Y. Attikiouzel

The paradoxical success of fuzzy logic

Fuzzy logic methods have been used successfully in many real-world applications, but the foundations of fuzzy logic remain under attack. Taken together, these two facts constitute a paradox. A second paradox is that almost all of the successful fuzzy logic applications are embedded controllers, while most of the theoretical papers on fuzzy methods deal with knowledge representation and reasoning. I hope to resolve these paradoxes by identifying which aspects of fuzzy logic render it useful in practice, and which aspects are inessential. My conclusions are based on a mathematical result, on a survey of literature on the use of fuzzy logic in heuristic control and in expert systems, and on practical experience in developing expert systems.<<ETX>>

Multiple-prototype classifier design

Five methods that generate multiple prototypes from labeled data are reviewed. Then we introduce a new sixth approach, which is a modification of Changs (1974) method. We compare the six methods with two standard classifier designs: the 1-nearest prototype (1-np) and 1-nearest neighbor (1-nn) rules. The standard of comparison is the resubstitution error rate; the data used are the Iris data. Our modified Changs method produces the best consistent (zero-error) design. One of the competitive learning models produces the best minimal prototypes design (five prototypes that yield three resubstitution errors).

A geometric approach to cluster validity for normal mixtures

Abstract We study indices for choosing the correct number of components in a mixture of normal distributions. Previous studies have been confined to indices based wholly on probabilistic models. Viewing mixture decomposition as probabilistic clustering (where the emphasis is on partitioning for geometric substructure) as opposed to parametric estimation enables us to introduce both fuzzy and crisp measures of cluster validity for this problem. We presume the underlying samples to be unlabeled, and use the expectation-maximization (EM) algorithm to find clusters in the data. We test 16 probabilistic, 3 fuzzy and 4 crisp indices on 12 data sets that are samples from bivariate normal mixtures having either 3 or 6 components. Over three run averages based on different initializations of EM, 10 of the 23 indices tested for choosing the right number of mixture components were correct in at least 9 of the 12 trials. Among these were the fuzzy index of Xie-Beni, the crisp Davies-Bouldin index, and two crisp indices that are recent generalizations of Dunn’s index.

A simple method for automatically locating the nipple on mammograms

This paper outlines a simple, fast, and accurate method for automatically locating the nipple on digitized mammograms that have been segmented to reveal the skin-air interface. If the average gradient of the intensity is computed in the direction normal to the interface and directed inside the breast, it is found that there is a sudden and distinct change in this parameter close to the nipple. A nipple in profile is located between two successive maxima of this parameter; otherwise, it is near the global maximum. Specifically, the nipple is located midway between a successive maximum and minimum of the derivative of the average intensity gradient; these being local turning points for a nipple in profile and global otherwise. The method has been tested on 24 images, including both oblique and cranio-caudal views, from two digital mammogram databases. For 23 of the images (96%), the rms error was less than 1 mm at image resolutions of 400 /spl mu/m and 420 /spl mu/m per pixel. Because of its simplicity, and because it is based both on the observed behavior of mammographic tissue intensities and on geometry, this method has the potential to become a generic method for locating the nipple on mammograms.

A probabilistic neural network based image segmentation network for magnetic resonance images

A network structure for segmenting magnetic resonance medical images is proposed. The incorporation of a probabilistic neural network structure into the segmentation process allows decisions regarding the characterization of each pixel to be made in a probabilistic manner, thus reducing the effect of an incorrect decision early in the process on the final segmentation result. The probabilistic neural network facilitates the generation of likelihood estimates for use in an iterative segmentation process, which was shown to produce good segmentation results on real magnetic resonance images.<<ETX>>

Automatic pectoral muscle segmentation on mammograms by straight line estimation and cliff detection

Mammograms, which are X-ray images of the female breast, are used widely by radiologists to screen for breast cancer. The first stage of any computerized analysis of the digitised mammogram is to divide the image into anatomically distinct regions. The pectoral muscle is one of these regions and it appears on mediolateral oblique views of mammograms. In this paper, the rationale and algorithms for fully automatic, two-part segmentation of the pectoral muscle are presented. The algorithm consists of (a) estimation of the muscle edge by a straight line; and (b) refinement of the detected edge by surface smoothing and edge detection in a restricted neighbourhood derived from the first estimate.

Gross segmentation of mammograms using a polynomial model

The breast and background on a mammogram form complementary, connected sets. Generally, the intensities comprising the background are spatially continuous, low in value and lie within a closed interval. The background may therefore be approximated by a polynomial in x and y on the basis of the Weierstrass approximation theorem. The authors include the whole background and a small portion of the breast in the region being modelled. The modelled background is subtracted from the original image, the resulting image thresholded, and the largest low intensity region taken to be the background. Connected regions are identified, labelled and merged. The background is floodfilled, and inclusions removed from the object, to yield a breast-background binary image. The method has been tested on 58 mammograms of two views from two digital mammogram databases. With one exception, it performs well and yields a skin-air interface with sufficient fidelity to preserve a nipple in profile.

Predicting axillary lymph node metastases in breast carcinoma patients.

Routine axillary dissection is primarily used as a means of assessing prognosis to establish appropriate treatment plans for patients with primary breast carcinoma. However, axillary dissection offers no therapeutic benefit to node negative patients and patients may incur unnecessary morbidity, including mild to severe impairment of arm motion and lymphedema, as a result. This paper outlines a method of evaluating the probability of harbouring lymph node metastases at the time of initial surgery by assessment of tumour based parameters, in order to provide an objective basis for further selection of patients for treatment or investigation. The novel aspect of this study is the use of Maximum Entropy Estimation (MEE) to construct probabilistic models of the relationship between the risk factors and the outcome. Two hundred and seventeen patients with invasive breast carcinoma were studied. Surgical treatment included axillary clearance in all cases, so that the pathologic status of the nodes was known. Tumour size was found to be significantly correlated (P < 0.001) to the axillary lymph node status in the multivariate analysis with age (P = 0.089) and vascular invasion (P = 0.08) marginally correlated. Using the multivariate model constructed, 38 patients were predicted to have risk of nodal metastases lower than 20%, of these only 4 (10%) patients had lymph node metastases. A comparison with the Multivariate Logistic Regression (MLR) was carried out. It was found that the predictive quality of the MEE model was better than that of the MLR model. In view of the small sample size, further verification of this model is required in assessing its practical application to a larger population.

A modified probabilistic neural network (PNN) for nonlinear time series analysis

A modified PNN (probabilistic neural network) is proposed that can be used for nonlinear time series analysis without loss of the advantages offered by D.F. Spechts PNN architecture (1988, 1990). It is shown how the Gaussian radial basis function, expressed as a Parzen probability density function estimator, can be used to estimate and implement nonlinear mappings, applied to time series data. The performance of this modified PNN is demonstrated by showing its effectiveness in smoothing a sinusoidal signal which has been compressed in amplitude and then corrupted with wideband non-Gaussian noise. The network is also compared with the multipass learning backpropagation network and the relative merits of the proposed modified PNN are discussed.<<ETX>>

Machine grading and blemish detection in apples

Five classifiers including the K-means, fuzzy c-means, K-nearest neighbour, multi-layer perceptron neural network and probabilistic neural network classifiers are compared for application to colour grade classification and detection of bruising of granny smith apples. A number of suitable discriminate features are determined heuristically for the categorisation of four classes including: high grade fruit, high grade fruit with bruising or blemishes, off-grade fruit, and off-grade fruit with bruising or blemishes. Robust features based on intensity statistics are extracted from enhanced monochrome images produced by special transformation from original RGB images. The best of the five classifiers using the optimal feature set, is shown to outperform human graders viewing the same images.