to complete and explain the variability produced by the samples’ properties. Therefore, including fractal information from the complete color variability (grayscale and RGB) in this study gave better results than each separate color channel (R, G and B). However the predominance of the red values, which are typical of these samples, allowed us to obtain a high coefficient tendency for the R isolated channel. It is well-known that Xf and Xw are strongly and inversely related in tissue systems like those studied herein (Grau et al., 2011). This feature also contributed to obtain these high coefficients, and proved that such sliced products are susceptible to be inspected based on this type of non destructive tools. By way of conclusion, the fractal information based on both different parameters (Fd and L) and image types denoted a strong dependency of not only tissue features and natural morphology, but also of their composition in terms of fat and water fractions. These results match previous works, in which tissue morphologies have also been successfully characterized by fractal information in fat content terms by varying certain factors, such as the color space, fractal parameter and segmentation protocol. Mendoza et al. (2009) reported the possibility of using the fractal dimension to classify different cooked meat products, including pork. In this case, good classification results were obtained by including color spaces L*a* b* and HSV, but using only one gray value to extract tissue features. Serrano et al. (2019) also used fractal procedures (a multifractal analysis in this case) to successfully characterize Iberian and white pork loins in the morphology terms of fatty infiltration. These authors demonstrated that lots of information can be collected by the multifractal analysis from images also segmented from a single gray value. Indeed good results have been reported by using different features to fractal parameters, such as the quantification of fatty tissue based on counting pixels in a given area (Liu et al., 2018). This approach is less complicated on advantage, but has its limitations for collecting morphology features.
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Fig. 6 – Evolution of the regression coefficients between Fd (from the grayscale and RGB data blocks) and Xf with the number of values included in study. Circumference: calibration; Dot: cross validation; Black line: R2 ; Dotted line: RMSE; A: Salmon grayscale; B: Salmon RGB; C: Pork loin grayscale; D: Pork loin RGB.
Regarding the reported results, the feasibility of these imaging techniques could be compared to other more sophisticated ones. Some examples are hyperspectral and NIR imaging, computerized tomography imaging, etc. NIR images have been successfully used to predict fat attributes and marbling both pork and salmon (Huang et al., 2016; Ivorra et al., 2016a). Those attributes have been used to predict the content of fatty tissue and morphology, and to also study the shelf life and generation of degradation compounds. This is possible due to the chemometric capacity of such image types within the infrared zone of spectra. Indeed computerized tomography also allows the collection of both compositional and morphological information from fat tissues of this sample type, as reported by Font-i-Furnols et al. (2013), but presents long processing times. As regards statistical methods to model information from any imaging type with composition properties, both linear and non linear methods have reported good results. Some are stepwise regression, multilinear regression (MLR), partial least square (PLS), support vector machine (SVM), etc., and depends on the data structure, the studied features and the imaging technique. In our case, after previous studies SVM was the method that best fitted the necessities related to the amount of analyzed data per sample.
4.
Conclusions
The capacity of fractal analytics of digital images gave satisfactory results to characterize the two different analyzed tissues. The fractal information collected the generated variability because of the differences caused by the composition in fat and water fraction terms for both pork loin and salmon. Likewise, the variability between pork loin and salmon was also characterized because of differences in tissue morphology, mainly the fat distribution in the system, and even in those samples with no fat fraction differences. The two tested fractal parameters (fractal dimension and lacunarity) displayed a strong dependency on fat and water fraction evolution, and both were able to characterize these sample properties. The channel of the image did not show any considerable differences in the results, and the feasible use of their collected information was the main conclusion drawn. However, it was demonstrated that including the entire color spectra and all the channels reduced errors. Overall, the experiment results showed how using the fractal information of images as spectral data could represent a simple, accessible non destructive technique for characterizing the differences in both the composition and morphologies of these tissue types. This approach could be
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used both directly and to complement inspection processes to help improve classification and selection operations in food production chains. However, the variability intrinsically presented by these products has to be taken into account because it could generate alterations that should be considered to maintain accuracy.
Acknowledgment This study was supported by the Universidad Politécnica de Valencia by program “Ayudas para la Contratación de Doctores ˜ para el Acceso al Sistema Espanol de Ciencia, Tecnología e Innovación, en Estructuras de Investigación de la UPV (PAID10-17)”
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