A framework for classiﬁcation of chronic lung disease from high-resolution CT scans is presented. We use a set of features which measure the local morphology and topology of the 3D voxels within the lung parenchyma and apply functional data classiﬁcation to the extracted features. We introduce the measures, Minkowski functionals, which derive from integral geometry and show results of classiﬁcation on lungs containing various stages of chronic lung disease: emphysema, ﬁbrosis and honey-combing. Once trained, the presented method is shown to be efﬁcient and speciﬁc at characterising the distribution of disease in HRCT slices

Bhalerao, Abhir

Parr, David

Thönnes, Elke

English

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http://wrap.warwick.ac.uk           Original citation: Thonnes, E., Bhalerao, Abhir and Parr, D. (2010) Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis. In: Proceedings of the Medical Image Understanding and Analysis (MIUA'10), Coventry, UK, 6-7 July, 2010. Published in: Proceedings of Medical Image Understanding and Analysis pp. 25-30  Permanent WRAP url: http://wrap.warwick.ac.uk/47479             Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions.  Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners.  To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.  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For more information, please contact the WRAP Team at: publications@warwick.ac.uk  THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCT 1Classification of Lung Disease in HRCTScans using Integral Geometry Measuresand Functional Data AnalysisDr Elke Thönnes Department of Statistics and Centre forScientific ComputingUniversity of WarwickCoventry, UKDr Abhir Bhalerao Department of Computer ScienceUniversity of WarwickCoventry, UKDr David Parr Coventry and Warwickshire UniversityHospitals, Coventryand Medical School, University ofWarwickCoventry, UKAbstractA framework for classification of chronic lung disease from high-resolution CT scansis presented. We use a set of features which measure the local morphology and topologyof the 3D voxels within the lung parenchyma and apply functional data classification tothe extracted features. We introduce the measures, Minkowski functionals, which derivefrom integral geometry and show results of classification on lungs containing variousstages of chronic lung disease: emphysema, fibrosis and honey-combing. Once trained,the presented method is shown to be efficient and specific at characterising the distribu-tion of disease in HRCT slices.1 IntroductionChronic obstructive lung diseases, such as emphysema and pulmonary fibrosis, are progres-sive respiratory diseases leading to a decline in lung function and, eventually, respiratoryfailure. High resolution computed tomography (HRCT) is currently the most accurate, non-invasive method of detecting and evaluating changes in lung parenchyma and so is used inclinical practice to diagnose and assess the severity of these diseases. The progress of diseasemanifests itself as textural changes of the imaged lung tissue and, in the case of emphysema,as a reduction of the mean lung density. In clinical practise, quantitative assessment ofemphysema is usually based on summary statistics of the histogram of lung voxel values.Common statistics are percentile points and the voxel index, which is the proportion of lungvoxels below a pre-defined threshold. However, such simple criteria can be unreliable, forexample, when the pathological process is mixed such as in the presence of inflammationand fibrosis along with emphysema.c© 2010. The copyright of this document resides with its authors.It may be distributed unchanged freely in print or electronic forms.2 THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCTAs chronic obstructive lung diseases express themselves as textural changes in HRCTscans, image texture analysis methods have been investigated as tools for a more robustquantification. The early work of Uppaluri et al. [10] used first and second order texture fea-tures together with fractal dimension to characterise emphysema. Chabat et al. [4] proposedthe use of texture measures based on grey-level co-occurrence matrices (GLCM). They alsoincluded a number of shape features. The use of GLCM and the related shape and connec-tivity measures suggested by Chabet et al. are also used in more recent work by Xu et al.[11]. In Hoffman et al. [7] and Zavaletta et al. [12] spatial maps of lungs have been producedthat graphically show the result of texture classification. The classifiers used in recent workvary from kNN classification [12], to Bayesian [11] and neural-network based methods [6].In the following we explore the use of a systematic framework of morphological descriptorsfrom integral geometry that integrates and extends current approaches based on histogramanalysis.2 Characterising Texture using Integral geometryIntegral geometry provides a family of measures, intrinsic volumes or Minkowski functionals,that characterise the morphology and topology of polyconvex sets. A set is polyconvex if itis a finite union of compact, convex sets. The foreground in a binary image is a finite unionof voxels and therefore a polyconvex set.In R3 there are four Minkowski functionals which are proportional to more commonlyknown quantities: volume V , surface area S, the mean breadth B (which is proportionalto the integral of mean curvature) and the Euler-Poincaré characteristic χ . More formally,Steiner’s formula can be used to define the Minkowski functionals for convex sets. In R3Steiner formula shows thatV (K⊕Br) = V (K)+S(K) r+2piB(K) r2+ 43χ(K) r3, (1)where K⊕Br = {x+ y,x ∈ K and y ∈ Br} is the dilation of the convex set K by a sphere ofradius r. Hence we haveW0(K) =V (K), W1(k) =13S(K), W2(K) =2pi3B(K), W3(K) =43χ(K). (2)In the following we will use the measures V , S, B and χ but refer to them collectively asMinkowski functionals.Minkowski functionals have convenient mathematical properties. They are invariant torigid motion, they are continuous in a certain sense and they are additive which allows forefficient computation of the functionals, see Section 3. Another important property is thatMinkowski functionals are complete in the sense of Hadwiger’s theorem: any image func-tional that is motion-invariant, continuous and additive is a linear combination of Minkowskifunctionals.Having been shown to be effective in materials science for classification of two-phasemedia (see for example [1]), more recently, the functionals have also been applied to HRCTlung scans. In [2, 3] the measures are used to classify regions of interest of size 40x40x40voxels into healthy, fibrotic and emphysematous tissue. The authors use an integrative filter-ing procedure to summarize the four integral geometry measures into a single quantity usedfor classification and provide evidence that these measures can outperform standard densito-metric methods. In [9] the same measures are computed on sub-windows covering the wholelung and calibrated maps are produced illustrating the spatial distribution of emphysema andpulmonary fibrosis.THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCT 3To apply the Minkowski functionals to HRCT scans, the images have to be binarized viathresholding. While [9] keep the threshold fixed, in this paper we extend the approach byletting the threshold vary and computing the Minkowski functionals for each threshold. Thisis a natural extension to the clinical densitometry approach as the zeroth order Minkowskifunctional (volume) as a function of attenuation is equivalent to the empirical cumulative dis-tribution function of voxel values. In contrast to [2, 3] who examine large regions of interest(40x40x40 voxels) we consider small sub-windows (5x5x1 voxels). While this sacrificessome of the separation between Minkowski functionals for the different disease classes itallows us to localize the spatial distribution of disease. Also, rather than summarizing themeasures into a single numerical quantity, we take account of the fact that we have functionsof Minkowski functionals by using a classification technique from functional data analysis.This overcomes the statistical issues posed by having a large number of predictors relativeto the sample size.3 Computation of Measures and Functional ClassificationLegland et al. [8] present an algorithm that computes Minkowski measures for 3D binaryimages. These Minkowski measures mi, i = 0, . . . ,3, are local versions of Minkowski func-tionals Wi, i= 0, . . . ,3, and are computed on voxel level. The Minkowski functional of a setX restricted to a windowΩ can then be computed by summing over the Minkowski values ofthe voxels in the window, that is Wi(X ∩Ω) = ∑x∈Ωmi(x). The algorithm is implemented asa marching cubes type algorithm with hhe Minkowski measure for any 3x3x3 binary voxelconfiguration being pre-computed and kept in a look-up table. Linear filtering is then usedto identify the voxel configuration for a given marching cube.To apply the algorithm to HRCT lung scans we binarised the lung images for a range ofdifferent thresholds. We subdivided each binary image into a grid of windows of size 5x5x1voxels and then computed the Minkowski functionals for each window. Thus we obtainedMinkowski functionals as functions of attenuation value, see Figure 1 for examples. Whenincreasing the window size the separation between the Minkowski functionals of differentdisease classification becomes more pronounced, however, spatial localisation of the classi-fication into disease states becomes reduced. In our experiments we used the non-parametricsupervised classification method by Ferraty and Vieu [5] to classify various diseased lungtissue. Our data represents functions which can pose problems for standard multivariatetechniques such as classical linear discriminant analysis because we have a large number ofpredictors relative to the sample size. Functional data analysis, like the method by Ferratyand Vieu, can overcome these limitations. We give a short overview of the method, furtherdetails can be found in [5].Let w = {w0,w1,w2,w3} be the observed Minkowski functionals which are functionsof attenuation value and let C denote the categorical variable denoting the class. The clas-sification method uses a Bayes rule as classification rule, that is it estimates the posteriorprobabilitiespc(w) = P(C = c∣∣∣W = w)= E(1[C=c]∣∣∣W = w) (3)and then assigns the class c with the highest estimated posterior probability to w. The pos-terior probabilities are estimated using a kernel estimator which is based on a functionalconcept of proximity. In our experiments we used the L2 metric applied to data smoothedvia multivariate partial least squares regression.4 THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCTFigure 1: Example Minkowski functionals from the training set.4 Results and DiscussionWe manually selected 28 regions of size 30x30x5 voxels as a training set. 10 of these regionswere examples of healthy lung, 10 fibrotic lung and 8 suffering from emphysema. (Thenumber of emphysematous training regions is smaller as there were fewer such regions inthe available HRCT scans). Both the training set and the lung tissue to be classified weresubdivided into 5x5x1 voxel windows. While we choose the vertical size of classified regionsto be just one voxel note that the Minkowski functional values each voxel take account of theconfiguration in the 3D neighbourhood. On the training set we achieved a misclassificationrate of 7%.Figure 2 illustrates some of our classification results. We should point out that the train-ing set was classified by a non-expert and is likely to underestimate the variability of thedisease patterns. Also, as the results are not based on a designed survey sample. Thus, atthis stage, the results are indicative only but illustrate the promise of the presented method.The resolution of classification was chosen as a compromise between spatial localisationand appropriate separation in the training sample. However, the additivity of the Minkowskimeasures presents the opportunity to develop a hierarchical classification approach in whichthe resolution in a spatial region can be varied and is determined as part of the algorithm.In summary, the classification method from functional data analysis has been shown toappropriately account of the fact that the integral geometry descriptors are functions of atten-uation. Furthermore, while enhancing the assessment of emphysema the presented frame-work could readily be applied to any other lung disease that leads to structural changes anddeformations of lung tissue, including pulmonary fibrosis and LAM. As well as further vali-dation of the framework, we are investigating its wider application.THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCT 5Figure 2: Classified lung slices: green regions denote healthy lung, red regions fi-brotic, honeycombed tissue and blue regions are classified as suffering from em-physema.References[1] C.H. Arns, M.A. Knackstedt, and K.R. Mecke. Characterising the Morphology of DisorderedMaterials, pages 37–74. Lecture Notes in Physics 600. Springer, 2002.[2] H.F. Boehm, C. Fink, U. Attenberger, C. Becker, J. Behr, and M. Reiser. Automated classificationof normal and pathologic pulmonary tissue by topological texture features extracted from multi-detector CT in 3D. European Radiology, 18, 2008. DOI: 10.1007/s00330-008-1082-y.[3] H.F. Boem, C. Fink, C. Becker, and M. Reiser. Automated Characterization of Normal andPathologic Lung Tissue by Topological Texture Analysis of Multi-Detector CT. In Giger andKarssemeijer, editors, Medical Imaging 2007: Computer-Aided Diagnosis, Proceedings of SPIEVol 6514, page DOI: 10.117/12.702697, 2007.[4] F. Chabat, G. Yang, and D. Hansell. Obstructive lung diseases: Texture classification for differ-entiation at CT. Radiology, 228:871–877, 2003.[5] Frédéric Ferraty and Philippe Vieu. Nonparametric Functional Data Analysis. Statistics.Springer, New York, 2006.[6] O. Friman, M. Borga, M. Lundberg, U. Tylén, and H. Knutsson. Recognizing Emphysema - ANeural Network Approach. In Proceedings of 16th Int. Conf. on Pattern Recognition - ICPR’02,page 10512, 2002.6 THÖNNES : CLASSIFICATION OF LUNG DISEASE IN HRCT[7] E. A. Hoffman, J. M. Reinhardt, M. Sonka, B. A. Simon, J. Guo, O. Saba, D. Chon, S. Samrah,J. Shikata, J. Tschirren, K. Palagyi, K. Beck, and G. McLennan. Characterization of the Inter-stitial Lung Diseases via Density-Based and Texture-Based Analysis of Computed TomographyImages of Lung Structure and Function. Academic Radiology, 10:1104–1118, 2003.[8] D. Legland, K. Kiêu, and M.-F. Devaux. Computation of Minkowski measures on 2D and 3Dbinary images. Image Analysis and Stereology, 26:83–92, 2007.[9] M. Charemza and E. Thönnes and A. Bhalerao and D. Parr. Integral Geometry Descriptors forCharacterizing Emphysema and Lung Fibrosis in HRCT Images. In First International Workshopon Pulmonary Image Processing (MICCAI 2008), pages 155–164, 2008.[10] R. Uppaluri, M. Theophano, M. Sonka, E. A. Hoffman, and G. McLennan. Quantification ofPulmonary Emphysema from Lung Computed Tomography Images. American Journal of Respi-ratory and Critical Care Medicine, 156:248–254, 1997.[11] Y. Xu, M. Sonka, G. McLennan, and E. A. Hoffman. MDCT-based 3-D texture classification ofemphysema and early smoking related lung pathologies. IEEE Transaction on Medical Imaging,25:464–475, 2006.[12] V. A. Zavaletta, B. J. Bartholmai, and R. A. Robb. High resolution multidetector CT-aided tissueanalysis and quantification of lung fibrosis. Academic Radiology, 7:769–771, 2007.

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Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis

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Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis

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