Real-Time Color Tone Detection on Video Basedon the Fuzzy Integral

Anton Albajes-Eizagirre, Aureli Soria-Frisch, Member, IEEE and Vanel Lazcano

Abstract—Color tone detection accomplishes the modeliza-tion of a color cluster for a set of pixels that present a huesimilar to a particular one, which is being detected. Image pixelscan be classified according to their membership to the particularcolor class through such cluster modelization. Such approachescan be employed in different computer vision application fields.Nevertheless few proposals in the literature report on the real-time detection of color clusters.This communication deals with the real-time implementation

of the fuzzy integral, which is employed in a color clusterdetection methodology. The resulting technique is applied toskin color detection and sport playground detection on videosequences. The method presented herein reaches a performancecomparable to state-of-art methodologies with a very lowcomputational cost, making real time color cluster detectionpossible. Both aspects, performance and computational cost,are commented herein and results are given in both standardbenchmark databases and real-world application sequences.Index Terms—Fuzzy integral, color detection, video process-

ing.

I. INTRODUCTION

Color tone detection accomplishes the modelization of acolor cluster for a set of pixels that present a hue similarto a particular one, which is being detected. Image pixelscan be classified according to their membership to theparticular color class through such cluster modelization. Suchapproaches can be employed in different computer visionapplication fields. Among all of them, the detection of skinhave been a longstanding research topic for some years.Skin cluster detection accomplishes the modelization of a

color cluster for skin tone pixels. Image pixels can be classi-fied according to their membership to the skin or the non-skinclasses through such cluster modelization. Many problemshave to been faced in order to get a good performance,e.g. luminance conditions variability, existing backgroundpixels with similar hue to this of skin, different tones indifferent human races. Skin detection has a wide range ofapplications. In face recognition processes, skin detection isoften one of the pre-processing steps. Skin detection becomesuseful also for human body tracking, like hand, face or fullbody tracking. Automatic information retrieval techniques,like pornographic filters also make profit of skin detectionmethods.

Anton Albajes-Eizagirre and Aureli Soria-Frisch are with StarlabBarcelona S.L. Teodor Roviralta 45 08022 Barcelona, Spain. (emails:{anton.albajes-eizagirre,aureli.soria-frisch}@starlab.es). Both performed thework while at Universitat Pompeu Fabra - Barcelona Media within thepremises of the project I3MEDIA of the Cenit Program.Vanel Lazcano is with the Fundacio Barcelona Media. Av. Diagonal, 177,

planta 9 08018 Barcelona, Spain

Fast detection becomes a requisite in order to set areliable system in most of these real-world applications.Many different approaches have been proposed for skindetection. Pixel-based methods use solely the color infor-mation of the pixel to perform the detection, resulting ina faster computation than context-based methods like [1].Among parametric methodologies, methods using multipleGaussian clusters[2], methods using an elliptic model[3], andthe methods using Fuzzy Integrals presented in [4] obtainthe best performance figures according to results reportedby authors. Some dynamic solutions[5], [6], [7], [8] havebeen proposed on tracking systems for video detection withadaptation to the illumination conditions. Although someof these methodologies are reported to be tested on videosequences, only [8] gives some figures on the computationalcost of the associated methodology. Hence the methodologyis claimed to run at 25 fps for resolutions of around 350×280.Furthermore such approaches can be applied in further

application fields. The detection of sports playing area, whichpresent some degree of uniformity, can be mentioned as afurther example of such applications. In this context someworks comment on the importance of this stage for dis-criminating among different sport disciplines [9]. Moreoversome works make use of this technique for off-line videosummarization [10]. Here a so-called cylindrical distancemeasure is computed for each pixel of a frame in order todetect the playing area in the HSI color space. In this workimages have to be down-sampled in order to achieve real-time color detection on 352×240 resolution at 30 fps. Othermethodologies based on the Mixture of Gaussians for sportgrass detection have also been presented [11],[12].Using the skin detection method proposed in [4], which

uses the fuzzy integral [13], we have developed a real-timepixel-based color cluster detection methodology capable ofperforming an excellent detection on real time. Classificationattains high performance results comparable to the mostcommonly used statical detection methods. This feature iscomplemented with low computational costs resulting indetection speed over the ones reported in the literature. Wepresent some results for the detection of both skin and soccerplaying area detection.This document is organized in five sections. Section 2

provides the theoretical background of our methodology.Section 3 presents the proposed method and describes thedevelopment process we followed in order to optimized thecomputational cost. Section 4 contains the results obtainedby our method together with their analysis. Final commentson the work presented herein can be read in Section 5.

978-1-4244-8126-2/10/$26.00 ©2010 IEEE

II. FUZZY INTEGRALS IN COMPUTER VISIONThe fuzzy integral is an aggregation operator developed

within the theoretical framework of soft computing [13]. Theoperator has been successfully used in different computervision applications [14], [15]. It mathematically generalizesother aggregation operators commonly used in real appli-cations like the average, the median, or the weighted sum.There are different types of fuzzy integrals, which are definedby the connective type they apply. The Choquet integraloutperforms other operators in classification problems [15].

A. Theoretical BackgroundThe Choquet Fuzzy Integral makes use of the sum (

∑)

and the product (·), as stated by the expression [16]:

Cμ[x1, .., xn] =

n∑

i=1

x(i) · [μ(A(i))− μ(A(i−1))], (1)

where μ(A(0)) = 0. In the color cluster detection proceduredescribed herein xi∀i = 1, 2, 3 denote the image gray valuesof each color channel in a particular color representation,and μ(A(i)) denote the coefficients of the so-called fuzzymeasure, which weight the importance of these color chan-nels. It is worth pointing out that the operands xi are sortedas part of the aggregation operation, which is denoted bythe () enclosing the sub-indices. Hence x(1) denote thelargest operand value, e.g. for x2 > x3 > x1, we takex(1) = x2, x(2) = x3, x(3) = x1.Fuzzy measures play the same role as weights in a

weighted sum expression. Hence the fuzzy integral is com-puted w.r.t. a fuzzy measure μ. Fuzzy measures weight theimportance of the operands xi. This weighting is not onlyapplied to the operands on its own, like in the weightedsum, but to any of the subsets that can be formed on them,e.g. {x1}, {x2, x3}, {x1, x2, x3}. Therefore the sorting resultdefines the subset weighting that is selected for a particularaggregation, i.e. μ(A(i)) = μ({x(1), ..., x(i)}). These areselected from the 2n − 1 coefficients that the fuzzy measureμ presents, where n denote the number of operands beingaggregated.When processing a color image the fuzzy integral is

usually applied on all the pixels of the image, wherebythe set of coefficients used for each pixel depends on theranking among the color channels. Therefore a non-linearprojection from the color domain into a gray value oneis achieved by applying the fuzzy integral on the colorimage. Since the ranking among color channels is invariantin front of a change in the illumination intensity, the non-linear projection can successfully cope with this kind oftransformation [15]. For deeper information on the fuzzyintegral and its utilization for computer vision, the user isreferred to [14], [15].

B. Algorithm DescriptionThe real-time implementation of the fuzzy integral pre-

sented in this communication follows the method presentedin Algorithm 1. This method makes use of a look-up table

to store and retrieve the weights of a fuzzy measure μ.The weights are located on this look-up table regarding thecorresponding aggregation. In this manner, for a particularaggregation A(i) = {x(1), ..., x(i)}, the position of its weighton the look-up table would be

∑i

j=1 2j .

The method, therefore, consists on sorting the input data,obtaining the sorted data and the indexes of the sort. Theindexes of the sort will determine the original position ofthe sorted data. This indexes will be used to select theweights from the look-up table. With the sorted data andthe corresponding weights we can transform the Choquetequation (eq. 1) into the expression F = F+(Si−Si+1)·Wi,being F the value resulting from the fuzzy integration, SN

the sorted values and WN the selected weights.This algorithm has also been presented in [17]. One key

aspect of this implementation is the way the position of theweights in the look-up table is calculated. The novelty ofour proposal, as presented in Algorithm 2, is that the powertwo operation is implemented by means of a bit-wise shiftof the integer 1. This operation equals the power two andresults computationally much more efficient than the power.In this way, the retrieving of the weights only consumestwo processor instructions per channel, instead of the severalprocessor instructions need for the power instruction.This algorithm and the novel indexation on the weights

look-up table used, together with an efficient sorting schema,result on a real-time implementation that requires only afew processor instructions per channel in order to attain thecomputation of the fuzzy integral.

Algorithm 1 Compute an optimized fuzzy integral for n

channels dataRequire: HN is the input data and LUT2N is a look uptable

Ensure: F is the value of the fuzzy integral of HN usingLUT

SN ← sorted data of HN

IN ← sorting indexes of HN

WN ← selected weights from LUT2N indexed by INfor i = 1 to N doF = F + (Si − Si+1) ·Wi

end for

Algorithm 2 Select the coefficients from a look-up tableRequire: LUT2N is a look-up table of weights and IN arethe indexes of the table

Ensure: WN contains the values on LUT indexed by I

ind = 0for i = 1 to N doind = ind+ (1 � Ii)Wi = LUTind

end for

III. FRAMEWORK FOR COLOR CLUSTER DETECTION INREAL-TIME

In this sections we comment on the base methodologyused in the implementation presented herein. Furthermorethe implementation details are given.

A. Difference of Fuzzy IntegralsThe skin detection algorithm presented in [4], which is

extended herein for the detection color clusters in video time,is based on the application of the fuzzy integral with respectto two different fuzzy measures μ1 and μ

2.A similar methodology was used for the segmentation of

ink seals on document images [18] and denoted as Differenceof Fuzzy Integrals (DoFI). Hence this methodology attainsthe detection of a color cluster on an input image. For thispurpose the two fuzzy measures, whereby the fuzzy integralis computed, change the value of the coefficients that mostlyaffect the pixels within the color cluster to be detected.The difference of the two resulting non-linear projections isthence computed. It is worth mentioning that the procedurecan be applied to any color space without changing the basicstructure. The following figure (Fig. 1) try to illustrate theprocess undertaken.

ch1

ch2

ch3

gr

d

Cμ1Cμ2

Fig. 1. Illustrative example of the non-linear projection to a gray value(gr) achieved by the application of the Choquet fuzzy integral C

μi w.r.t.fuzzy measures μ1 and μ2 in the application of the DoFI methodology on acluster in a particular color space {ch1, ch2, ch3}. The distance between thetwo resulting projections d is maximized by selecting the right coefficientsof the fuzzy measures.

The DoFI methodology results in a difference image.This difference image D(x, y) is obtained in the describedprocedure by applying [4]:

D(x, y) = ‖Cμ1(x, y)− Cμ2(x, y)‖, (2)

where Cμi states for the gray value images that result fromthe computation of the Choquet fuzzy integral, as expressedby (1).Hence real values of the resulting image D(x, y) are

proportional to the membership degree of the pixels to aparticular color class. In the application described herein this

class corresponds to the skin class. The particular values ofthe fuzzy measure coefficients, of both μ

1 and μ2, fix up

the color cluster to be detected by the procedure. This isattained by maximizing the distance between the non-linearprojections that are obtained through the fuzzy integral. Theassessment of the fuzzy measure coefficients can be donemanually, but is better to apply an automate procedure forthat.The automated parametrization of theDoFI can be realized

by applying genetic algorithms [19], which have been suc-cessfully employed in the assessment of the fuzzy measures[20], [21], [4]. For this purpose the standard mutation,crossover, and selection operators [19] can be applied onbinary coded genomes. One important question is how tocompute the fitness function that drives the genetic search.We have decided to set up a fitness function that takesinto consideration the true and false detection rates on twodifferent training databases with skin and non-skin colors.The details on this procedure are given in Sec.IV.

B. ImplementationImplementation of the DoFI method has been developed

on C++ and integrated into the ColorLib library. For thegenetic algorithms applied for training the DoFI parameterswe used GALib library 1. The implementation was then tunedup by obtaining a full profiling report and improved thememory management of the execution. Also, logic operationswere improved to speed up the computational cost. Final im-plementation achieved, thus, optimum performance regardingDoFI methodology schema.The ColorLib library is GPL licensed. Source file

and code documentation of this library can be found athttp://sourceforge.net/projects/colorlib/.

IV. PERFORMANCE ANALYSISWe tested DoFI color cluster detection performance on two

applications: Skin color detection and sports field grass de-tection. Afterwards, we tested computing costs performancein order to attain real-time detection.

A. Skin Color Detection on Video SequencesFor skin color detection, in order to train parameters for

our DoFI method by applying genetic algorithms we useda subset of two databases downloaded from the repositoryof the Universidad de Chile 2. From the two availabledatabases, we obtained two different subsets, one for thetraining process and the other for the test process. For thetraining set we randomly extracted 200,000 pixels with skincolors and 300,000 pixels with non-skin colors.For the parameters of the genetic algorithm, used for

training the DoFI parameters, we set 200 generations with200 individuals each. Replacement probability was set to0.85, mutation probability to 0.2 and crossover probability to0.9 an a Steady-State GA. As a fitness function we used one

1A C++ library of Genetic Algorithm Components http://lancet.mit.edu/ga2http://vision.die.uchile.cl/skindiff/dbs.html

involving TPR (true-positive rate) and FPR (false-positiverate) indexes:

φ = TPR+ (1− FPR) (3)

With the trained parameters we run the DoFI detectionmethod over the images of the test subset and obtained theaverage ROC curve. Together, we run MoG [2] and Hsu [3]detection methods over the same images and obtained theaverage ROCs. It is worth mentioning at this point that theimplementation of MoG and Hsu methods was developedby us in C++ and using the parameters specified on [2],[3].In Fig 2 the three ROCs of the three methodologies areshown. Observing those curves we see that the DoFI andMoG methodologies outperform the Hsu methodology. OurDoFI method gives a performance close to the performanceof MoG method. Although for some particular TPR-FPRcombinations the corresponding curve is under the MoGone, the equal error rate, a performance measure usuallygiven in detection procedures, is almost the same for bothmethodologies, as it can be observed in Fig. 2.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

TP

R

FPR

eDoFI, MoG and Hsu ROC curves

eDoFIHsu

MoG

Fig. 2. ROC curves of DoFI, MoG and Hsu methods performance on skindetection.

In Fig. 3 we can observe the binarized and gray valueimages result of the detection of the three methods over animage of the test subset. The gray value of the depictedimages correspond to the membership to skin class valuedetermined by each detection method. We can see thatvisual results confirm numerical results. DoFI attains a goodperformance again, close to MoG performance and betterthan Hsu’s.In Fig. 4 we can observe the result of the skin detection

attained by DoFI over the extracted frames of a knowncommercial movie obtained from the database of the BostonUniversity 3. Left column shows original frames extractedfrom the movie and right column the results of skin detectionover those frames. As shown in equation 2, DoFI method-ology outputs a real value proportional to the membershipof the pixel to the color class, skin in this case. In order toobtain the binarized image, we apply a threshold to the real

3http://csr.bu.edu/colortracking/pami/Data/

Fig. 3. Gray value and binarized results of skin detection performed byDoFi, Mog and Hsu. The image corresponds to the test set.

values. Values lower than the threshold are pictured as blackon the binarized image, and values higher are pictured aswhite. Hence, white areas correspond to skin areas.

B. Soccer Field Grass DetectionFor sports field grass detection, in order train parameters

for DoFI method by applying genetic algorithms we used aset of video sequences provided by Televisio de Catalunya4.Videos contained sequences of soccer games shot on pro-fessional stadiums. Random frames were extracted fromeach sequence on the training set and the pixels on themmanually labeled in order to obtain a ground-truth databasefor field grass pixels. Sequences contained different sceneconditions, such different types of grass, different illumi-nation conditions - daylight with shadows, nightlight withartificial light, etc. - and different focus distance - wideviews, close-ups. Analogously to the skin detection training,we used 250,000 pixels with grass colors and 400,000 pixelswith non-grass colors. Genetic algorithm parameters werethe same as the ones used on skin detection training process.Results on sports field grass detection can be observed in Fig.5. We can see that DoFI obtains robust detection, includingdifferent illumination conditions - such shadows on daylightor artificial light - and different grass types on different fields.Images on this figure correspond to the test set, and theresults have been binarized as explained in sub section IV-A.In order to numerically study the generalization capability

of the DoFI methodology for grass detection, we run themethodology over the train set and over the test set. Systemwas trained on the training set and obtained the ROC curveof the classification attained over the same training set.Afterwards, we obtained the ROC curve of the classificationattained by this set up over the test set. In figure 6, the two

4The videos and its images are property of TVC, Televisio de Catalunya,SA, and are copyrighted. The TVC images used in this work are providedfor research purposes by TVC within the I3MEDIA Project.

Fig. 4. Frames extracted from a movie,skin detected by DoFI and binarizedto a white and black images applying a threshold. White correspond to skinareas.

ROCs, for the train and the test sets, are shown. The ROCcurve corresponding to the train set presents a very goodperformance, close to perfect classification. This indicatesthat the system is able to adapt to the training set and, thus,that the training schema is correct. The ROC correspondingto the test set presents also a good performance, almost asgood as the train set. This indicates that the system is alsocapable to generalize the results, and therefore attains agood segmentation on images no included on the training set.

In figure 7 the gray value results of grass detection attainedby DoFI over two images from the test set are shown.Pixel values on the images correspond to the values outputby the DoFI methodology, without any further binarizationperformed. Original images present different focus distances,being the top one a long distance image, and the bottom onea close view of the grass field. Gray values show on bothcases a good detection attained.

C. Color Detection Real-time AnalysisPursuing real-time performance analysis, we used some

video frame streams to obtain the frame rate that the imple-mentations of MoG, Hsu and DoFI methods were capable to

Fig. 5. Binarized images resulting of grass detection by DoFI. Imagesfrom the test set showing different lighting conditions.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

TP

R

FPR

Roc curves for grass segmentation using eDoFI

Test SetTraining test

Fig. 6. ROC curves of DoFI method performance on grass detection overthe training set and over the test set.

detect. We firstly used an scaled video stream with frames at320x240 pixels of resolution coded with Mpeg-4 divx codecusing Planar YV12 colors pace at 23.97 fps.Each frame was extracted and processed with the detection

method at a time. Obtained frame rate was calculated every25 frames. This process was repeated with MoG, Hsu andDoFI methods. Result values are shown in figure 9. If weobserve the frame rates obtained by the methods, we seethat MoG performance was too low to run a detection on realtime speed even at low resolutions. Hsu performance allowsto expect real time detection at low refresh frequencies and

Fig. 7. Gray value images resulting of grass detection by DoFI. Imagesfrom the test set showing two different focus distance.

Fig. 8. Frames extracted from a soccer game video stream, grass detectedby DoFI and binarized to white and black images applying a pre-determinedthreshold. The grass detection on this images performed by DoFI wasattained on real-time at frame rates exposed in the table on figure 9.

low resolution. Meantime, DoFI performance gives a framerate 3 or 4 times faster than usual video frame rate. Thosevalues of DoFI performances allows a perfect real-time withlow resolutions, such is 320x240.In order to check DoFI performance detecting a high

resolution video stream, we used a video coded with thesame options as used in the previous videos, but with a frameresolution of 624x352. This resolution is commonly used inInternet broadcasted videos and close to the resolution ofcurrent DVDs. Observing table on figure 9 we see that inthis resolution MoG and Hsu obtained frame rates don’t reachlevels close to real time detection. Meantime, DoFI performsa detected frame rate of 27, 62 frames per second, whichis over common video frame rates. This values make realtime detection on high definitions available. Again, profilingreports showed that DoFI detection computation took 83%of the execution time.All these test times were obtained running executions over

a Intel(R) Core(TM)2 CPU 6420 @ 2.13GHz with 2GB ofmemory using one single core. This computational systemis similar to the one used for reporting in [8] taking intoconsideration that we do not make use of threading. Inthis last work a half rate was achieved for similar videoresolutions.

Resolution MoG Hsu DoFItime 25 fr (s) fps time 25 fr (s) fps time 25 fr (s) fps

320x240 6803 4,01 920 27,17 312 80,12624x352 18350 1,36 2730 9,15 905 27,62

Fig. 9. Time costs of MoG, Hsu and DoFI modules while detecting skincolor clusters

Figure 8 shows a real-time grass detection on a soccergame. Video sequence was grass detection processed asexplained and this figure show the resulting frames.

V. CONCLUSIONSThe real-time implementation of an approach for color

cluster detection [4] was presented herein. The approachis based on the application of the fuzzy integral, whichattains a non-linear projection of color images into the grayvalue domain. This projection depends on the selection ofthe so-called fuzzy measure coefficients. The fuzzy integralis computed w.r.t. two different sets of coefficients, whosevalues are determined through an evolutionary search. Thegoal of this search is the maximization of the differencebetween the two achieved projections.The implemented methodology is adaptive, due to the

training procedure embedded in the overall methodology.Therefore it can be easily adapted to the detection of differentcolor clusters. This can be easily attained by providing thesuitable training database including examples of images withpixels presenting the color to be detected. Taking all thesefacts into consideration, it can be stated that the methodologyis flexible enough in order to be successfully included indifferent computer vision applications. Indeed its applicationhas successfully been tested in different application domainssuch skin detection or grass detection.

The implementation presented herein attains an analogousperformance as the Mixture of Gaussians for skin detection[2] in terms of Equal Error Rate (EER). The sample im-plementation was also used for a novel methodology forsport grass segmentation, attaining a high performance onclassification as well as a strong generalization capability.Together with a high classification performance, DoFI

method presents low computation costs. This feature al-lows real-time robust color cluster detection with DoFI.The viability of real-time processes must be discarded withother methods, such are the ones based on the Mixture ofGaussians [11],[12].Therefore we can state that the presented implementation

constitutes an interesting advance in color clusters detection,which can be successfully employed in real applications.Moreover the methodology is robust enough to cope withillumination changes, due to the mathematical properties ofthe fuzzy integral. Furthermore his feature could be improvedby adaptively changing the coefficients in real-time. Therobustness while coping with illumination changes and theperformance on real-time detection have been particularlyproved on the sports grass application presented herein.However a faster learning procedure should be envisaged forthe purpose of real-time adaptively segmentation.

ACKNOWLEDGEMENTSThe authors would like to thank Anna Bosch from Media

Pro and Vicent Caselles from Universitat Pompeu Fabra fortheir support and advice. They would also thank XavierVives, from Corporacio Catalana de Radio i Televisio forhis support and for providing some of the images used inthis work.

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