Dynamically learned PSO based neighborhood influenced fuzzy c-means for pre-treatment and post-treatment organ segmentation from CT images

Highlights

• An unsupervised model is designed for segmentation of organ from pre-treatment and posttreatment CT images of same patient.

• The main objective function is reformulated as a single variable function while taking the advantages of neighborhood influence on image pixels, for the easy integration with an advanced heuristic technique namely Dynamically Learned Particle Swarm Optimization (DLPSO).

• This model is specially designed for the real medical environment where despite the limited amount of raw data, an overall outstanding performance in terms of accuracy and convergence can be ensured.

Abstract

Background and Objective

The accurate segmentation of pre-treatment and post-treatment organs is always perceived as a challenging task in medical image analysis field. Especially, in those situations where the amount of data set is limited, the researchers are compelled to design unsupervised model for segmentation. In this paper, we propose a novel dynamically learned particle swarm optimization based neighborhood influenced fuzzy c-means (DLPSO-NIFCM) clustering (unsupervised learning model) for solving pre-treatment and post-treatment organs segmentation problems. The proposed segmentation technique has been successfully applied to segment the liver parts from the Computed Tomography (CT) images of abdomen and also the lung parenchyma from the lungs CT images.

Methodology

In the proposed method, we formulate a primary convex objective function by considering the membership value of a pixel as well as the membership of its other neighboring pixels. Then we apply a new algebraic transformation on the primary objective function to design a new and more suitable objective function without losing convexity of the primary objective function. This new objective function is compatible for hybridization with any heuristic search technique in true sense. In this work, we propose a dynamically learned PSO to obtain the initial cluster centroids from the final objective function. Finally, we use a graph-based isolation mechanism for refining the segmentation results.

Results and Conclusion

This hybrid method, along with the restructured single variable objective function of the distance, leads to accurate clustering results with relatively lesser converging time as compared to the state-of-the-art methods. The segmentation results, obtained through several experiments with real CT images, are encouraging. The numerical values of different performance metrics obtained over the same data set confirm that the proposed algorithm performs better with respect to the state-of-the-art methods. Hence, we may consider the proposed method as a promising tool for clustering and CT image segmentation in a Computer Aided Diagnostic (CAD) system.

Introduction

In the domain of medical image analysis, the rapid development of medical data acquisition devices has made the disease detection more accurate and faster, in an invasive way. However, the analysis of medical images becomes cumbersome and tedious due to the complex structures and the burden of the huge image data obtained from the acquisition system [1], [2]. Since medical images inherently contain complex overlapping physiological tissues and noise, the study of medical image analysis has become a challenging task compared to conventional image analysis [3], and sometimes the traditional manual data analysis becomes inefficient as it provides serious decision errors. Moreover, the visual inspection by human beings often creates an interpersonal variation of opinions based on the qualitative analyzing approach [4]. Hence, computer-based image analysis and diagnostic systems have become indispensable, nowadays. A lot of computer-based image analysis algorithms have been developed and used for the diagnosis of different kinds of diseases to provide a decision support system to the medical experts. These techniques encompass statistical methods, soft computing based methods, heuristic and meta-heuristic methods, machine learning algorithms, etc [5], [6], [7]. Most recently deep learning based algorithms have got tremendous importance in designing computer-aided medical diagnostic systems to assist the physicians [8].

A major part of medical image analysis is the segmentation of the region of interest (ROI) of the diseased or suspicious organ or tissue. Image segmentation is a procedure of partitioning an image into a set of non-overlapping zones depending upon some similarity criterion. The resultant segmented image contains different parts of interest which are more prominent in some sense compared to the other [9]. Statistical models are mostly used to realize the insights for a certain set of data. The solution is achieved through the inferences made by analyzing the underlying nature of data [10]. Inherently, statistical models employ an approximation over reality, so not always suitable in solving the delicate problem such as segmentation of organs from medical images. In machine learning models, data must be organized in such a way that the machine can decipher the information distinctly. But, in the supervised approach of machine learning technique, the apprehension of data over-fit (when there is an excessive load of data) or under-fit (when there is not enough data for a clear understanding) remains throughout [11]. That is why this particular method might not seem convenient in medical imaging research all the time, as the amount of data is exclusively dependent on the specific problem. Due to the accurate prediction with lesser training overload, soft computing models, as well as heuristic models, are more preferred in medical imaging applications[7]. Data clustering is an unsupervised machine learning approach that assigns $n$ data points into $m$ ($m\ge 2,$ $m<n$) number of clusters (data points are the real number in $d$ dimensional space $x_i\in R^d$), where more similar data should be the member of the same cluster and dissimilar data in different clusters, so that inter-cluster variance should be minimum and intra-cluster variance is large [12], [13]. A common feature between image segmentation and data clustering algorithms is that both are the process of assigning objects or data points (pixels, in case of images) into similar sets or groups. Hard K-means algorithm is based on the classical set-theoretic approach and implements a rigid and sharp classification, in which each data point is either assigned to a class or not [14], [15]. This process works fast and the corresponding implementation mechanism is easy. But, in many cases, it is burdensome to find proper clusters when the distribution structure is complicated. On the other hand, the fuzzy set-theoretic approach produces soft cluster results. Ruspini [16], [17] coined the root concept of fuzzy partition which forms the base of the fuzzy c-means clustering algorithm by using core concepts of fuzzy set theory of Zadeh [18]. In the year 1981, this fuzzy factor was incorporated by Bezdek and he proposed FCM [19]. The utilization of fuzzy concept in a clustering method makes the class membership become a relative one, and a data point can be affiliated to multiple classes simultaneously with different membership values. This feature of fuzzy c-means clustering handles overlapping data compared to hard clustering techniques. Also, it yields an important feature for medical diagnostic systems to increase sensitivity. The main advantage of FCM is that it is more capable of handling the overlapping clustering problem compared to K-means clustering [20], [21]. However, FCM has some limitations too. In most of the cases, it is perplexing to determine the total number of clusters and the initial centroids. Henceforth, the convergence process is very prolonged when the data set is significantly large. Due to its dependency on the random selection of initial cluster prototypes, it easily falls into local optima [22]. These loopholes of FCM inspired many researchers to amalgamate FCM with evolutionary mechanisms, that can improve clustering speed and accuracy [23], [24]. The key idea behind combining FCM with various evolutionary algorithms is that, instead of random guessing of the initial cluster centroids, firstly an evolutionary algorithm determines the cluster centers irrespective of the data distribution. After that, FCM algorithm will compute the partition matrix for the clustering result using those centroids. In this regard, a lot of attention was achieved by Particle Swarm Optimization (PSO), which is an informed searching algorithm based on population statistics, initially proposed by Kennedy et al. [25]. Some researchers successfully hybridized FCM and PSO and applied them in different fields [26], [27]. PSO usually tries to mimic the collective behavior of various social entities, for instance, bees, fishes, insects, etc. Alike the genetic algorithm, in PSO, multiple agents usually explore and exploit search space along with information passing in a mesh-like manner that improves collective behavior of searching technique [28]. PSO can be implemented easily and computationally inexpensive. Another advantage is that it has only a few parameters to adjust. Thus, many enhanced versions of PSO have been proposed in recent years [29], [30].

An alternative form of FCM applied in the image segmentation problem, is the incorporation of the influence spatial information within the clusters. Since pixels in an image are correlated with their neighborhood and constitute homogeneous regions, the membership value is also influenced by neighborhood pixels. In this regard, some researchers developed new variants of FCM for image segmentation, such as spatial information based image segmentation techniques [31], [32]. This makes the clustering noise-robust since the impact of spatial information is considered for determining membership and centroid values as well as the objective function [33]. Perpetual strength of FCM is maintained in these variants of FCM. But, hybridizing an evolutionary algorithm with this version of FCM for iterative searching of the initial cluster prototype becomes computationally intensive due to the complex structure of the corresponding objective function. Hence, using that variant of the objective function without any change is not so beneficial to compute initial cluster prototype concerning convergence and accuracy.

In our study, we are mainly interested to segregate the organ, before and after the treatment accordingly, from the CT images of patients. The automated pre-treatment and post-treatment segmentation of organs can help the physicians in treatment evaluation with more accuracy and, consequently, improve the quality of treatment. For example, the accurate segmentation of pre-treatment and post-treatment organs helps the physicians knowing the degree of the patient’s disease after the treatment. Based on that, a physician may decide on further treatment of the patient. Coming to such a specific issue, such as dealing with the pre-treatment and post-treatment CT images of the same patient, we have observed that, due to limited numbers of collected pre-treatment and post-treatment raw data, an unsupervised model is preferred here. To implement our proposed method, initially, we convert neighborhood influenced fuzzy objective function, containing both the membership and centroid, into a single variable function of distance or centroid. The reformulation of the objective function does not change its nature and characteristics but makes it compatible to be amalgamated with other optimization algorithms to search the initial cluster prototypes easily. In this study, we have suggested a new neighborhood-influenced FCM based on dynamically-learned particle swarm optimization (DLPSO), where the dynamic adaptation makes the convergence faster, and at the same time, it omits the possibility of being trapped in local optima. Along with that, due to its unsupervised nature, this technique can perform well enough irrespective of the large data size.