Postharvest Biology and Technology 51 (2009) 311–319
Contents lists available at ScienceDirect
Postharvest Biology and Technology journal homepage: www.elsevier.com/locate/postharvbio
‘Rocha’ pear firmness predicted by a Vis/NIR segmented model Ana M. Cavaco a,∗ , Pedro Pinto c,d , M. Dulce Antunes a , Jorge Marques da Silva b , Rui Guerra c a
CDCTPV, Universidade do Algarve, Campus de Gabelas, 8005-139 Faro, Portugal CEB, Faculdade de Ciências da Universidade de Lisboa, Ed. C2, Campo Grande, 1749-016 Lisboa, Portugal c CEOT, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal d Instituto de Soldadura de Qualidade, Taguspark, Oeiras, Av. Prof. Doutor Cavaco Silva, 33, 2740-120 Porto Salvo, Portugal b
a r t i c l e
i n f o
Article history: Received 3 June 2008 Accepted 30 August 2008 Keywords: Diffuse reflectance Postharvest Pyrus communis L. Non-invasive Shelf-life
a b s t r a c t We present a segmented partial least squares (PLS) prediction model for firmness of ‘Rocha’ pear (Pyrus communis L.) during fruit ripening under shelf-life conditions. Pears were collected from three different orchards. Orchard I provided the pears for model calibration and internal validation (set 1). These were transferred to shelf-life in the dark at 20 ± 2 ◦ C and 70% RH, immediately after harvest. External validation was performed on the pears from the other two orchards (sets 2 and 3), which were stored under different conditions before shelf-life. Fruit was followed in the shelf-life period by visible/near infrared reflectance spectroscopy (Vis/NIRS) in the range 400–950 nm. The correlation between firmness and the reflectance at some wavelength bands was markedly different depending on ripening stage. A segmented partial least squares model was then constructed to predict firmness. This PLS model has two segments: (1) unripe and ripening/ripe pears (high firmness); (2) over-ripe pears (low firmness). The prediction is done in two steps. First, a full range model (full model) is applied. When the full model prediction gives a low firmness value, then the over-ripe model is applied to refine the prediction. The full model is reasonably significant in regression terms, robust, but allows only a coarse quantitative prediction (standard deviation ratio, SDR = 2.48, 1.50 and 2.40 for sets 1, 2 and 3, respectively). Also, RMSEP% = 139%, 91% and 56%, indicating large relative errors at low firmness values. The segmented model improved moderately the correlation, and the values of RMSEC, RMSEP and SDR; it improved significantly the RMSEP% (29%, 55% and 31%), providing an improvement of the relative prediction errors at low firmness values. This method improves the ordinary PLS models. Finally, we tested whether chlorophyll alone was enough for a predictive model for firmness, but the results showed that the absorption of chlorophyll alone does not explain the performance of the PLS models. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Assessment of ‘Rocha’ (Pyrus communis L.) pear ripening is of major concern in both pre- and postharvest long-term storage periods. Currently, this depends on the destructive determination of fruit firmness through pressure tests using a penetrometer on the fruit surface. ‘Rocha’ pears are considered at harvest optimal maturity when fruit have a firmness of 55–65 N (Alexandre, 2001), at the optimal eating ripe stage when firmness is ∼20 N (Isidoro and Almeida, 2006), and are considered over-ripe at lower values. The pattern of softening and ripening of ‘Rocha’ pear closely follows the climacteric ethylene rise (Fonseca et al., 2004a). When pre-climacteric ‘Rocha’ fruit are not exposed to low temperatures before a shelf-life period, they do not ripen or soften uniformly, acquiring in many cases a rubbery texture (Fonseca et al., 2005).
∗ Corresponding author. Tel.: +351 289 800900x7614; fax: +351 289800066. E-mail address:
[email protected] (A.M. Cavaco). 0925-5214/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2008.08.013
Furthermore, although while not loosing their capacity to ripen, as is the case with the ‘Anjou’ variety (Wang and Mellenthin, 1975), ripening of ‘Rocha’ pears is influenced by storage atmosphere conditions (Sánchez and Morais, 2001; Galvis-Sánchez et al., 2003, 2004). Visible/near infrared reflectance spectroscopy (Vis/NIRS) has been used to assess firmness in a wide number of fruit such as apples (Zude et al., 2006), kiwifruit (Clark et al., 2004), peaches (Slaughter, 1995), watermelon (Tian et al., 2007), grapes (Herrera et al., 2003), oranges (Cayuela, 2008), and tomatoes (Shao et al., 2007). In particular, the influence of the fruit development stage on the relationship between mechanical and spectral optical properties has been described in apple (Zude-Sasse et al., 2000). Also, recent work has shown that NIR spectroscopy (wavelengths above 780 nm) failed to provide an appropriate prediction model for firmness of ‘Conference’ pears (Nicolaï et al., 2008). A typical fruit reflectance spectrum contains information on both absorption and scattering. While absorption is related to the presence of chemical components, scattering is related to the size,
312
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
shape and microstructure of the tissue (Nicolaï et al., 2007). Scattering results from multiple refractions at phase changes inside the material, particularly at the cell wall interfaces since they induce abrupt changes in the refractive index (McGlone et al., 1997). The roles of scattering and absorption in the production of R spectra are different. Indeed, the scattering process affects the intensity level of the R spectrum rather than the shape, this being more related to the absorption process (Nicolaï et al., 2007). Hence, the information provided by NIR spectroscopy is mainly determined by the absorption. Recent investigations enhance the scattering-related information through multispectral or hyperspectral imaging, by measuring also the spatial profile of the backscattered light intensity on the fruit surface (Lu, 2004; Qing et al., 2008). The main goal of this study was the construction of a segmented partial least squares (PLS) model for firmness of ‘Rocha’ pears during ripening under shelf-life conditions. We present the physiological justification and validate the model with internal and external fruit sets, demonstrating that this method improves the ordinary PLS models. 2. Materials and methods 2.1. Fruit Pear fruit (P. communis L. cv. Rocha) were collected from three different orchards. Orchard I, located in Mafra (Portugal), provided the pears for model calibration and internal validation (set 1). External validation was performed using different sets of pears from two other orchards: orchard II (set 2), located also in Mafra (Portugal), and orchard III (set 3), located 60 km north, separate from orchards I and II, in Cadaval (Portugal). Pears ranging from 71 to 295.6, 114.2–224.5 and 116.3–162.2 g were collected from orchards I, II and III, respectively, at harvest ripening stage (Alexandre, 2001), by the end of August 2007. Pears were immediately transported to commercial packinghouses (Frutoeste/Mafra or Coopval/Cadaval), and hand-sorted to select undamaged fruit. Pears from orchards II and III were further treated with Imazalil (commercial dose) and drenched with 636 mg L−1 DPA. Fruit set 1 (157 pears) were immediately transferred from orchard I to shelf-life conditions in the dark at 20 ± 2 ◦ C and 70% RH and evaluated regularly, using 10–20 fruit per assay, over a 46 d period. Fruit sets 2 (70 pears) and 3 (60 pears) underwent different storage conditions before shelf-life, namely, 7 months at 0 ◦ C, RH 90–95% and CA (1.5 kPa O2 + 0.5 kPa CO2 ), and 8 months at −0.5 ◦ C, RH 94–96% and CA (2 kPa O2 + 0.5 kPa CO2 ), respectively. Shelf-life of sets 2 and 3 was 13 and 18 d, respectively. The distribution statistics of all fruit sets are presented in Table 1. The first measurements started after 24 h of equilibration under shelf-life conditions. All measurements were carried out on two Table 1 Distributional statistics of data sets used for model calibration and validation of ‘Rocha’ pear firmness (N). Firmness (N) Samples indices N Orchard I full set Calibration set Internal validation set 1 External validation set 2 External validation set 3
157 105 52 70 60
Mean
S.D.
Max
Min
36.7 36.7 36.6 20.4 22.7
26.6 26.7 26.5 15.6 18.9
77.5 77.5 72.6 50.6 65.4
1.5 1.5 2.2 9.7 3.8
No statistically significant difference (p < 0.05) was found among the various fruit sets.
opposite sides on the equator of each pear. Each value represents the average of the two positions and is presented as the fruit value. 2.2. Vis/NIR reflectance spectroscopy The spectroscopic measurements were taken with an optical Vis/NIR spectrometer (USB4000-VIS-NIR, Ocean Optics, USA), in the range 350–1035 nm with an average resolution of 1.4 nm (optical resolution imposed by the entrance slit of 25 m). All the measurements were taken with an integrating sphere (IS) (ISP-50-8-R-GT, Ocean Optics, USA), in the 0◦ /d SCI configuration (quasi-normal incidence, specular component included). Light from a tungstenhalogen source (HL-2000-FHSA, Ocean Optics, USA) was sent to the fruit through an optical fibre and the re-emerging light collected by a second fibre and sent to the spectrometer. For acquisition, processing and calibration, specific software was used (Spectra Suite, Ocean Optics, USA). The low radiation from the light source below 400 nm and the low sensitivity of the CCD camera in the lower and upper ( 950 nm) parts of the spectrum produced a low signal to noise ratio and determined the useful wavelength range between 400 and 950 nm. Each fruit spectrum was recorded as diffuse reflectance (R), by averaging 5 scans, taking 2 s to measure each side of a pear. R was calculated automatically taking the raw sample spectrum (RS ), the dark spectrum (RD ) and the reference spectrum (RR ) (Spectralon white surface, WS-1, Ocean Optics, USA), according to R = 100(RS − RD )/(RR − RD ). All Vis/NIRS measurements were carried out in the dark at 20 ± 2 ◦ C. 2.3. Fruit quality attributes Immediately after spectra acquisition, sampled pear fruit were weighed and the respective surface colour determined at three different positions around the fruit equator with a colorimeter (Minolta CR-200 Chroma meter, Japan) in the CIE L*a*b* colour space. Firmness was determined by puncture, after skin removal, with a Chatillon Force TCD200, Digital Force Gauge Dfis50 penetrometer, (Chatillon, USA) fitted with an 8 mm diameter plunger at a depth of 7 mm. Dry matter (DM, %) was assessed after drying the pulp and fruit peel separately at 60 ◦ C for at least 3 d. 2.4. Data analysis The raw spectra obtained from the spectrometer consisted of 2685 data points (3648 in the full range), corresponding to the average software resolution of 0.19 nm. However, only the optical resolution of about 1.4 nm should be taken into account. This corresponds to approximately 8 pixels in the spectrometer CCD sensor and a corresponding data reduction to ∼360 points. We have further introduced a factor of ∼3 obtaining a final spectra with 114 wavelength data points. These Vis/NIR spectra were correlated with firmness using the partial least squares algorithm (Wold et al., 2001). The PLS was implemented by us in FORTRAN and validated by reproducing the results of Geladi and Kowalski (1986), a paper with a working example. Data manipulation and auxiliary calculations were performed in MATLAB® (The MathWorks, Inc., Natick, MA, USA, 1998). Other data pre-treatments were also tried. This included the calculation of the derivative spectra and their logarithmic transformation. However, no advantage was found in using these procedures. From set 1, 105 pears were used for calibration and 52 for internal validation. The model was then applied to set 2 (60 pears) and set 3 (70 pears), for external validation. All data sets were compared by a one-way ANOVA for a significant level of p < 0.05 (SigmaStat 2.0, SPSS Science, USA) and found statistically equivalent, despite their apparent differences in means and ranges (Table 1). Model perfor-
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
313
mance was expressed as root mean squared errors of calibration (RMSEC) and prediction (RMSEP), and the correlation coefficient (r) between the predicted and measured parameter. For the calculation of RMSEC a “leave two out” procedure was adopted. We have also calculated the RMSEP% (RMSEP calculated with the relative errors), the standard deviation ratio (SDR = valid /RMSEP, where valid is the standard deviation of the validation set) and the percentage of predictions with error below 30% [denoted % (error< 30%)]. 3. Results and discussion 3.1. Relations between the reflectance spectra and fruit softening and ripening physiology Firmness, determined by pressure testing, has been shown to be an excellent indicator of ‘Rocha’ maturity on the tree (Alexandre, 2001), and of ripening stage during shelf-life after storage (Cavaco et al., 2008). The latter was confirmed in fruit sets 2 and 3, which showed uniform decreasing firmness values during a shelf-life of about 3 weeks (data not shown). Yet, as reported by Fonseca et al. (2005), ‘Rocha’ pears transferred directly to shelf-life after harvest (as in set 1), exhibited a non-uniform softening rate, showing after 46 d the same probability of finding firm and soft pears (data not shown). In general, softening of ‘Rocha’ pears coincides with the climacteric rise, reaching optimal eating ripe stage at a firmness of around 20 N (Isidoro and Almeida, 2006), after which they are considered over-ripe and/or post-climacteric. Fruit ripening and softening, however, are complex processes and in ‘Rocha’ pears, softening seems to be a consequence of progressive cell wall modification and disassembly by enzyme action, leading to the solubilisation and depolymerisation of pectins and hemicellulases (Fonseca et al., 2004b, 2005 and references therein). The flesh softening leads to a lower opacity, increasing light penetration depth and decreasing the level of diffuse reflectance. However, this scattering effect may be obscured by absorption effects. We have found that the plot of the correlation r() between the pear firmness (F) and the reflectance (R) is a good way to understand how ripening contributes to the reflectance spectra obtained. Correlations were calculated for three cases: (i) all pears (solid line); (ii) only for pears with firmness >10 N (high-F range) (open circles); and (iii) only for pears with firmness 40 N, had mainly positive t[1] values. Thus, one expects that the model has, at least, the ability to discriminate between low and high firmness values. The graph also shows three different groups inside set 1, coinciding with low-firmness, gradient and high-firmness. This points to the possibility of obtaining better results through separate modelling. The gradient group, however, has just a few elements and we will consider first a model for all the pears (the full model) and then a specific model for the low firmness pears (the low-F model). The scarcity of intermediate F values might be associated with sudden and non-uniform climactericdependent ripening changes among the full set of these ‘Rocha’ pears that were not exposed to cold, prior to shelf-life (Fonseca et al., 2005). Data presented in this and in the last section have thus provided a firm basis for the main hypothesis followed in this work: that for climacteric fruit ripening, a segmented model possibly produces better results in respect to firmness prediction, since the segments are identified with the pre-climacteric/unripe to postclimacteric/over-ripe fruit (F < 10 N) changes. As a consequence, the following approach was undertaken to obtain the best prediction model for firmness of ‘Rocha’ pears during shelf-life: (i) to construct a full range model able to discriminate between high and low values, which is expected to present large relative errors at low-F values; (ii) to construct a PLS model for the low-F range and investigate the differences between this and the PLS model for the full range; (iii) to incorporate a local refinement to the full PLS model by using a model calibrated only for the range 2–10 N. The mixed/segmented model applies the low-F model to pears with low-F values (as predicted by the full range PLS model in a first stage) and the full range model predictions are kept for all the other pears.
Fig. 2. PLS scores plot for the first component showing the existence of three groups inside the calibration data set (from set 1).
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
315
Table 2 Summary of the models presented in this work concerning firmness of ‘Rocha’ pear in the shelf-life along ripening. Model Full-range Set 1 (cal) Set 1 (valid) Set 2 Set 3 Low-F Set 1 (cal) Set 1 (valid) Set 2 Set 3 Segmented Set 1 (cal) Set 1 (valid) Set 2 Set 3
Range (N)
No. of LV
1.5 –77.5
8
1.5 –9.6
3
1.5 –77.5
Colorimetry only a* Set 1 (cal) 1.5 Set 1 (valid) –77.5 Set 2 Set 3
3+8
RMSEC/RMSEP (N)
RMSEP%
10.9 10.7 10.4 7.9
139 91 56
0.9 1.1 1.5 1.7 8.9a 10.1 8.3 6.8
rc 2 /rp 2
Bias (N)
SDR
% (error < 30%)
Pred. mean (N)
Pred. std dev (N)
0.88 0.85 0.74 0.83
0.0 −0.1 0 0
2.90 2.48 1.50 2.40
66 60 44 55
36.7 36.7 20.4 22.7
25.1 22.3 20.2 18.7
21 21 27
0.71 0.53 0.16 0.02
0.0 0.1 0 0
1.88 1.49 1.00 0.88
89 83 83 86
3.8 3.7 7.7 7.7
1.3 1.2 1.3 1.1
29 55 31
0.90 0.86 0.79 0.86
1.6 2.7 −0.6 0.8
3.00a 2.63 1.89 2.77
86 83 64 80
35.1 33.9 21.0 21.9
26.3 25.2 18.4 18.2
1
18.3 15.9 7.6 5.6
155 43 28
0.53 0.64 0.77 0.92
2.1 1.1 0.8 1.9
1.46 1.67 2.06 3.35
47 58 67 78
34.6 35.5 19.6 20.8
21.9 23.4 14.9 16.4
63 36
0.71 0.59 0.83
1.7 3.9
1.75a 1.49 2.30
66 67 73
35.1 32.7 23.6
24.4 26.7 19.3
0.83 0.55 0.88
1.7 0.4 −1.8
2.41 1.38 2.72
72 63 68
34.9 33.9 24.5
25.2 27.0 20.6
Colorimetry full Set 1 (cal) Set 1 (valid) Set 3
1.5 –77.5
6
15.3a 17.8 8.2
R (689 nm) Set 1 (cal) Set 1 (valid) Set 3
1.5 –77.5
1
11.1 19.2 7.0
107 36
“Pred. mean” and “pred. std dev” stand for the mean and standard deviations of the predicted data (compare with true values from Table 1. See Section 2.4 for any details concerning definition and/or calculation of the various parameters included in this table. a Not a true RMSEC, but RMSEP applied to the calibration set.
3.2.2. PLS full-range model for firmness The best full range calibration model parameters obtained for the firmness of set 1 are presented in Table 2. We have then applied the model to the external sets, differing in both orchard and the storage conditions, in order to challenge the model in extreme conditions. In doing that, we have performed a bias correction, usually done in commercial instruments (e.g. QS200, Unitec, Italy), which corresponds to shifting the predictions by the amount ( − < Fpred > ), where is the average of the real firmnesses and is the average of the firmness predictions. In practice, given a new batch of fruit, one collects a representative sample of its population and performs intrusive measurements in order to introduce a bias correction in the model. The respective scatter plots of predicted vs. measured firmness by using the penetrometer for the calibration and the prediction data sets are depicted in Fig. 3 and the results quantified in Table 2. Overall, it was found that the external samples were reasonably well modelled. External validation set 3 had an even lower value of RMSEP than the internal validation set 1. This is probably due to the more uniform ripening behaviour (smaller variability) which approximates all the pears from the average behaviour defined by the internal set (with larger variability). The external validation set 2 had similar RMSEP but worse SDR. Mathematically this is understood by the smaller range of variation of firmness for this data set. The model constructed for ‘Rocha’ pears was reasonably significant in regression terms (rp 2 = 0.85) for set 1, but the respective SDR gave a 2.48 value, which confirms that only a coarse quantitative prediction for firmness is possible (McGlone et al., 2002; Nicolaï et al., 2007), as formerly expected. Finally, the RMSEP% had a value of 139%, which is essentially caused by overestimation in the low-F range. For set 1, the percentage of predictions below 30%
error was about 60%. Again, this is due to the bad model performance in the low-F range. The external sets, however, were again more uniform in the low-F region and gave lower values of RMSEP%. Either way, the dispersion of the predictions in the low-F range was visible for all data sets. As a practical result, this model classifies as medium-firm a significant number of pre- and senescent pears (Fig. 3).
Fig. 3. Full-range prediction model for firmness of ‘Rocha’ pear. Orchard I fruit transferred directly from the tree to the shelf-life was used to construct the model (+ calibration set). Internal and external validations results are also represented. () Internal validation set 1; () external validation set 2; () external validation set 3. The central line represents the ideal prediction and the dotted lines the error bars corresponding to RMSEP of set 1. It is clear that the model produces very inaccurate results, in relative terms, for the low-F pears.
316
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
The uniformity of the maturation process may represent an important limitation to the predictive ability of the model. The PLS predictions for fruit firmness (and other characteristics) are not based, in general, on physical measures directly related with firmness, but in the measurement of other factors that, like firmness, change during ripening. For example, Zude et al. (2006) argue that flesh firmness and chlorophyll content are explained by parallel metabolic processes of chloroplast degradation and pectin conversion due to fruit maturation. The PLS model thus, relates changing trends during ripening, usually not directly related by cause and effect. The correlation between these trends will be stronger for uniform ripening processes and weaker in the opposite case. This is precisely observed in Fig. 3. Nevertheless, even without any refinement, the results compare well with some recent investigations in apple. We compare mainly the prediction correlations, rp 2 , and the SDR values; comparing directly RMSEP values is not very elucidating, unless the populations’ statistics are similar. ‘Rocha’ pear prediction model for firmness showed a better performance in both regression (rp 2 = 0.85 vs. 0.59) and prediction (SDR = 2.48 vs. 1.6) terms than that constructed for ‘Royal Gala’ apple in the 500–750 nm range by McGlone et al. (2002). The paper by Peirs et al. (2002) does not allow for calculation of SDR values, since the statistical parameters of the population are not indicated; however, the standard errors of prediction vary between 8 and 12 N, which is comparable to our RMSEP. In the work of Zude et al. (2006), merging NIRS and acoustic testing, the value of SDR is not available also. However, from their Fig. 3, one can estimate that the standard deviation of the population firmness is about 14 N/cm2 . Since the lowest standard error of cross validation is 7.73 N/cm2 , one obtains SDR ∼1.8 in the best case. With regard to other fruit, the Vis/NIR (350–2500 nm) was used for ‘Heatwave’ tomato (Shao et al., 2007), with a worse correlation (rp 2 = 0.69) but much better prediction capability (SDR = 7.82/2.24 = 3.5). With ‘Satsuma’ mandarin (Gómez et al., 2006), the predictions for the compression force are also worse than ours (rp 2 = 0.68, SDR = 1.7). Prediction of kiwifruit firmness was done by McGlone and Kawano (1998), the best result being rp 2 = 0.76 and SDR = 2.0. The comparison with other models should be done with care. Particularly, the wavelength range of the measurements is very important. Measurements extending more deeply into the NIR region have access to more information. Of particular interest may be the absorption by water (overtone absorption bands due to the water OH bonds at ∼970 nm, ∼1450 nm and ∼1940 nm). For example, a good model was constructed for firmness in watermelon (Tian et al., 2007), both in regression and prediction terms (Rp = 0.974; RMSEP = 0.589 N) using the Vis/NIR spectra range (350–1000 nm), while Nicolaï et al. (2008) did not succeed in constructing a significant prediction model for firmness in ‘Conference’ pears, even using the 780–1700 nm wavelength range. 3.2.3. PLS model for firmness in the low-F range (F < 10 N) We have constructed a PLS model for the low firmness pears from the subset of calibration data with F < 10 N (35 pears for calibration and 18 pears for validation) (Table 2). The small number of elements for calibration is acceptable because LV for the model was only 3. The low-F model SDR is 1.49, low but expected, given the small range of firmness values and consequent limited variability available to calibrate the model (Fig. 4). The calculation of the SDR value for the full model applied to the low-F region only gave SDR = 0.18. Fig. 4 also shows the predictions for the low firmness pears of the external sets (again, a bias correction has been made to the low firmness model), which were much better than those obtained with the full model (Fig. 3).
Fig. 4. Predictions for firmness of ‘Rocha’ pear in the low-F range (F < 10 N). Low-F model: () calibration set; () internal validation set 1; (♦) external validation set 2; () external validation set 3. Full-range model: (+) calibration set; (×) internal validation set 1; (–) external validation set 2; (*) external validation set 3. (–) Ideal prediction. It is clear that a local bias correction did not solve the problem of the full range model.
3.2.4. Segmented PLS model for firmness Considering (i) the evidence supporting the suggestion that reflectance spectra behave according to the fruit ripening stage, (ii) the inadequacy of the full range model to give good relative predictions for pears with low firmness, and (iii) the adequacy of the low firmness model for the same pears, we have built a mixed model based on the following algorithm: 1. to apply the full range model to all pears, 2. then, for each pear: (a) if prediction < 30 N, then apply the low firmness model; (b) otherwise, keep the full range model prediction. The last step could be “apply the high firmness model” instead of “keep the full range model”. However, this approach did not produce the best results, probably because the number of samples in the range 10–40 N was very reduced and insufficient to calibrate properly the high firmness model. Thus, we have kept the full range model. The threshold of 30 N was chosen based on Fig. 4, where it can be seen that the full-range model may overestimate the firmness by more than 20 N in the low-F range. It is expected that this model produces better results in the low-F range. There is a problem, however: if the full range model underestimates a given high firmness value by predicting a number smaller than 30 N, the low-F range model will produce an even lower prediction, enhancing the underestimation. The balance between positive and negative aspects of model segmentation is, however, favourable to this approach. Results obtained for the calibration and validation sets are depicted in Fig. 5 and Table 2. The segmentation algorithm was not implemented in the stage of calibration, and thus a true RMSEC is not available. However, a RMSEP may be calculated for the calibration set. This gives RMSEP (for cal. set) = 8.9 N. The model represents a slight improvement in RMSEP, r and SDR. On the other hand, RMSEP% and % (error < 30%) were significantly enhanced, due to the significant improvement in relative prediction error at low firmness values (Figs. 3 and 5 and Table 2). Model validation sets are also depicted in the same figure (again, bias corrections were performed on external validations). The most important point to notice is that all the validations, internal or external, improved their statistical parameters, specifically RMSEP, RMSEP% and SDR (Figs. 3 and 6 and Table 2). The principle that seg-
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
Fig. 5. Predictions for the firmness of ‘Rocha’ pear using the segmented PLS model. (+) Calibration set; () internal validation set 1; () external validation set 2; () external validation set 3. The central line represents the ideal prediction and the dotted lines the error bars corresponding to RMSEP of set 1.The predictions at low firmness are much better than those of Fig. 3. The drawback is the appearance of about 4–5% new under-predictions.
mentation may improve the modelling of climacteric fruit is thus sustained. Indeed, the comparison of Figs. 3 and 5 shows that the mixed model is clearly better in the low-F range. There is, however, a small drawback: the appearance of new underestimations by the mixed model, as discussed above. There were two new underestimations for the internal validation set (∼4% of internal validation samples) and five new underestimations for the calibration set (∼5% of calibration samples). The corresponding percentage for the external sets was much lower (Fig. 5). 3.3. Models for firmness based on colorimetry and single wavelength analysis The r() curves depicted in Fig. 1 and the PLS regression coefficients for the full-range model, which peaked around 689 nm (data not shown), suggest that the predictive capability of the Vis/NIRS model relies heavily on the reflectance values around the absorption band of chlorophyll. Thus, one is led to think that a simpler method of measurement could also produce reliable predictions, as
Fig. 6. Predictions for the firmness of ‘Rocha’ pear based on the colorimetric a* value. Left: relation between firmness and a* for all data points. Right: predictions for firmness. (+) Calibration set; () internal validation set 1; () external validation set 2; () external validation set 3. The central line represents the ideal prediction and the dotted lines the error bars corresponding to RMSEP of set 1. The linear regression was done on the calibration set and the regression coefficients applied to the validation set. The model was also segmented, with regression coefficients for low and full firmness range.
317
long as information about chlorophyll is kept. Otherwise, in some cases, this fact has been pointed out as a limitation to the construction of reliable models, since it would bury the direct dependence of firmness on texture (McGlone et al., 2002). Hence, the reliability of firmness predictions based on the simpler method of colorimetry was investigated, in order to check its positive or negative impact on the previously constructed Vis/NIRS model. The colorimetric parameter a* is closely related to the peel chlorophyll content, since it measures the red to green colour variation. Thus, we assayed a simple linear fit between a* and the respective firmness values (Fig. 6, left). A clear difference between the internal and external sets was shown. In the latter, the correlation between firmness and a* was much better than in the former. This was particularly evident for external validation set 3. The graph with the model predictions based on the a* values is depicted in Fig. 6 (right). Again, we have performed a refined fit for low-F values and combined the full range fit with the lowF fit in a segmented prediction model, exactly as we have done in the last section for the PLS model. The regression coefficients were determined from the same calibration set used in the PLS model. Then, we used these regression coefficients to predict firmness values for the calibration, internal validation and external validation sets, enabling the calculation of RMSEC and RMSEP values. All the other parameters were calculated in the same way as those for PLS (including bias corrections for external validations) (Table 2). Briefly, all the main parameters (RMSEP, RMSEP%, r and SDR) became much worse for set 1 and better for sets 2 and 3. The PLS model describes correctly an average ripening behaviour, and this is why it gives good results with external sets 2 and 3. However, being built upon the less uniform set 1, it picked correlations at other wavelengths without meaning for sets 2 and 3, effectively representing noise for the external predictions. This why the a* model performed better for the external sets. The conclusion from this test is that the success of the PLS model does not rely only on chlorophyll information (predictions for set 1 got much worse). Also, it worked well with the external sets. However, an a*-based model may result even better, especially for uniformly ripening sets. However, there are two questions that remain to be answered, (1) taking into account L*, a* and b* simultaneously might improve the prediction model (since they cover the visible spectrum); (2) a single wavelength model based at 689 nm could be better than the a* value model (since the a* value is obtained by a superposition of a large range of wavelengths, smearing out the contribution of the more firmness-correlated wavelengths, such as 689 nm). To answer (1) we built a PLS model with seven independent variables: L*, a*, b* and four other variables of interest in colorimetry, constructed from nonlinear expressions involving the first three. These variables were chroma, C* = [(a*)2 + (b*)2 ]1/2 , hue angle, h = tan−1 (a*/b*) (variables of the L*C*h colour space), the colour difference E* = [(L*)2 + (a*)2 + (b*)2 ]1/2 , where means variation, in this case relative to the L*, a* and b* values of the most firm pear in the calibration set, and the hue difference, h = [(E*)2 − (L*)2 − (C*)2 ]1/2 , again relative to the E*, L* and C* values of the same pear. We have only done this test on sets 1 and 3, since the external set 2 seems to have an intermediate behaviour. All the main four parameters got worse relative to the a* and PLS segmented models (except RMSEP% for set 1, which improved by changing from the a* to the PLS color model – Table 2). The PLS colour model does not have the detail allowed by the spectroscopic PLS model and thus it performed worse for set 1. Relative to the a* model, it brings noise from the wavelength bands not related with a*, and hence it is also worse for the external set 3. The final answer to question (1) is that the inclusion of L* and b* (and even other colorimetric variables) degrades the predictive capability of the a* data alone and does not rival the PLS model.
318
A.M. Cavaco et al. / Postharvest Biology and Technology 51 (2009) 311–319
Table 3 Main correlations between DM (%) (peel, pulp and fruit), firmness (F) and the colorimetric parameters described in the text (L*, a*, b*, C*,E*, h) of orchard I ‘Rocha’ pear. Type of correlation
r2
Attribute 1 (X)
Attribute 2 (Y)
Strong
DM pulp
DM fruit
0.97
0.93
Moderate
F F F DM peel
E* Hue a* DM fruit
−0.78 −0.74 −0.74 0.71
0.60 0.54 0.54 0.50
Weak
F DM peel
L* DM pulp
−0.59 0.55
0.34 0.30
Meaningless
All other combinations (except between colorimetric parameters)
Finally, to answer question (2) we performed the linear regression of the reflectance values at 689 nm [R(689)] vs. firmness for predictions based on that regression (again just for calibration, internal validation set 1 and external validation set 3). The model based on R(689) performed worse than the a* model for all main four parameters except RMSEP% for set 1. The conclusion is that the single wavelength model is less immune to the effect of natural variability on model performance. In this case a wavelength average over a meaningful band, as it is the case with a*, gives a more stable model. Again, the a* model is better than a single wavelength model. Table 3 shows auxiliary data to characterize the data set 1, which are the main correlations between dry matter (peel, pulp and fruit), firmness and the colorimetric parameters. It is shown that Emax and hue also correlated well with firmness, while L* had a weak correlation with it. On the other hand, the dry matter did not correlate meaningfully with any of the colorimetric parameters. A last test was done in order to understand better the difference between sets 1 and 3. We constructed for each set a PLS model for predicting the a* value from the spectroscopic data. For set 1, 7 LV were needed, while for set 3 only 3 LV were needed. The respective PLS regression coefficients are shown in Fig. 7. The coefficients have negative extremes in the green band, as expected, and are similar for both sets. The coefficients in the red band, however, have a noisier pattern for set 1. Hence the spectroscopic data of set 3 are more directly and simply correlated with the a* value. In conclusion, the results of this section reinforce the perspective that the information about chlorophyll is not enough to explain the success of the PLS Vis/NIRS segmented model for firmness. Models based on colorimetric parameters or even on reflectance by a single wavelength may produce results comparable to those of the Vis/NIRS model only for uniformly ripening populations. In addi-
Fig. 7. PLS regression coefficients for the models predicting a* from the spectroscopic reflectance data. Up: model for data set 3. Down: model for data set 1.
r
–
