COMMUNICATION

Comparison of Whiteness Index vs. Fractal Fourierin the Determination of Bloom ChocolateUsing Image Analysis

Roberto Quevedo & Emir Valencia & Felipe Alvarado &

Betty Ronceros & José Miguel Bastias

Received: 10 June 2011 /Accepted: 7 November 2011 /Published online: 13 December 2011# Springer Science+Business Media, LLC 2011

Abstract Modeling of bloom is essential to evaluate theeffectiveness of processes in chocolate and to determine itsshelf life. Computer vision and the fractal kinetic method wereused to quantify bloom in samples of chocolate coating andcocoa chocolate subjected to a 3- or 6-h temperature cycle.Bloom was also determined by classical methods (L*lightness and whiteness index). In the results, the kineticbloom rate derived by the fractal kinetic method was higherthan that obtained with the L* or white index. Fractal methodcan be used to determine kinetic bloom and to detectdifferences in chocolate coating affected by 3 or 6 h oftemperature cycle. The bloom rate derived by the fractalmethod was higher that the mean L* value and whitenessindex methods; no differences could be registered betweenthe last two methods. In general, the fractal method can beseen as a new means of quantifying bloom in chocolate andallows registering the bloom faster than the L* value andwhite index methods.

Keywords Bloom . Fractal . Kinetic . Chocolate .

Computational vision

Introduction

Fat bloom in chocolate is still a major concern for manychocolate manufacturers as it results in an undesirable white,dusty surface appearance. However, the exact mechanismsinvolved in fat bloom formation have not been resolved (Tietzand Hartel 2000). A bloomed chocolate is characterized by achange in color and loss of gloss, giving a grayish whiteappearance to the chocolate surface. Fat bloom can havedifferent appearances, ranging from a uniform dull gray to amarble aspect, as well as from small individual white dots tolarge white spots on the chocolate (Nopens et al. 2008).

Fat bloom is directly related to the fat in chocolateproducts, either cocoa butter or vegetable oils. Cocoa butterrepresents not less than 95% of chocolate fat. In the USA,the addition of other vegetable fats above this level meansthe products are named compound coatings. Another typeof bloom, sugar bloom, can also occur with humidityproblems (Lonchampt and Hartel 2004). Two main types offat bloom can be discriminated: fat bloom on plainchocolate and fat bloom on filled chocolate. Fat bloomdevelopment on plain chocolate has already been studiedintensively. Several situations are known to lead to thedevelopment of this type of fat bloom: improper tempering,cooling too quickly, or storage temperatures that are toohigh or fluctuating (De Graef et al. 2005). Fat bloom (orsurface changes) can appear quickly after process problemsor, more precisely, after poor tempering. Tempering inducesthe crystallization of cocoa butter into a relatively stablepolymorph that protects chocolate against bloom. Duringtempering,βV seeds are formed at such a concentration that the

R. Quevedo (*) : E. Valencia : F. Alvarado :B. RoncerosDepartamento de Ciencia y Tecnología de los Alimentos,Universidad de Los Lagos,Unidad de FITOGEN. Av. Fuchslocher 1305,Osorno, Chilee-mail: rquevedo@ulagos.cl

B. RoncerosFacultad Tecnológica,Departamento de Ciencia y Tecnología de los Alimentos,Universidad de Santiago de Chile,Avenida Ecuador No. 3769, comuna de Estación Central,Santiago, Chile

J. M. BastiasDepartamento de Ingeniería en Alimentos,Universidad del Bio-Bio,Av. Andrés Bello s/n,Chillán, Chile

Food Bioprocess Technol (2013) 6:1878–1884DOI 10.1007/s11947-011-0729-x

chocolate mass crystallizes directly into the βV polymorphduring subsequent cooling (Lonchampt and Hartel 2006).

In practice, the fat bloom assessment is often performedon a semiquantitative basis using a (trained) human panelevaluating chocolate samples based on a scoring scale.Moreover, this approach is quite subjective as differentmembers of the panel might use different “reference” levelsand, hence, tend to give higher or lower scores comparedwith other panel members (Nopens et al. 2008). Anotheralternative is the use of the whiteness index (WI; Bricknelland Hartel 1998; Tietz and Hartel 2000), which is the mostwidely used color parameter in chocolate storage studies. Itis determined by measuring the L*, a*, and b* values usinga commercial colorimeter and converting them to WI valuesaccording to the following equation:

WI ¼ 100� 100� L»

� �2þ a

»2 þ b»2

� �0:5ð1Þ

However, Lonchampt and Hartel (2006) discovered thatthe WI did not change significantly despite visual detectionof numerous white spots. Apparently, the WI method ofcharacterizing bloom is thus not as sensitive as visualdetermination.

Other alternative applications that apply image analysis toquantify fat bloom in chocolate have been undertaken byBriones and Aguilera (2005) and Nopens et al. (2008). In thefirst case, analysis of the Fourier spectrum of an image, topermit the extraction of a single descriptor that represents theimage texture (i.e., the spatial variability of the gray levels ofpixels over the whole image), was applied. They observed thatthis descriptor E (energy of Fourier, Eq. 2) stayed close to 0for the first 36 days of storage, meaning that the image textureremained unchanged. Major changes occurred betweendays 39 and 45, followed by slower progress up to the endof the storage period. The shape of the curve seemed toindicate that texture image development (as represented by E)trails development of the whitish background by a few days.In the second case, two procedures for detecting migration fatbloom were compared: a human panel giving scores and anewly developed image analysis procedure. The imageanalysis procedure consists of two parts: determination of“whitish” patches on the chocolate surface determined byshifts in a grayscale histogram and the disappearance of gloss,based on the disappearance of a reflection band. In theirresults, a mean pixel threshold value of 75 was adopted todetect the change in acceptability of the chocolate samples. Inboth cases, gray intensity values were used from the images inorder to quantify fat bloom.

E ¼Xj;k

F j; kð Þ2��" #1

2

ð2Þ

where E is the energy of Fourier and F(j,k) is the matrixcontaining the amplitudes of the spectrum.

Normally, WI is calculated using L*, a*, and b* meanvalues in the region of interest on the chocolate surface.However, during fat bloom, non-homogenous color patternsare formed as a result of improperly formed fat crystalslarger than 5 μm located on the surface of the chocolate(Hodge and Rousseau 2002). To quantify this event, a moreeffective method could be the application of the fractaltheory because it has been demonstrated that the fractalconcept can characterize heterogeneous surfaces on food(Quevedo et al. 2002; Russ 1994; Zheng et al. 2006). Infact, recently, the fractal method has been applied to modelenzymatic browning in food based on the distribution ofsurface colors in pears (Quevedo et al. 2009aa), apples(Quevedo et al. 2009c), and bananas (Quevedo et al.2009bb). According to this method, the kinetic is describedusing the L* lightness distribution based on the areas thatappear more highly colored as a result of non-homogenouscolor patterns that emerge on the food surface. Accordingto these studies, non-homogenous color patterns are notquantified when an average L* value is used.

In this study, we propose the use of the fractal kineticmethod, based in the L* lightness, in order to quantify fatbloom in chocolate as an alternative to WI. Our hypothesis isthat the fractal kinetic method can derive a kinetic bloom ratewith statistical differences to those derived by WI or the useof the mean L* lightness. The objectives of the study were:(1) to apply the fractal Fourier method in order to quantifyfat bloom in chocolate stored at fluctuating temperatures and(2) to detect statistical differences in the kinetic rates derivedby the fractal method and the use of WI.

Materials and Methods

Samples

Two types of chocolate (20 samples each) were purchasedfrom a local department store: cocoa chocolate, cocoa mass38% (60% cocoa butter, Nestlé®), and chocolate coating,31% fat (lauric compound coating, Costa®). Lauric com-pound coating was based on palm kernel oil, usually in theform of either a palm kernel stearine or a fully hydroge-nated palm kernel stearine.

Bloom Induction Experiments

The samples (ten samples for each type) were placed insideenvironmental test chambers that cycled the temperaturebetween 15 °C (±1 °C) and 26 °C (±1 °C) every 3 and 6 hover 22–25 days. The chambers enable users to simulateenvironmental conditions and provide precise temperature

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and humidity control. Inside the chamber, a computervision system was introduced. The relative humidity wasmaintained between 45% and 50% to avoid sugar bloom.The experiment was replicated three times.

Image Texture Analysis

A computer vision system described by Quevedo et al.(2009b) was used to capture the images (1,700×1,500 RGB

color). Color images were transformed from RGB spacecolor to L*a*b* space color using the model proposed byLeon et al. (2006). These transformation functions allowedthree intensity colors to be obtained from an image. Surfaceintensity from L* (SI) was described using the fractaltheory. The fractal Fourier method (Chan 1995; Quevedo etal. 2008; Russ 1994) was used to compute the fractaldimension of the SI corresponding to the L* data. Fractaldimension (FD) was determined from the Fourier power

Fig. 1 Three selected images(left) and their surface (right)intensity L* value (SI)corresponding to cocoachocolate subjected to a3-h temperature cycle. FD is thefractal dimension calculatedfrom the fractal method

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spectrum of the selected area (2×2 cm) from image data(spatial resolution was 1 cm of chocolate=100 pixels) inorder to quantify SI (fractal method). In the method, theaverage power spectrum (D) of the surface images isplotted as a function of the frequency, f, according to thefollowing equation (Gonzales-Barron and Butler 2008):

D ¼ f �2� 3�FDð Þ ð3Þ

If a linear variation is established from the log(D)) vs.log(f) and after taking the fast Fourier transform of theregion under study in 12 directions on image (0°, 30°, 60°,90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, and 330°),an average of the FD value can finally be obtained. It isrecognized that an increment in the FD value in a surface isindicative of an increment in its complexity (Russ 1994).

Bloom Kinetic

Bloom was quantified using the mean value, WI (Eq. 1),and FD (derived by the fractal method) from the images.During the experiments, one picture was taken every 3 h(in the case of the 3-h temperature cycle experiment) or6 h (in the case of the 6-h temperature cycle experiment).According to Quevedo et al. (2005), bloom varies with thesquare root of time, and the data plotted yield a straight

Fig. 4 Kinetics bloom of the first 11 days for chocolate coating at6-h temperature cycle (time is expressed as s0.5). NV is the extension ofthe kinetic [(actual value−final value)/(initial value−final value)]

Fig. 3 Kinetics bloom of the first 11 days for chocolate coating at3-h temperature cycle (time is expressed as s0.5). NV is the extension ofthe kinetic [(actual value−final value)/(initial value−final value)]

Fig. 2 Kinetic bloom (measured by FD) for a cocoa chocolatesubjected to a 3-h temperature cycle (time is expressed in days). FD isthe fractal dimension calculated from the fractal method

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line, between the induction period (lag period) and thesaturation period:

NV ¼ K � ffiffit

p ð4Þ

It can be assumed that the left-hand side of Eq. 4 isproportional to the normalized L*, WI, or FD value. NVvalue [(actual value−final value)/(initial value−final value)]can be seen as a result of the amount of fat crystallized overthe surface, t is the time of the kinetic, and K is the kineticbloom rate. The slope of the linear portion (linear period) ofthe kinetic was assumed to be the kinetic bloom rate, and themodel was adjusted to data using a linear least squaresregression. ANOVA test (95% of accuracy) was used inorder to detect statistical differences in the kinetic ratebetween chocolates.

Results and Discussion

Three selected images (left) and their surface (right) L*lightness (SI) corresponding to cocoa chocolate subjected toa 3-h temperature cycle are shown in Fig. 1. SI is formedrepresenting L* values as a z-coordinate axis from a regionof interest (ROI) in the chocolate image.

The fractal kinetic method was used in order to measure thecomplexity of the SI during the kinetic bloom. Possibly, this isbecause the fat crystals, present as white spots in images,increase in number and size as blooming proceeded. Thesechanges are evidenced by an increase in the intensity of peaks

at discrete positions, giving a rougher and jagged appearance(more complexity) to the SI (Quevedo et al. 2002).

In Fig. 1, the complexity of the SI increased during thekinetic caused by the transformation of small individualwhite dots to large white spots that appear on the chocolateduring the kinetic. This is evidenced in Fig. 1a where alower FD value (2.08) was measured by the SI and themean L* value was 73 units, at zero time. Over longerperiods (at large times) of the kinetic, the complexity of thesurface (FD) increased to 2.3 at 13 days (Fig. 1b) and to 2.7at 17 days (Fig. 1c). The L* value also increased during thekinetic, from 78 units at 14 days to 88.5 units at 15 days,respectively. In general, the surface of unbloomed choc-olates was smooth, as reflected by the low initial FD value(between 2.04 and 2.08). This value increased as bloomingprogressed, reaching values from 2.7 to 2.95 at 11–17 days.In other words, a more and major heterogeneous distribu-tion of the L* values over the ROI in the chocolate occursduring blooming, as can be seen in Fig. 1. This phenom-enon is not quantified when a mean L* value is used toquantify bloom in chocolates.

In Fig. 2, the kinetic bloom, measured by FD, for a cocoachocolate subjected to a 3-h temperature cycle is shown. Fromthis figure, the kinetic appeared to present a lag or inductionperiod (around 14 days). Bricknell and Hartel (1998) reportedlonger lag times for fat bloom in cocoa chocolate. After10 days, an asymptotic value of FD is reached around17 days of the cycling. Accordingly, in studies of migrationin chocolate (Ziegleder et al. 1996; Quevedo et al. 2005), thetime (or square-root-of-time) dependence is only observed inthe early stages of fat migration, whereas in a later stage theprocess slows down and approaches saturation.

The analysis presented in this paper is based on the square-root-of-time dependence shown in Eq. 4. NV values(normalized FD, L*, or WI value), corresponding to thelinear period, were fitted to Eq. 4 when working withchocolate samples by using a linear least square fittinganalysis. To evaluate the goodness of fit, the correlationcoefficient was calculated. In Figs. 3 and 4, the kinetics forchocolate coating at 3- and 6-h temperature cycle are shown,respectively. Similar to Fig. 2, the kinetics appeared topresent a lag or induction period, after that a linear period,followed by a saturation period (constant value near to 1 isreached). Lag period (9–10 days) was longer for samplessubjected to a 3-h temperature cycle than samples subjectedto a 6-h temperature cycle (4–5 days); our results establishedthat lag period in the kinetic was independent of the type ofsamples. Tietz and Hartel (2000) established a lag period ofaround 3–4 days in samples of chocolate made with winteranhydrous milk fat cycled at 6 h at between 19 and 26 °C.Lonchampt and Hartel (2006) established a lag period ofaround to 6–7 days in untempered chocolates at 20 °C. Theshorter lag period in samples subjected to 6 h of temperature

Table 1 Kinetic bloom rates (slope of the linear period for chocolatecoatings subjected to 3- and 6-h temperature cycles)

Cycles KFD KL* KWI

3 h 0.087±0.009a 0.054±0.006b 0.053±0.006b

r=0.95 r=0.93 r=0.92

6 h 0.0213±0.0067c 0.009±0.001d 0.009±0.001d

r=0.93 r=0.90 r=0.92

Different letters indicate significant difference by LSD test

Table 2 Kinetic bloom rates (slope of the linear period for cocoachocolate subjected to 3- and 6-h temperature cycles)

Cycles KFD KL* KWI

3 h 0.060±0.025ac 0.018±0.004b 0.017±0.003b

r=0.95 r=0.89 r=0.91

6 h 0.041±0.001c 0.016±0.003b 0.017±0.003b

r=0.94 r=0.91 r=0.93

Different letters indicate significant difference by LSD test

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cycle, compared to the 3-h temperature cycle, can be attributedto the fact that samples spent more time at high temperatures(26 °C), and this could produce a rapid destabilization of thechocolate structure (fast appearance of fat on the surface at anearly stage). Besides, the bloom appears to occur moremarkedly when samples were subjected to 6 h, allowing thethree methods to record the bloom at the same time.

From Figs. 3 and 4, it was observed that bloomdescribed by the fractal method always shows a fasterlinear period than kinetic bloom calculated using the meanL* value or WI value; in fact, the mean L* value and WIvalue were overlapped during the kinetic. This behavior wasnoted for all samples independent of whether samples weresubjected to a 3- or a 6-h cycle. This can be evidenced inTables 1 and 2 where kinetic bloom rates (slope of the linearperiod) for chocolate coating and cocoa chocolate, subjectedto 3- and 6-h temperature cycles, are shown respectively.

Table 1 shows that chocolate coating values obtained for Kwere significantly different between samples subjected to 3-and 6-h temperature cycles, respectively. Kinetic bloom rateswere higher at the 3-h than at the 6-h temperature cycle.Similar conclusions were reported by Quevedo et al. (2005)where bloom was recorded using topographic data from thechocolate surface. Nevertheless, of greater relevance to thisresearch was the magnitude of the rate parameter K obtainedwith the fractal method when compared with traditionalmethods (mean L* value or WI). Kinetic bloom rate derivedfrom the fractal method (KFD) was always higher than kineticbloom rate based on the mean L* (KL*) or WI (KWI). Thefractal method can be seen as a new means of quantifyingbloom in chocolate and allows registering the bloom fasterthan the WI method. A similar result was obtained for cocoachocolate (Table 2) given that the kinetic bloom rate derivedfrom the fractal method value was always higher than thekinetic bloom rate based on mean L* or WI. However, in thiscase, no statistical differences were detected between kineticsat the 3- and 6-h temperature cycles.

Conclusion

Fractal kinetic was applied in order to quantify bloom insamples of chocolate coatings or cocoa chocolate usingcomputer vision and image analysis when samples weresubjected to a 3- or 6-h temperature cycle. Differences inthe kinetic behavior were observed between fractal methodand traditional indicators of bloom (mean L* or whitenessindex). Fractal kinetic derived higher kinetic bloom ratevalues than those obtained using the mean L* value or WI.For chocolate coating, differences in the kinetic rates weredetected between experiment cycles; in cocoa chocolate, nodifferences were observed. No differences could be regis-tered between bloom kinetics recorded by L* lightness and

the whiteness index. The fractal method can be seen as anew means of quantifying bloom in chocolate and allowsregistering the bloom faster than the other two methods.This is due to the fact that the FD value increased fasterthan the mean L* value during the bloom kinetic becausethe fractal method appears to be more sensitive to theapparition of white spots on the surface of the chocolate.Further research should be carried out in order todeterminate this phenomena. Fractal method based on theFourier method has several advantages for studying kineticsfrom surface images where colors are not homogeneouslydistributed. It is insensitive to the presence of the noise inimages; the method is well understood and easilyprogrammed and no too slow to compute. The fractalmethod resolves the fact of quantify food surfaces in whichthe colors are not homogenous.

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