Sinan Batman

Design and analysis of fuzzy morphological algorithms for image processing

A general paradigm for lifting binary morphological algorithms to fuzzy algorithms is employed to construct fuzzy versions of classical binary morphological operations. The lifting procedure is based upon an epistemological interpretation of both image and filter fuzzification. Algorithms are designed via the paradigm for various fuzzifications and their performances are analyzed to provide insight into the kind of liftings that produce suitable results. Algorithms are discussed for three image processing tasks: shape detection, edge detection, and clutter removal. Detailed analyses are given for the effect of noise and its mitigation owing to fuzzy approaches. It is demonstrated how the fuzzy hit-or-miss transform can be used in conjunction with a decision procedure to achieve word recognition.

Size distributions for multivariate morphological granulometries: texture classification and statistical properties

As introduced by Matheron (1975), granulometries depend on a single sizing parameter for each structuring element forming the filter. Size distributions resulting from these granulometries have been used to classify texture by using as features the moments of the resulting pattern spectra. The concept of granulometry is extended in such a way that each structuring element has its own sizing parameter and the size dis- tribution is multivariate. Whereas with univariate granulometries the nor- malized size distribution (pattern spectrum) is easily shown to be a prob- ability distribution function, this proposition is more difficult to show for multivariate granulometries. Its demonstration is the main theoretical re- sult. The classical single-structuring-element granulometries appear as marginal size distributions and the single-parameter multiple-structuring- element granulometries result from setting all parameters equal in a mul- tivariate granulometry. Because of the greatly expanded freedom in choosing parameters, multivariate granulometries can discriminate tex- tures that are indistinguishable using single-parameter granulometries. Texture classification proceeds by taking either the Walsh or moment transform of the multivariate pattern spectrum, obtaining a reduced fea- ture set by applying the Karhunen-Loeve transform to the Walsh or mo- ment features, and classifying textures via a Gaussian maximum- likelihood classifier. For the disjoint multiprimitive random set model, multivariate granulometric moments are represented in terms of sizing- distribution moments and shown to be asymptotically normal. Formulas are given for their asymptotic mean and variance.

Unsupervised iterative detection of land mines in highly cluttered environments

An unsupervised iterative scheme is proposed for land mine detection in heavily cluttered scenes. This scheme is based on iterating hybrid multispectral filters that consist of a decorrelating linear transform coupled with a nonlinear morphological detector. Detections extracted from the first pass are used to improve results in subsequent iterations. The procedure stops after a predetermined number of iterations. The proposed scheme addresses several weaknesses associated with previous adaptations of morphological approaches to land mine detection. Improvement in detection performance, robustness with respect to clutter inhomogeneities, a completely unsupervised operation, and computational efficiency are the main highlights of the method. Experimental results reveal excellent performance.

Unsupervised morphological granulometric texture segmentation of digital mammograms

Segmentation via morphological granulometric features is based on fitting structuring elements into image topography from below and above. Each structuring element captures a specific texture content. This paper applies granulometric segmentation to digitized mammograms in an unsupervised framework. Granulometries based on a number of flat and nonflat structuring elements are computed, local size distributions are tabulated at each pixel, granulometric-moment features are derived from these size distributions to produce a feature vector at each pixel, the Karhunen–Loeve transform is applied for feature reduction, and Voronoi-based clustering is performed on the reduced Karhunen–Loeve feature set. Various algorithmic choices are considered, including window size and shape, number of clusters, and type of structuring elements. The algorithm is applied using only granulometric texture features, using gray-scale intensity along with the texture features, and on a compressed mammogram. Segmentation results are clinically evaluated to determine the algorithm structure that best accords to an expert radiologist’s view of a set of mammograms.

Heterogeneous morphological granulometries

Abstract The most basic class of binary granulometries is composed of unions of openings by structuring elements that are homogeneously scaled by a single parameter. These univariate granulometries have previously been extended to multivariate granulometries in which each structuring element is scaled by an individual parameter. This paper introduces the more general class of filters in which each structuring element is scaled by a function of its sizing parameter, the result being multivariate heterogeneous granulometries. Owing to computational considerations, of particular importance are the univariate heterogeneous granulometries, for which scaling is by functions of a single variable. The basic morphological properties of heterogeneous granulometries are given, analytic and geometric relationships between multivariate and univariate heterogeneous pattern spectra are explored, and application to texture classification is discussed. The homogeneous granulometric mixing theory, both the representation of granulometric moments and the asymptotic theory concerning the distributions of granulometric moments, is extended to heterogeneous scaling.

Segmentation of mammograms into distinct morphological texture regions

Presents a comprehensive discussion on the segmentation of mammograms using morphological texture features. These features are derived from morphological granulometries with various structuring elements. Each structuring element captures a specific texture content. The segmentation is carried out in an unsupervised manner by applying the KL (Karhunen-Loeve) transform feature reduction and Voronoi clustering on the extracted morphological texture features. The evaluation of the segmentation outcome by a trained radiologist is provided.

Clustering analysis for gene expression data

The recent development of cDNA microarray allows ready access to large amount gene expression patterns for many genetic materials. Gene expression of tissue samples can be quantitatively analyzed by hybridizing fluor-tagged mRNA to targets on a cDNA microarray. Ratios of average expression level arising from co-hybridized normal and pathological samples are extracted via image segmentation, thus the gene expression pattern are obtained. The gene expression in a given biological process may provide a fingerprint of the sample development, or response to certain treatment. We propose a K-mean based algorithm in which gene expression levels fluctuate in parallel will be clustered together. The resulting cluster suggests some functional relationships between genes, and some known genes belongs to a unique functional classes shall provide indication for unknown genes in the same clusters.

Robust morphological detection of sea mines in side-scan sonar images

The automated detection of sea mines remains an increasingly important humanitarian and military task. In recent years, research efforts have been concentrated on developing algorithms that detect mines in complicated littoral environments. Acquired high-resolution side-looking sonar images are often heavily infested with artifacts from natural and man-made clutter. As a consequence, automated detection algorithms, designed for high probability of detection, suffer from a large number of false alarms. To remedy this situation, sophisticated feature extraction and pattern classification techniques are commonly used after detection. In this paper, we propose a nonlinear detection algorithm, based on mathematical morphology, for the robust detection of sea mines. The proposed algorithm is fast and performs well under a variety of sonar modalities and operating conditions. Our approach is based on enhancing potential mine signatures by extracting highlight peaks of appropriate shape and size and by boosting the amplitude of the peaks associated with a potential shadow prior to detection. Signal amplitudes over highlight peaks are extracted using a flat morphological top-hat by reconstruction operator. The contribution of a potential shadow to the detection image is incorporated by increasing the associated highlight amplitude by an amount proportional to the relative contrast between highlight and shadow signatures. The detection image is then thresholded at mid-gray level. The largest p targets from the resulting binary image are then labelled as potential targets. The number of false alarms in the detection image is subsequently reduced to an acceptable level by a feature extraction and classification module. The detection algorithm is tested on two side-scan sonar databases provided by the Coastal Systems Station, Panama City, Florida: SONAR-0 and SONAR-3.

Morphological granulometric estimation of random patterns in the context of parameterized random sets

Abstract Morphological features are used to estimate the state of a random pattern (set) governed by a multivariate probability distribution. The feature vector is composed of granulometric moments and pattern estimation involves feature-based estimation of the parameter vector governing the random set. Under such circumstances, the joint density of the features and parameters is a generalized function concentrated on a solution manifold and estimation is determined by the conditional density of the parameters given an observed feature vector. The paper explains the manner in which the joint probability mass of the parameters and features is distributed and the way the conditional densities give rise to optimal estimators according to the distribution of probability mass, whether constrained or not to the solution manifold. The estimation theory is applied using analytic representation of linear granulometric moments. The effects of random perturbations in the shape-parameter vector is discussed, and the theory is applied to random sets composed of disjoint random shapes. The generalized density framework provides a proper mathematical context for pattern estimation and gives insight, via the distribution of mass on solution manifolds, to the manner in which morphological probes discriminate random sets relative to their distributions, and the manner in which the use of additional probes can be beneficial for better estimation.

Digital measurement of gene expression in a cDNA microarray

Gene expression can be quantitatively analyzed by hybridizing fluor-tagged mRNA to targets on a cDNA micro- array. Comparison of expression levels arising from co- hybridized samples is achieved by taking ratios of average expression levels for individual genes. The present paper concerns image processing to automatically segment digitized micro-arrays and measure median gene expression levees across cDNA target sites. The main difficulty arises from determination of the target site when signal intensity is low. Segmentation must be accomplished for target sites that can possess highly unstable geometry and consist of a relatively small number of pixels. Segmentation must also be computationally efficient. The present paper proposes a nonparametric statistical method that separates target site from local background using the Mann-Whitney test.