Duncan Fyfe Gillies

A maximum uncertainty LDA-based approach for limited sample size problems - with application to face recognition

A critical issue of applying Linear Discriminant Analysis (LDA) is both the singularity and instability of the within-class scatter matrix. In practice, particularly in image recognition applications such as face recognition, there are often a large number of pixels or pre-processed features available, but the total number of training patterns is limited and commonly less than the dimension of the feature space. In this study, a new LDA-based method is proposed. It is based on a straightforward stabilisation approach for the within-class scatter matrix. In order to evaluate its effectiveness, experiments on face recognition using the well-known ORL and FERET face databases were carried out and compared with other LDA-based methods. The classification results indicate that our method improves the LDA classification performance when the within-class scatter matrix is not only singular but also poorly estimated, with or without a Principal Component Analysis intermediate step and using less linear discriminant features. Since statistical discrimination methods are suitable not only for classification but also for characterisation of differences between groups of patterns, further experiments were carried out in order to extend the new LDA-based method to visually analyse the most discriminating hyper-plane separating two populations. The additional results based on frontal face images indicate that the new LDA-based mapping provides an intuitive interpretation of the two-group classification tasks performed, highlighting the group differences captured by the multivariate statistical approach proposed.

A review of feature selection and feature extraction methods applied on microarray data.

We summarise various ways of performing dimensionality reduction on high-dimensional microarray data. Many different feature selection and feature extraction methods exist and they are being widely used. All these methods aim to remove redundant and irrelevant features so that classification of new instances will be more accurate. A popular source of data is microarrays, a biological platform for gathering gene expressions. Analysing microarrays can be difficult due to the size of the data they provide. In addition the complicated relations among the different genes make analysis more difficult and removing excess features can improve the quality of the results. We present some of the most popular methods for selecting significant features and provide a comparison between them. Their advantages and disadvantages are outlined in order to provide a clearer idea of when to use each one of them for saving computational time and resources.

A new covariance estimate for Bayesian classifiers in biometric recognition

In many biometric pattern-recognition problems, the number of training examples per class is limited, and consequently the sample group covariance matrices often used in parametric and nonparametric Bayesian classifiers are poorly estimated or singular. Thus, a considerable amount of effort has been devoted to the design of other covariance estimators, for use in limited-sample and high-dimensional classification problems. In this paper, a new covariance estimate, called the maximum entropy covariance selection (MECS) method, is proposed. It is based on combining covariance matrices under the principle of maximum uncertainty. In order to evaluate the MECS effectiveness in biometric problems, experiments on face, facial expression, and fingerprint classification were carried out and compared with popular covariance estimates, including the regularized discriminant analysis and leave-one-out covariance for the parametric classifier, and the Van Ness and Toeplitz covariance estimates for the nonparametric classifier. The results show that, in image recognition applications whenever the sample group covariance matrices are poorly estimated or ill posed, the MECS method is faster and usually more accurate than the aforementioned approaches in both parametric and nonparametric Bayesian classifiers.

Vision based navigation system for an endoscope

A vision based navigation system to guide an endoscope inside a human colon has been designed and tested. It uses low level vision techniques to extract two types of navigational landmarks, dark regions and curved contours. Dark regions correspond to the distant inner space of the colon, called the lumen. The curved contours represent occlusions due to the inner colon muscles. A hierarchical search space and environment representation, called the QL-tree, was developed to integrate the visual features and implement the navigation system. It uses multiple quadtrees which are linked at all hierarchical levels. A multiprocessor system was employed to achieve real-time performance. The endoscope navigation system has been used successfully in artificial colon models.

Motion Analysis in the Assessment of Surgical Skill

Abstract Manual skill is now widely recognised as an important aspect of training in surgery. However, measurement of the skill of a surgeon has in the past been rather subjective in nature, relying on the judgement of experts in the analysis of videotapes. Objective measurements can be made by analysing the velocities of a surgeons hands during a procedure. In particular, we have found that the number of movements made during a typical procedure will decrease as the surgeons skill increases. Velocity traces display purposeful movements corrupted by uncorrelated noise from sources such as hand tremor and measurement artefacts. However, we have found that it is possible to filter the noise effectively. Furthermore, we have shown that the skill measurement obtained by counting movements is highly robust to over or under filtering.

Using a Maximum Uncertainty LDA-Based Approach to Classify and Analyse MR Brain Images

Multivariate statistical learning techniques that analyse all voxels simultaneously have been used to classify and describe MR brain images. Most of these techniques have overcome the difficulty of dealing with the inherent high dimensionality of 3D brain image data by using pre-processed segmented images or a number of specific features. However, an intuitive way of mapping the classification results back into the original image domain for further interpretation remains challenging. In this paper, we introduce the idea of using Principal Components Analysis (PCA) plus the maximum uncertainty Linear Discriminant Analysis (LDA) based approach to classify and analyse magnetic resonance (MR) images of the brain. It avoids the computation costs inherent in commonly used optimisation processes, resulting in a simple and efficient implementation for the maximisation and interpretation of the Fisher’s classification results. In order to demonstrate the effectiveness of the approach, we have used two MR brain data sets. The first contains images of 17 schizophrenic patients and 5 controls, and the second is composed of brain images of 12 preterm infants at term equivalent age and 12 term controls. The results indicate that the two-stage linear classifier not only makes clear the statistical differences between the control and patient samples, but also provides a simple method of analysing the results for further medical research.

A Maximum Uncertainty LDA-Based Approach for Limited Sample Size Problems — With Application to Face Recognition

A critical issue of applying Linear Discriminant Analysis (LDA) is both the singularity and instability of the within-class scatter matrix. In practice, particularly in image recognition applications such as face recognition, there are often a large number of pixels or pre-processed features available, but the total number of training patterns is limited and commonly less than the dimension of the feature space. In this paper, a maximum uncertainty LDA-based method is proposed. It is based on a straightforward stabilisation approach for the within-class scatter matrix. In order to evaluate its effectiveness, experiments on face recognition using the well-known ORL and FERET face databases were carried out and compared with other LDA-based methods. The results indicate that our method im-proves the LDA classification performance when the within-class scatter matrix is not only singular but also poorly estimated, with or without a Principal Component Analysis intermediate step and using less linear discriminant features.

Multivariate Statistical Differences of MRI Samples of the Human Brain

Abstract Multivariate statistical discrimination methods are suitable not only for classification but also for characterization of differences between a reference group of patterns and the population under investigation. In the last years, statistical methods have been proposed to classify and analyse morphological and anatomical structures of medical images. Most of these techniques work in high-dimensional spaces of particular features such as shapes or statistical parametric maps and have overcome the difficulty of dealing with the inherent high dimensionality of medical images by analysing segmented structures individually or performing hypothesis tests on each feature separately. In this paper, we present a general multivariate linear framework that addresses the small sample size problem in medical images. The goal is to identify and analyse the most discriminating hyper-plane separating two populations using all the intensity features simultaneously rather than segmented versions of the data separately or feature-by-feature. To demonstrate the performance of the multivariate linear framework we carry out experimental results on artificially generated data set and on a real medical data composed of magnetic resonance images (MRI) of subjects suffering from Alzheimer’s disease (AD) compared to an elderly healthy control group. To our knowledge this is the first multivariate statistical analysis of the human brain in AD that uses the whole features (texture + shapes) simultaneously rather than segmented version of the images. The conceptual and mathematical simplicity of the approach involves the same operations irrespective of the complexity of the experiment or nature of the spatially normalized data, giving multivariate results that are plausible and easy to interpret by the clinicians.

Extracting contours by perceptual grouping

Abstract A new contour extraction method is described in this paper. It is based on organization of the image data using perceptual grouping rules, and is therefore largely domain independent. The first step is to form an intermediate line segment representation of the contours by grouping edge points in parallel and at different resolutions. The main feature of the line segment extraction process is the identification, by perceptual criteria, of weak but significant edge points for participation in the grouping process. In the second stage the line segments are grouped into contours, again on the basis of perceptual criteria. This grouping stage is carried out hierarchically using a pyramid structure. In both cases, the use of perceptual grouping allows the filtering of noisy edges and line segments regardless of their strength.

Using Fourier information for the detection of the lumen in endoscope images

An endoscope is a viewing instrument used for examining the inside surfaces of the human body for the purpose of diagnosis and minor surgical treatment. To date, only highly skilled specialists have been able to perform endoscopic investigations. We are proposing to rectify this situation by using computer vision to provide automatic guidance and advice during colonoscopy. In order to navigate an endoscope automatically through the colon, we need to process colon images to extract information, in particular, the position of the lumen (the point to which the endoscope should be directed) with respect to the centre of the image. To achieve this, we have devised and implemented a new Fourier Domain method. Since real time performance is required, we have devised simplified mathematical equations that effectively reduce a 2D FFT (Fast Fourier Transform) into two 1D FFTs. We found it was necessary to use a tapering window to minimize the edge discontinuity problem that leads to mis-classification. The results that we have obtained demonstrate that the method is highly effective in identifying the lumen position.<<ETX>>