The histopathological analysis of colon biopsy samples is a very important part of screening for colorectal cancer. There is, however, significant inter-observer and even intra-observer variability in the results of such analysis due to its very subjective nature. Therefore, quantitative methods are required for the analysis of histopathological images to aid the histopatholgists in their diagnosis. In this paper, we exploit the shape and structure of the gland nuclei cells for the classification of colon biopsy samples using two-dimensional principal component analysis (2DPCA) and Support Vector Machine (SVM). We conclude that the use of textural features extracted from non-overlapping blocks of the histopathological images results in a non-linear decision boundary which can be efficiently exploited using a SVM with appropriate choice of parameters for its Gaussian kernel. The SVM classifier outperforms all the remaining methods by a clear margin

Masood, Khalid

Rajpoot, Nasir M. (Nasir Mahmood)

English

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http://wrap.warwick.ac.uk/            Original citation: Masood, K. and Rajpoot, Nasir M. (Nasir Mahmood) (2007) Classification of colon biopsy samples by spatial analysis of a single spectral band from its hyperspectral cube. In: 11th Medical Image Understanding and Analysis (MIUA 2007), Aberystwyth, Wales, 17-18 Jul 2007  Permanent WRAP url: http://wrap.warwick.ac.uk/61638        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.  Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge.  Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.  A note on versions: The version presented in WRAP is the published version or, version of record, and may be cited as it appears here.For more information, please contact the WRAP Team at: publications@warwick.ac.uk    Classification of Colon Biopsy Samples by Spatial Analysis of aSingle Spectral Band from its Hyperspectral CubeKhalid Masood and Nasir RajpootDepartment of Computer Science, University of Warwick, Coventry, CV4 7AL, UKemail: {khalid, nasir}@dcs.warwick.ac.ukAbstract.The histopathological analysis of colon biopsy samples is a very important part of screening for colorectal cancer.There is, however, significant inter-observer and even intra-observer variability in the results of such analysis due toits very subjective nature. Therefore, quantitative methods are required for the analysis of histopathological imagesto aid the histopatholgists in their diagnosis. In this paper, we exploit the shape and structure of the gland nucleicells for the classification of colon biopsy samples using two-dimensional principal component analysis (2DPCA)and Support Vector Machine (SVM). We conclude that the use of textural features extracted from non-overlappingblocks of the histopathological images results in a non-linear decision boundary which can be efficiently exploitedusing a SVM with appropriate choice of parameters for its Gaussian kernel. The SVM classifier outperforms all theremaining methods by a clear margin.1 IntroductionColon cancer is one of the leading forms of cancer and second most fatal, after the lung cancer, in England andWales [1]. The disease can be treated very effectively if detected in its early stages. Routine screening (ie, colonoscopyin this case) can save lives by nipping the problem in the bud. However, the screening process relies heavily onthe accuracy of the judgement made by histopathologists analysing the biopsy samples taken from suspected polyps.Unfortunately, the histopathological analysis is very subjective in nature and is marred by both intra- and inter-observervariability, potentially leading to different treatment regimes. The purpose of this study in the grand scheme of thingsis to increase the reliability of the screening process by introducing objectivity to the screening process.Several researchers have looked at the problem of classification of biopsy slides. However, due to the limited space here,it is not possible to give a comprehensive literature review. In [2], classification of tumors is done using expressionlevels of gene patterns in the tissue samples. In [3], it is proposed that metrics based on the responses of receptivefield operators modelling the orientation selectivity of the neurons found in the early visual pathway are capable ofdiscriminating between images of normal, dysplastic (transitional) and cancerous samples. A related computationalmodel of light interaction with colon tissue and classification using the tissue reflectance spectra is analyzed in [4].In this paper, we address two important questions: First, does the spatial analysis of a single spectral band (as opposedto the spatial-spectral analysis of the corresponding hyperspectral image cube) suffice for efficient classification ofbiopsy sample? An obvious advantage of using spatial analysis on a single band is its reduced computational andstorage complexity. Spectral analysis has been used in [5] and our goal is to determine whether the spatial analysis canachieve similar or even better classification performance. The second question addressed in this paper is: How effectiveare the features extracted using linear subspace projection of raw image blocks as compared to textural features fromthe same blocks?Our approach is based on the idea that development of colon cancer alters the macroarchitecture of the tissue glands.The cancerous stimuli cause cells to adapt by altering their pattern of growth. This phenomena results in the increase inthe size of existing nuclei and also considerable increase in their number. The nice tubular structure for a normal tissuechanges to deformed structure for malignant tumors. The malignant tumor shows considerable variation in nuclei sizeand shape. The following sections present materials and methods used in our experimentation, followed by quantitativeresults and their discussion. The paper ends with some concluding remarks and future directions.2 Materials and MethodsA tissue micro-array of stained biopsy samples for several different patients is prepared using standard Haematoxylinand Eosin (H&E) staining procedures. Standard digital colour or greyscale images for histopathological analysis ofeach of the biopsy samples are normally obtained by placing the micro-array under a microscope equipped with aPatches (64x64)Textural FeaturesCovariance MatrixLDA TrainingSelectionSVM ModelSVMLDAParametersModel ..BenignMalignantBiopsy MBiopsy 1Biopsy 2NearestNeighbourClassifierPatches (64x64) Projection CoordinatesProjection Vectors and CoordinatesPCA/2DPCASelectionBenignMalignantTextural Features SVM ClassifierBiopsyM+1Patches (64x64)BiopsyM+123Training 113TestingTesting2 orFigure 1. Block Diagramvisible light source and a CCD camera. In our case, however, the imaging setup (same as that used in [5]) consistedof a Nikon Biophot microscope and a unique tuned light source based on a digital mirror device (DMD). The DMDbased light source is capable of transmitting any combination of light frequencies. Hyperspectral image cubes of thebiopsy sample at a magnification of 400X are captured at 128 different wavelengths, with narrow bandwidths, in therange of 400–800nm. In this way, each image cube consists of 128 spectral bands (spectral resolution) while the spatialresolution of each spectral band is 448 × 691. The image cubes are spatially cropped to obtain spectral bands with aspatial resolution of 448 × 640, in order to facilitate our local spatial analysis which operates by analysing 64 × 64blocks of a single hand-picked spectral band for each cube. After experimentation with number of bands, observing theeffect of a particular band on the classification performance, we found that a number of spectral bands in the middle partof the visible light spectrum for most datasets seemed to contain sufficient textural information for biopsy classificationpurposes. We picked one of the middle bands, the 75th band, for all our experiments reported in this paper.A unified block diagram of the methods investigated is shown in Figure 1. As depicted in the Figure, there are twotypes of classification paradigms employed for comparison purposes: first type using raw image blocks and subspaceprojection methods (classical principal components analysis, PCA, and two-dimensional PCA), and the second typeusing textural features for the image blocks and utilising LDA or SVMs. The methodology is described in more detailin the following sections.2.1 Classification using Raw Image PatchesIn order to address the second question in Section 1, we investigate whether features obtained by maximising theoverall scatter of the raw image blocks contain sufficient information for discrimination purposes. Such features can beobtained by the classical linear subspace projection (or dimensionality reduction) method of PCA. We also investigatethe use of two-dimensional PCA (2DPCA) [6] for feature extraction from raw image blocks. First, we give a briefdescription of the two methods.2.1.1 Subspace Projection of Raw Patches with PCAThe subspace projection methods operate by projecting a given n×n image block, or patch, Pi(i = 1, 2, . . . ,M),whereM is the total number of training image blocks) onto a small number d of projection vectors X(1)k , for k = 1, 2, . . . , d..In case of PCA, the projection vectors are the eigenvectors corresponding to the largest d eigenvalues of a covariancematrix C(1) obtained from all the M training image blocks as follows,C(1) =1MM∑i=1(vi − v¯)(vi − v¯)Twhere vi denotes the patch Pi rearranged into a one-dimensional (1D) vector (normally, in a row-by-row fashion) andv¯ denotes the average of all such vectors for the training patches. The above equation results in a potentially largecovariance matrix C(1) having dimensions n2 × n2, although the so-called transpose trick can be used to reduce itsdimensions to M ×M , nevertheless requiring extra computations for calculating the projection coordinates.2.1.2 Two-dimensional Principal Component Analysis (2DPCA)2DPCA is a new linear subspace projection method particularly developed for image classification. It was recentlyshown to be successful for face recognition [6]. The basic idea behind 2DPCA is that the covariance matrix is computedusing the training images without requiring to first convert them to 1D vectors. This is done as follows,C(2) =1MM∑i=1(Pi − P¯ )T (Pi − P¯ )As a result of the above computation, the covariance matrix C(2) is of the size n × n, which could be much smallerthan its conventional counterpart C(1). Furthermore, the linear subspace projection using 2DPCA is a more accuratereflection of the spatial relationship between image pixels in all the training samples as it maximises the overall scatterof all the training images. Just as matrices for training images are used for computation of C(2), the computaion ofprojection coordinates for Pi is also done by projecting the corresponding matrix onto the first d eigenvectors of C(2)as follows,aik = PiX(2)kwhere X(2)k is the n× 1-dimensional eigenvector of C(2) corresponding to its kth largest eigenvalue λk. One funda-mental difference between 2DPCA and conventional PCA is that the projection coordinates (or the 2DPCA featurematrix) for Pi in case of 2DPCA can be represented in the form of a n× d matrix Ai given byAi = [ai1, ai2, . . . , aid]as opposed to a d-dimensional feature vector in case of the classical PCA obtained by projecting vi onto X(1)k , fork = 1, 2, . . . , d. The classification of a test sample is done by computing the sum of Euclidean distances between thecolumns of feature matrices of the test image and those stored in the database for training samples. A nearest neighbourclassifier can be used to assign label to the test sample.2.2 Classification using Textural FeaturesAlthough 2DPCA has been shown to be more efficient than classical PCA for image classification, it has some draw-backs too, such as the large dimensionality of the features (ie, the feature matrices) and the high computational com-plexity of classification of a test sample due to potentially large number of distance calculations. Therefore, we alsoinvestigate the effectiveness of local textural features for biopsy classification using a single spectral band.Grey level co-occurrence matrix features are calculated for every patch Pi of the image corresponding to a singlespectral band of the given hyperspectral cube for a biopsy sample. A co-occurrence matrix is computed using secondorder joint conditional probability density function f(i, j|d, θ) by counting all pairs of pixels separated by distance sin direction θ and having grey level i and j. By using two distance values and four values of θ (0, 45, 90, 135 degrees),we can compute a relatively small feature vector, which we used with a classical linear discriminant analysis (LDA)classifier and also appropriately tuned SVMs.2.2.1 Linear Discriminat Analysis (LDA)One of the major drawbacks of the two kinds of PCA discussed above is that they maximise the overall scatter butdo not take into account the variability between samples belonging to the same class and those belonging to differentclasses. LDA overcomes this limitation by making use of both within-class and between-class scatter. For a moredetailed coverage of LDA, the reader is referred to [7]. It suffices to mention here that the LDA projection vectors canbe used in the same way the projection coordinates or feature vectors for training samples can be obtained using theclassical PCA.(a)Benign B1 (b)Benign B2 (c)Benign B3 (d)Benign B4 (e)Benign B5(f)Malignant M1 (g)Malignant M2 (h)Malignant M3 (i)Malignant M4 (j)Malignant M5Figure 2. Images of Colon Biopsy Samples2.2.2 Support Vector Machine (SVM)SVMs utilise a nonlinear mapping from the input feature space to an implicit high-dimensional feature space, wherethe nonlinear boundary between patterns in the input space is linearized [8]. The SVM kernel function allows one toavoid the explicit evaluation of mapping by using the so-called kernel trick. The choice of kernel depends on the dataand its clustering. Gaussian kernel is defined belowK(xi, xj) = e−γ(xi−xj)2+ C,where xi and xj denote feature vectors corresponding to two patches Pi and Pj , is used in most cases because ofits widely reported superior classification performance, also in this context [9]. In the above equation, C is a constantwhich normally does not significantly affect the classifier’s performance, whereas the choice of γ (width of the Gaussianbasis function) can have a significant influence on the performance. A variety of selection methods have been usedincluding grid search and Newton’s bisection methods [9]. Once a kernel is tuned properly, classification of test datacan be performed effectively.3 Results and DiscussionWe conducted experiments with ten biopsy samples using a leave-one-out (LOO) testing strategy. As shown in Figure2, five of these were benign and the remaining five malignant. The 75th spectral band of the hyperspectral image cubesfor these biopsies was each divided into non-overlapping blocks of 64 × 64. For spectral band selection, we performseveral experiments on different bands using SVM and found that middle bands have more textural information thaninitial and final bands, whereas the 75th band gives highest classification accuracy. In a 10-fold cross-validation setting,each time the training set consisted of patches from nine images, while the remaining tenth image was used for testing.The PCA and 2DPCA classifiers used 60 and 40 projection coordinates, respectively. For textural features, two valuesof s (namely, 1 and 2) and four values of θ as mentioned above are used and three features (namely, energy, varianceand homogeneity) are used, yielding a 24-dimensional feature vector for each of the biopsies. LDA further used only20 projection vectors for computing the linearly discriminating feature vectors. The Gaussian kernel for the SVM wastuned with a bisection search. A summary of block-wise classification accuracy results are shown in Table 1.Correct classification accuracy of image blocks by all four methods for all the biopsy slides is shown in Figure 3(a).Each biopsy slide is given a label according to a cutoff threshold on the accuracy of labels assigned to its blocks. Ifwe choose a 50% threshold, we get 10 slides out of 10 (except PCA) correctly labelled for each of the classifiers,although by doing that we risk having too many false positives or false negatives in practise. At 60% threshold, PCAperformance degrades and only 6 slides are correctly classified while 2DPCA labels 9 slides in the right class. At thisthreshold, SVM has 100% classification accuracy. When we select the threshold to be 70%, LDA accuracy is down to70% while SVM still performs at 100% accuracy. A plot of true positive rate (TPR) versus false positive rate (FPR),also known as the receiever operating characteristic (ROC) curve, is shown in Figure 3(b). SVM with textural featuresis the clear winner, as it has the largest area under the convex hull (AUCH) of all the ROC curves. It is our view thatmore than 70% is a reasonable value for the threshold if we consider that upto one third of some of the images containonly background information. It is worth noting that SVM yields 100% accuracy with a 80% threshold.Non-Overlapping Blocks Classification Accuracy (%)Biopsy No. Raw data Textural dataPCA 2DPCA LDA SVM(65) SVM(70) SVM(75) SVM(80)B1 68.57 85.71 80.00 77.14 95.71 95.71 95.71B2 55.71 65.71 68.57 61.43 81.43 88.57 84.29B3 50.00 64.29 78.14 48.57 64.29 91.43 78.57B4 58.57 70.00 64.29 54.29 51.43 84.29 75.71B5 48.57 51.43 54.21 30.00 30.00 82.86 41.43M1 82.86 70.00 78.14 98.57 98.57 98.57 98.57M2 72.86 74.29 81.43 94.29 81.43 94.29 84.29M3 65.71 68.57 72.86 94.29 97.14 92.86 94.29M4 72.86 74.29 75.71 84.29 84.29 85.71 80.00M5 70.00 75.71 92.86 98.57 92.86 97.14 92.86Average 64.57 70.00 74.63 74.14 77.72 91.14 82.57Table 1. SVM (with different Bands) and PCA, 2DPCA, LDA (Band 75) Results(a) Classification Accuracy (b) ROC CurveFigure 3. Performance Curves for 75th Spectral Band4 Conclusions and Future WorkOur experimental results demonstrate that by taking only single band from a hyperspectral data cube, it is possibleto perform a reasonable classification for histopathological analysis of colon biopsy samples. An appropriately tunedSVM coupled with textural features yields the best performance as compared to other subspace projection methods withand without textural features. This is because SVM introduces a nonlinear mapping where the decision boundary islinearized and hence separation is performed much more efficiently. The segmentation of glands and the measurementof features related to glandular shapes will be subjects of our future study.References1. N. S. Office. “Cancer statistics and registrations for england and wales.” HMSO 1999.2. T. Furey, N. Cristianini & N. D. et al. “Support vector machine classification and validation of cancer tissue samples usingmicroarray expression data.” Bioinformatics 2000.3. 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Classification of colon biopsy samples by spatial analysis of a single spectral band from its hyperspectral cube

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Classification of colon biopsy samples by spatial analysis of a single spectral band from its hyperspectral cube

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