This paper is concerned with the classification of tumoral tissue in the small bowel by using capsule endoscopic images. The followed approach is based on texture classification. Texture descriptors are derived from selected scales of the Discrete Curvelet Transform (DCT). The goal is to take advantage of the high directional sensitivity of the DCT (16 directions) when compared with the Discrete Wavelet Transform (DWT) (3 directions). Second order statistics are then computed in the HSV color space and named Color Curvelet Covariance (3C) coefficients. Finally, these coefficients are modeled by a Gaussian Mixture Model (GMM). Sensitivity of 99% and specificity of 95.19% are obtained in the testing set.Centre Algoritm

Barbosa, Daniel

Lima, C. S.

Martins, Maria M.

Ramos, Jaime

English

Universidade do Minho: RepositoriUM

Abstract— This paper is concerned with the classification oftumoral tissue in the small bowel by using capsule endoscopicimages. The followed approach is based on textureclassification. Texture descriptors are derived from selectedscales of the Discrete Curvelet Transform (DCT). The goal is totake advantage of the high directional sensitivity of the DCT(16 directions) when compared with the Discrete WaveletTransform (DWT) (3 directions). Second order statistics arethen computed in the HSV color space and named ColorCurvelet Covariance (3C) coefficients. Finally, thesecoefficients are modeled by a Gaussian Mixture Model (GMM).Sensitivity of 99% and specificity of 95.19% are obtained in thetesting set.I. INTRODUCTIONNLIKE conventional endoscopy the endoscopic capsuleallows to examine the entire gastrointestinal tract (GI)with a minimal invasive procedure, not requiring highlytrained personal for navigating the equipment anddiminishing the injury risks for the patients [1]. The patientingests the CE and the images are captured as the capsulemoves through the GI, propelled by peristalsis. More than50.000 images are acquired per exam at a rate of two persecond for about 8 hours [2]. Usually the physician isrequired to analyze this huge amount of data, selecting theframes that he considers important regarding diagnosispurposes. This task is prone to subjective errors, timeconsuming (40-60 min) and increases costs. So, it’simportant to develop a computer assisted diagnosis tool toassist in this task. The texture alteration of the small intestinemucosa has been previously reported in the work ofKarkanis et al. [3] where the use of statistic texturaldescriptors has been successfully applied in classificationschemes for identification of abnormalities in colonoscopyvideos. Therefore this is a promising classification techniquefor automatic detection of abnormalities. The extraction of arelevant feature set is usually done using wavelet methods.During the past two decades, wavelets theory has beenwidely used because wavelets provide a powerful tool formulti-resolution analysis of images [4].In two-dimensional case the commonly used separablewavelets obtained by a tensor-product of 1D wavelets areonly good at capturing discontinuities at edge points, but donot see the smoothness along edges. As a matter of fact,Manuscript received April 1, 2010.C. S. Lima and Maria M. Martins are with the Industrial ElectronicsDepartment, Minho University, Portugal.Daniel J. Barbosa is with the Catholic University of Leuven, Belgium.Jaime Ramos is with the Capucho’s Hospital, Lisbon, Portugal..wavelets transform extracts directional details that onlycapture horizontal, vertical and diagonal activities in animage, and these three directions cannot in general provideenough directional information in images. In an attempt toovercome the weakness of traditional multiscalerepresentations using wavelets and to capture moredirectional features in an image, Discrete CurveletTransform (DCT) has recently emerged as a new multi-resolution analysis tool. This approach is proposed in thispaper to extract the textural descriptors from CE videoframes.Texture classification techniques have been based onseveral classifiers such as Multi layer Percepton (MLP)networks, Radial Basis Functions (RBF’s) and SupportVector Machines (SVM). These techniques have beenshown to have a great ability to differentiate the normalregions of abnormal regions, presented by the images of theCE. Unfortunately, these techniques have unavoidabledrawbacks when dealing with the modeling of statisticaldependence between the various features [5]. In factstatistical dependence is not explicitly modeled in neuralbased pattern recognition schemes. So, in order to cover thisdrawback, we discuss in this paper, the use of GaussianMixture Model (GMM), which allows extending theapproach to time series modeling by extending the GMM toHidden Markov Model (HMM). In this framework thediagnosis will be based on frame sequence analysis, whichmeans that contextual information can be capturedimproving the knowledge that can be used in theclassification process. The Expectation-Maximization (EM)Algorithm was used for finding maximum likelihoodestimates of the GMM parameters and can be easilyextended to the HMM framework.The classification system described in this article usesstatistical texture descriptors extracted from CurveletDiscrete Transform, and a Gaussian mixture model as apattern recognition module.II. DISCRETE CURVELET TRANSFORMIn an attempt to overcome the weakness of traditionalmultiscale representations and to capture more directionalcharacteristics in an image, curvelet transform has recentlyemerged as a new multi-resolution analysis tool. In 2000,Candes and Donoho introduced the Curvelet Transform [6].The basic idea of curvelet transform is to represent a curveas a superposition of functions of various lengths and widthsobeying a specific scaling law. Regarding 2D images, it canbe done first by decomposing an image into wavelet sub-Small Bowel Tumors Detection in Capsule Endoscopy by GaussianModeling of Color Curvelet Covariance CoefficientsMaria M. Martins, Daniel J. Barbosa, Jaime Ramos and Carlos S. Lima, Members IEEEUbands, i.e., separating the object into a series of disjointscales. Curvelet exhibits optimally sparse representation ofotherwise smooth objects, and as such it has generated agreat deal of interest in recent years [7].So the Continuous Curvelet Transform (CCT) can bedefined by a pair of windows W(r), a radial window, andV(t),  an  angular  window.  These are smooth, nonnegative,and real-valued, with W taking positive real arguments andsupported on r ∈ (1/2, 2) and V taking real arguments andsupported on t ∈ [−1, 1]. These windows will always obeythe admissibility conditions:(2 ) = 1∞∞, 34 , 32 (1)( − 1) = 1∞∞, − 12 , 1/2 (2)Now, for each j ≥ jo , it is introduced the frequencywindow Uj defined in the Fourier domain by:( , ) = 2 (2 ) 22 (3)where |j/2| is the integer part of j/2, r and θ are polarcoordinates in frequency domain. The support of thiswindow is called polar wedge which depends on the supportof W and V.Assuming Uj is the Fourier transform of a function φj(x),we can consider φj(x) as the “mother” curvelet function sinceall the curvelets at scale 2-j may be obtained by rotations andtranslations of φj(x). We further introduce equispacedsequence rotation angles = 2 . 2 | |, 0 ≤ ≤ 2| | − 1,and translation parameters = ( , ). With the abovenotation, a curvelet can be defined as a function of =( , ) at scale 2-j, orientation and position ( , )by, , ( ) = − ( , ) (4)where ( , ) = . 2 , . 2 and is the rotationmatrix in radians:= cos− sin sincos (5)A curvelet coefficient is then defined as the inner productof an element ∈ ( ) and a curvelet , , , i.e.,( , , ) = 〈 , , , 〉 = ( ) , , ( ) (6)Fig. 1a) shows the polar wedge represented by Uj in thefrequency domain. Hence, in Fourier space curvelets aresupported by “parabolic” wedges, and the shaded arearepresents such a generic wedge.a) b)Fig. 1 a) Curvelet wedge in frequency domain; b) Basic wedge of the digitalcoronization processReference [8] proposes two different schemes for thediscretization of the CCT, namely the USFFT algorithm andthe wrapping algorithm. Both rely in the transformation ofthe frequency coronae of  the  CCT  of  Fig. 1b) in  a“Cartesian coronae”, which are based  on  concentricsquares  (instead of circles) and shears, in a processdesignated by digital coronization. The motivation for thisdigital coronization is  the  fact  that  coronae  and  rotationsare  not  especially adapted  to  Cartesian  arrays,  whichdifficult  their  computation.  Since it is stated that thewrapping algorithm may be simpler to understand andimplement, this approach was chosen to calculate theDiscrete Curvelet Transform (DCT) in the present work.Further details about the CCT and its discretization can befound in [8]. In the proposed approach, the CE frames wereprocessed with the wrapping algorithm for three scales, withsixteen angles.III. GAUSSIAN MIXTURE MODELMixture Models are a composite density model whichcomprises a number of component functions, usuallyGaussians. These component functions are combined toprovide a multimodal density [9]. They can be employed tomodel the texture descriptors of an image captured by CE inorder to perform tasks such as the classification of the stateof the intestine mucosa. Mixture models are a semi-parametric alternative to non-parametric histograms [10](which can also be used as densities) and provide greaterflexibility and precision in modelling the underlyingstatistics of sample data.Once a model is generated, conditional probabilities canbe computed for textural descriptors [9]. Let the probabilitydensity function ( ̅) of vector observations x (correspondsto the curvelets coefficients) be a mixture with M componentdensities:( ̅) = p(x|j)c (7)where a mixing parameter c corresponds to the priorprobability of observation x has been generated by thedensity j and where ∑ = 1 .Each mixture component isa Gaussian with mean vector ̅ and covariance matrix Σ:( ̅/ ) = 12π Σ exp μ ∑ μ (8)The Expectation-Maximisation (EM) algorithm [11] is atwo step based procedure that iteratively maximizes thelikelihood of the training data.IV. STATISTICAL TEXTURE DESCRIPTORSVarious statistical features can be extracted from thecurvelet domain as texture descriptors, and the mostcommon are the mean, standard deviation, energy andentropy of each DCT sub-band [12].Although the images captured by the capsule are square,the information is restricted to a circular area in the center ofthe image, by restrictions in the acquisition process. Giventhe scale anisotropy of the DCT, the calculation of texturaldescriptors will be made only for the coefficientscorresponding to the circular region of CE frames, N.The proposed texture descriptors on this paper can becalculated as:= { ( , )} = 1 ( , ) (9)= {( ( , ) − ) } = 1 ( ( , ) − ) ) (10)where P(i,j) is the pixel at position (i,j).The most important scales of the DCT, regarding textureencoding information are those in which high frequenciesare present. As suggested in [13] the most relevantinformation for classification purposes are encoded as highfrequency content in the scale corresponding to the highestlevel of detail. Thus, for the scales whose coefficientscorrespond to low and medium frequency content (coarsestscale coefficients), the texture descriptors weren’t computed.Besides, the coarsest scale coefficients of the DCT do notpossess directional sensitivity as a consequence for not beingdirectional.It is expected that textural descriptors correlate among thedifferent color channels as supposed in [3] and thesecorrelations allow distinguishing normal from abnormaltexture patterns. Thus, in the present work it is proposed ananalogous framework, named as Color Curvelet Covariance(3C) coefficients, where the classification feature is thecovariance of textural descriptors in the different colorchannels. In this framework, the high directional sensitivityof the DCT will be expected to lead to more vigorousdescriptors than a similar scheme used in textural descriptorstaken from Discrete Wavelet Transform coefficients. TheColor Curvelet Covariance of a texture descriptor can becalculated as:( , , , ) = ( ( , , ) − { ( , , )}). ( ( , , ) − { ( , , )}) (11)where . stands for the multiplication operation, a, bcorrespond to the different color channels in the covariancecomputation, Fm is the statistic textural descriptor, α is theangle of the DCT coefficients, s is the DCT scale andE{Fm(a,s,α)} the average of the statistical textural descriptorFm over the different angles α, in the color channel a or b.See that if i=j, the previous equation is nothing more thanthe variance of the textural descriptor Fm with the DCT angleα. In opposition, CCC(i,j,s,m), for i≠j, gives a measure ofthe likeness of the variation of the textural descriptor Fmtaken from the DCT coefficients at different angles, betweentwo color channels.As the value of the statistical descriptor Fm already hasuseful information for the texture classification process, andas the proposed CCC (i,j,s,m) features only report for thecovariance of Fm between color channels, it is proposed toalso include in the feature set the average value E{Fm}. Thisportion is the mathematical expectancy for the value of Fmand so does not have as much information as the sequence ofthe different Fm values taken from the DCT coefficients atdifferent angles, but the insertion of the full sequence wouldlead to feature vectors with very high dimensionality, whichwould compromise the training of the classifier and thespeed of the classification step.V. IMPLEMENTATION AND RESULTSThe set of experimental data was built with frames ofvideo capsule endoscopy segments from different patients.The data set consists of 400 normal frames, which weredivided into two sets, one for the Gaussian training andanother for the test; and 200 abnormal frames, which werealso equally divided into two sets. An example of each typeof frame from CE that was used for the experiment is shownin Fig. 2.Fig. 2. Example of a normal (a) and an intestinal tumor (b) CE framesA 2.4 GHz Pentium Core Duo processor-based, with 3 GBof RAM, was used with MATLAB to run the proposedalgorithm and the average processing time is approximately1.5 seconds per frame. As the proposed algorithm has notbeen optimized for speed, the processing can still beimproved. The DCT calculation was done with the routinesimplemented in the tool CurveLab (available for researchpurposes at www.curvelet.org). In the proposed approach,the CE frames were processed with the wrapping algorithmwith sixteen angles, leading to finest detail coefficients inthe DCT domain for each color channel. The selected colorspace was the HSV, since is more similar to thephysiological perception of human eye [14], and thereforemore satisfactory than the standard RGB color space. Toevaluate the performance of GMM as a classification systemin this approach, we used the values of sensitivity andspecificity from previous work [15] that calculated thecoefficients with the DCT, as well, but used the Multi layerPercepton, as a classification system. The feature set wasconstructed with the Color Curvelet Covariance values,since it was shown in [15], that the Color CurveletCovariance features can be successfully used for CE framesclassification purposes and that the best statistical texturaldescriptors in the present framework are the mean and thestandard deviation of the DCT coefficients.Instead of measuring the rate of successful recognizedpatterns, more reliable measures for the evaluation of theclassification performance can be achieved by using thesensitivity (true positive rate) and the specificity (100-falsepositive rate) measures.Table 1 shows the results for the different classificationsystems. Note that the proposed system has a significantbetter sensitivity than the MLP, but in terms of specificity itis slightly poorer.VI. CONCLUSION AND FUTURE WORKThis paper proposes modeling the Color CurveletCorrelation (3C) coefficients by a Gaussian Mixture Model.3C coefficients are obtained by processing endoscopiccapsule imaging in the HSV color space. Although theresults can be highly dependent on the used database GMMclassification seems to be superior to MLP classification.The advantage of using GMM is that statistical dependencecan be explicitly modeled if full covariance matrices areused. Additionally context information can be easilyincluded if GMM is changed to HMM modeling. Inclusionof context information will be considered as near futuredevelopments and is frequently used by physicians forimproving the diagnosis.REFERENCES[1] G. Idden, G. Meron, A. Glukhovsky and P. Swain. “Wireless capsuleendoscopy”, Nature. 2000, pp. pp. 415-417.[2] Pennazio, M. “Capsule endoscopy: Where are we after 6 years ofclinical use?,”. 2006, Vols. 38, pp. 867–878.[3] S. Karkanis, D. Iakovidis, D. Maroulis, D. Karras and M. Tzivras.“Computer-Aided Tumor Detection in Endoscopic Video Using ColorWavelet Features”. IEE Trans. On Information Technology in Biomedicine,Vols. 7, no. 3, Sep. 2003.[4] N.D. Minh, Martin Vetterli. The finite ridgelet transform for imagerepresentation. IEEE Transactions on Image Processing 12 (1) pp. 16-28,2003.[5] Yanfang Han, Pengfei Shi. An adaptive level-selecting wavelettransform for texture defect detection. Image and Vision Computing 25(2007) pp.1239-1248.[6] Donoho, E. Candes and D. “Curvelets, multi-resolutionrepresentation, and scaling laws”. Wavelet Applications in Signal andImage Processing VIII, SPIE vol. 4119, pp 1-12, 2000. .[7] J.L Starck, D.L. Donoho, E.J. Candes. Astronomical imagerepresentation by the curvelet transform. Astronomy and Astrophysics (398)(2003) pp. 785-800.[8] Candes E, Demanet L, Donoho D and Ying L. Fast Discrete curvelettransforms. SIAM Multiscale Modeling Simul, 2006.[9] Y. Raja, S. McKenna, and S. Gong. "Segmentation and trackingusing colour mixture models,'' . in Asian Conference on Computer Vision,Hong Kong, January 1998.[10] Bishop, C. Neural Networks for Pattern Recognition. OxfordUniversity Press, 1995.[11] A. P. Dempster, N. M. Laird and D. B. Rubin. "MaximumLikelihood from Incomplete Data via the EM Algorithm," . Journal of theRoyal Statistical Society, B, vol. 39, no. 1, pp. 1-38, 1977.[12] Semler, L. Dettori and L. “A comparison of wavelet, ridgelet, andcurvelet-based texture classification algorithms in computed tomography,”Computers in Biology and Medicine, vol. 37, no. 2, pp 486-498, 2007.[13] D. Barbosa, J. Ramos and C. Lima. “Detection of Small BowelTumors in Capsule Endoscopy Frames Using Texture Analysis based on theDiscrete Wavelet Transform,” in Proceedings of the IEEE-EMBC2008,Vancouver, Canada, 2008, pp 3012-3015.[14] L. Baopu  and M. Meng, “Computer-based detection of bleeding andulcer in wireless capsule endoscopy images by chromaticity moments,Computers in Biology and Medicine, vol. 37, no. 4, pp 141-147, 2009[15] D. Barbosa, J. H. Correia, J. Ramos and C. S. Lima, TextureClassification of Images from Endoscopic Capsule by Using MLP andSVM – A Comparative Approach” Proceedings of the World Congress onMedical Physics and Biomedical Engineering 2009; Munich 7-12September 2009, Vol. 5 pp. 271-274.TABLE ICLASSIFICATION PERFORMANCE OF DIFFERENT SYSTEMSFeature Set GMM MLPSpecificity (%) 95.19 95.9Sensitivity (%) 99 95.9

Small bowel tumors detection in capsule endoscopy by gaussian modeling of color curvelet covariance coefficients

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Small bowel tumors detection in capsule endoscopy by gaussian modeling of color curvelet covariance coefficients

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