Co-Occurrence and Morphological Analysis for Colon Tissue Biopsy
ClassificationKhalid Masood, Nasir Rajpoot, Kashif Rajpoot*, Hammad Qureshi
Signal and Image Processing Group, University of Warwick (UK) * Wolfson Medical Vision Lab, Oxford University (UK)
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Problem Definition• Given hyperspectral image cube of a patient’s colon tissue
biopsy sample, automatically label the sample as Benign or Malignant
• Our approach is based on the idea that malignancy of a tumor alters the macro-architecture of the tissue glands:– Nice tubular structure of the glands for benign tumors– No such structure for malignant tumors
Benign Malignant
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Motivation for Colon Biopsy Classification
• Useful for screening of the colon cancer
• Visual assessment by pathologists is very subjective
• Significant intra- and inter-observational variation between pathologists
• Quantitative histopathological analysis techniques offer objective, reliable, accurate, and reproducible assessment
Source: NIH
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Hyperspectral Imaging
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Ordinary cameras only capturereflections from RGB colorsHyperspectral cameras capture reflections from a range of visible wavelengths
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Hyperspectral Imaging (HSI)
• HSI is a fast and reliable means of characterizing the histochemistry of tissues– HSI is also used extensively in remote sensing, satellite
imaging, and defence (target detection etc.) applications
• The Nuance multispectral imaging system can acquire 20 subbands in visible wavelength range of 420-720nm
• Each hyperspectral image is a 3D data cube with a spectral coordinate in the z direction representing 20 subbands
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Our Classification Algorithm• Based on a spectral-spatial analysis of the input
data cube, our algorithm consists of three stages:
– Stage I: Dimensionality reduction, followed by segmentation
– Stage II: Morphological/textural analysis of the segmented results
– Stage III: Classification using Subspace Projection methods and Support Vector Machines (SVM)
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Stage I: Segmentation• Dimensionality reduction (from 20 to 4 bands of the multispectral
image cube) is achieved using independent component analysis (ICA) and k-means clustering
Nuclei, cytoplasm; gland secretions; stroma of the lamina propria
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Stage II: Feature Extraction• Four binary images are extracted
from each segmented image
• Two sets of features are calculated: morphological and co-occurrence matrix features:
• Morphological Features:– These describe the shape, size,
orientation and other attributes of the cellular components
– These features are calculated on patches (blocks) of the segmented image
• Co-Occurrence Features:– These describe the textural
properties of a given neighborhood
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Morphological Features• Morphological features describe the shape and texture of the image
• Feature vector consists of five to ten morphological features
• Discriminant morphological features are:– Euler Number : number of contiguous parts– Convex Area : number of pixels in convex image– Extent : the proportion of pixels in the bounding box– Solidity : the proportion of pixels in the convex hull – Area : the actual number of pixels in the patch– EquivDiameter : the diameter of a circle with the same area as of the
patch
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Co-occurrence Features• The co-occurrence matrix is constructed by
analysing the gray levels of neighboring pixels• The (i,j)th element of a co-occurrence matrix for a
particular angle and distance is given by the joint conditional pdf:
• Three attributes used are:
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Stage III : Classification• Subspace Projection methods
– Principle Component Analysis (PCA)– Linear Discriminant Analysis (LDA)– Kernel PCA– Kernel LDA
• Support Vector Machines (SVM)– Polynomial kernel– Gaussian kernel
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Principal Component Analysis (PCA)
• Eigenvectors of the data in the embedding space can be used to detect directions of maximum variance.
• The principal components can be computed
by solving the eigenvalue problem:
• The coefficients of projection along a few top
principal directions can be used as features
• Nearest-neighbor classifier is used for
assigning label to a biopsy sample
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Linear Discriminant Analysis (LDA)• Limitations of the PCA
• As opposed to PCA, which maximises the overall scatter, LDA maximises the ratio of between-class scatter Sb to within-class scatter Sw
• The wi can be computed by solving the generalised eigenvalue problem:
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Linear Boundary Assumption• In most real-world problems, separating
boundaries are not necessarily linear! Consider, for instance, the following example:
Will a linear classifier work?
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The Kernel Trick
• Kernel machines (eg, SVMs) transform non-linear decision boundaries to linear ones in higher dimensional feature space
• Two dimensional features (let us say) are mapped to a three dimensional feature space through a non-linear transform
• Non-linear ellipsoidal decision boundary is replaced to linear boundary in higher dimensional space
• The trick is to replace dot products in F with a kernel function in the input space R so that the non-linear mapping is performed implicitly in R
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SVM Kernel Functions• A few commonly used kernel functions are:
• Classifier’s performance highly sensitive to parameter values
• Best kernel parameter values are searched
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Experimentation• Two sets of Experiments: Mixed testing and Leave one out (LOO)
• For mixed testing:– 4096 patches (blocks) per image of 16x16 dimensions per patch– Morphological features– Training set contains one quarter of the patches while remaining three
quarters make the test set – PCA and modular LDA are used in mixed testing
• Leave one out testing is done on gray level co-occurrence features– 16x16 patches– Support Vector Machines (polynomial kernel and gaussian kernel are
used)– Kernel parameters are optimized
• Classification label is assigned to a slide according to the class of the majority of the patches
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Experimental Results
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Experimental Results
AUCH of the ROC curve for LDA goes up to 0.92 for 5 features.
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Conclusions and Future Work
• Conclusions– Tissue segmentation affects the performance– Implementation of LDA saves the computational cost
and the performance achieved by it is encouraging– Gaussian kernel SVM gives no false alarm
• Future Work– More effective segmentation– Combination of classifiers
– Shape modelling of nuclei glands
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Acknowledgements
• Prof David Rimm, Department of Pathology, Yale University School of Medicine (USA)
• Prof Gustave Davis, Department of Pathology, Yale University School of Medicine (USA)
• Prof Ronald Coifman, Department of Applied Mathematics, Yale University (USA)
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Thanks for your attention
Any Questions?