Sándor M. Szilágyi

A modified fuzzy C-means algorithm for MR brain image segmentation

Automated brain MR image segmentation is a challenging pattern recognition problem that received significant attention lately. The most popular solutions involve fuzzy c-means (FCM) or similar clustering mechanisms. Several improvements have been made to the standard FCM algorithm, in order to reduce its sensitivity to Gaussian, impulse, and intensity non-uniformity noises. This paper presents a modified FCM-based method that targets accurate and fast segmentation in case of mixed noises. The proposed method extracts a scalar feature value from the neighborhood of each pixel, using a context dependent filtering technique that deals with both spatial and gray level distances. These features are clustered afterwards by the histogram-based approach of the enhanced FCM algorithm. Results were evaluated based on synthetic phantoms and real MR images. Test experiments revealed that the proposed method provides better results compared to other reported FCMbased techniques. The achieved segmentation and the obtained fuzzy membership values represent excellent support for deformable contour model based cortical surface reconstruction methods.

Intensity inhomogeneity compensation and segmentation of MR brain images using hybrid c-means clustering models

Abstract Medical image segmentation and registration problems based on magnetic resonance imaging are frequently disturbed by the intensity inhomogeneity or intensity non-uniformity (INU) of the observed images. Most compensation techniques have serious difficulties at high amplitudes of INU. This study proposes a multiple stage hybrid c -means clustering approach to the estimation and compensation of INU, by modeling it as a slowly varying additive or multiplicative noise. The slowly varying behavior of the estimated inhomogeneity field is assured by a context sensitive smoothing filter based on a morphological criterion. The qualitative and quantitative evaluation using 2-D synthetic phantoms and real T1-weighted MR images place the proposed methodology among the most accurate segmentation techniques in the presence of high-magnitude inhomogeneity.

Generalization rules for the suppressed fuzzy c-means clustering algorithm

Intending to achieve an algorithm characterized by the quick convergence of hard c-means (HCM) and finer partitions of fuzzy c-means (FCM), suppressed fuzzy c-means (s-FCM) clustering was designed to augment the gap between high and low values of the fuzzy membership functions. Suppression is produced via modifying the FCM iteration by creating a competition among clusters: for each input vector, lower degrees of membership are proportionally reduced, being multiplied by a previously set constant suppression rate, while the largest fuzzy membership grows to maintain the probabilistic constraint. Even though so far it was not treated as an optimal algorithm, it was employed in a series of applications, and reported to be accurate and efficient in various clustering problems. In this paper we introduce some generalized formulations of the suppression rule, leading to an infinite number of new clustering algorithms. Further on, we identify the close relation between s-FCM clustering models and the so-called FCM algorithm with generalized improved partition (GIFP-FCM). Finally we reveal the constraints under which the generalized s-FCM clustering models minimize the objective function of GIFP-FCM, allowing us to call our suppressed clustering models optimal. Based on a large amount of numerical tests performed in multidimensional environment, several generalized forms of suppression proved to give more accurate partitions than earlier solutions, needing significantly less iterations than the conventional FCM.

A Modified FCM Algorithm for Fast Segmentation of Brain MR Images

Automated brain MR image segmentation is a challenging problem and received significant attention lately. Several improvements have been made to the standard fuzzy c-means (FCM) algorithm, in order to reduce its sensitivity to Gaussian, impulse, and intensity non-uniformity noises. In this paper we present a modified FCM algorithm, which aims accurate segmentation in case of mixed noises, and performs at a high processing speed. The proposed method extracts a scalar feature value from the neighborhood of each pixel, using a filtering technique that deals with both spatial and gray level distances. These features are classified afterwards using the histogram-based approach of the enhanced FCM classifier. The experiments using synthetic phantoms and real MR images show, that the proposed method provides better results compared to other reported FCM-based techniques.

A patient specific electro-mechanical model of the heart

This paper presents a patient specific deformable heart model that involves the known electrical and mechanical properties of the cardiac cells and tissue. The whole heart model comprises ten Tusschers ventricular and Nygrens atrial cell models, the anatomical and electrophysiological model descriptions of the atria (introduced by Harrild et al.) and ventricle (given by Winslow et al.), and the mechanical model of the periodical cardiac contraction and resting phenomena proposed by Moireau et al. During the propagation of the depolarization wave, the kinetic, compositional and rotational anisotropy is handled by the tissue, organ and torso model. The applied patient specific parameters were determined by an evolutionary computation method. An intensive parameter reduction was performed using the abstract formulation of the searching space. This patient specific parameter representation enables the adjustment of deformable model parameters in real-time. The validation process was performed using simultaneously measured ECG and ultrasound image records that were compared with simulated signals and shapes using an abstract, parameterized evaluation criterion.

A fast hierarchical clustering algorithm for large-scale protein sequence data sets

TRIBE-MCL is a Markov clustering algorithm that operates on a graph built from pairwise similarity information of the input data. Edge weights stored in the stochastic similarity matrix are alternately fed to the two main operations, inflation and expansion, and are normalized in each main loop to maintain the probabilistic constraint. In this paper we propose an efficient implementation of the TRIBE-MCL clustering algorithm, suitable for fast and accurate grouping of protein sequences. A modified sparse matrix structure is introduced that can efficiently handle most operations of the main loop. Taking advantage of the symmetry of the similarity matrix, a fast matrix squaring formula is also introduced to facilitate the time consuming expansion. The proposed algorithm was tested on protein sequence databases like SCOP95. In terms of efficiency, the proposed solution improves execution speed by two orders of magnitude, compared to recently published efficient solutions, reducing the total runtime well below 1min in the case of the 11,944proteins of SCOP95. This improvement in computation time is reached without losing anything from the partition quality. Convergence is generally reached in approximately 50 iterations. The efficient execution enabled us to perform a thorough evaluation of classification results and to formulate recommendations regarding the choice of the algorithm׳s parameter values.

A modified Markov clustering approach to unsupervised classification of protein sequences

In this paper we propose a modified Markov clustering algorithm for efficient and accurate clustering of large protein sequence databases, based on previously evaluated sequence similarity criteria. The proposed modification consists in an exponentially decreasing inflation rate, which aims at helping the quick creation of the hard structure of clusters by using a strong inflation in the beginning, and at producing fine partitions with a weaker inflation thereafter. The algorithm, which was tested and validated using the whole SCOP95 database, or randomly selected 10-50% sections, generally converges within 12-14 iteration cycles and provides clusters of high quality. Furthermore, a novel generalized formula for the inflation operation is given, and an efficient matrix symmetrization technique is presented, in order to improve the partition quality with relatively low amount of extra computations. Finally, an extra speedup is achieved via excluding isolated proteins from further processing. The proposed method performs better than previous solutions, from the point of view of partition quality, and computational load as well.

Application of hybrid c-means clustering models in inhomogeneity compensation and MR brain image segmentation

Intensity inhomogeneity or intensity non-uniformity (INU) is an undesired phenomenon that represents the main obstacle for MR image segmentation and registration methods. Various techniques have been proposed to eliminate or compensate the INU, most of which are embedded into clustering algorithms. This paper proposes a hybrid c-means clustering approach to replace the FCM algorithm found in several existing solutions. The novel clustering model is assisted by a pre-filtering technique for Gaussian and impulse noise elimination, and a smoothening filter that helps the c-means algorithm at the estimation of inhomogeneity as a slowly varying additive or multiplicative noise. The slow variance of the estimated INU is assured by a smoothening filter that performs a context dependent averaging, based on a morphological criterion. The experiments using 2-D synthetic phantoms and real MR images show that the proposed method provides more accurate and more efficient segmentation than the FCM based approach. The produced segmentation and fuzzy membership values can serve as excellent support for 3-D registration and segmentation techniques.

Efficient feature extraction for fast segmentation of MR brain images

Automated brain MR image segmentation is a challenging problem and received significant attention lately. Various techniques have been proposed, several improvements have been made to the standard fuzzy c-means (FCM) algorithm, in order to reduce its sensitivity to Gaussian, impulse, and intensity non-uniformity noises. In this paper we present a modified FCM algorithm, which aims at accurate segmentation in case of mixed noises, and performs at a high processing speed. As a first step, a scalar feature value is extracted from the neighborhood of each pixel, using a filtering technique that deals with both spatial and gray level distances. These features are clustered afterwards using the histogram-based approach of the enhanced FCM algorithm. The experiments using 2-D synthetic phantoms and real MR images show, that the proposed method provides better results compared to other reported FCM-based techniques. The produced segmentation and fuzzy membership values can serve as excellent support for level set based cortical surface reconstruction techniques.

Volumetric analysis of the heart using echocardiography

This paper presents a volumetric cardiac analysis and movement reconstruction algorithm from echocardiographic image sequences and electrocardiography (ECG) records. The method consists of two-dimensional (2-D) echocardiogram transformation, shape detection, heart wall movement identification, volumetric analysis and 4-D model construction. Although the semi-periodic behavior of the ECG and the breath caused heart rate variance disturbs spatial and temporal reconstruction, the presented algorithm is able to overcome these problems in most cases for normal and ventricular beats. The obtained model provides a tool to investigate volumetric variance of the heart and the phenomenon of normal and abnormal heart beating that makes possible to explore continuously the hearts inner structure.