An adaptive spatial information-theoretic fuzzy clustering algorithm for image segmentation

Highlights

• We incorporate the spatial context to the conventional fuzzy c-means (FCM) algorithm for image segmentation.

• We incorporate the information-theoretic framework into the FCM algorithm to improve its robustness.

• The new clustering algorithm can effectively improve the image segmentation results and is useful for brain image analysis.

Abstract

This paper presents an adaptive spatial information-theoretic fuzzy clustering algorithm to improve the robustness of the conventional fuzzy c-means (FCM) clustering algorithms for image segmentation. This is achieved through the incorporation of information-theoretic framework into the FCM-type algorithms. By combining these two concepts and modifying the objective function of the FCM algorithm, we are able to solve the problems of sensitivity to noisy data and the lack of spatial information, and improve the image segmentation results. The experimental results have shown that this robust clustering algorithm is useful for MRI brain image segmentation and it yields better segmentation results when compared to the conventional FCM approach.

Introduction

Image segmentation is one of the most important steps in many computer vision applications. The goal of image segmentation is to partition a given image into regions or parts that have a strong correlation with patterns or areas corresponding to objects in the real world. In the last few decades, data clustering techniques had been widely used in image segmentation and had achieved great successes in the areas of medical image analysis [1], [2], face recognition [3], [4], and machine vision [5], [6]. The fuzzy clustering method, especially the fuzzy c-means (FCM) algorithm [7], is one of the most popular data clustering algorithms for image segmentation. It has been shown to be more advantageous than crisp clustering in that the crisp assignment of a data point to cluster center is not reasonable in real applications. Further, when compared to the crisp approaches, the FCM method is more tolerant to variations and noise in the input data [8].

Like many other standard unsupervised clustering methods, the FCM method suffers the lack of spatial information when applying to image segmentation applications. They rely only on the intensity distribution of the pixels, and disregard their geometric information, which make them very sensitive to noise and other artifacts introduced during the imaging process. In order to make the standard FCM algorithm [7] more robust to noise and outliers for image segmentation, many modified fuzzy clustering approaches had been reported in [9], [10], [11], [12], [13], [14], [15]. These methods are better than the conventional fuzzy clustering algorithms because the clustering decision of a single pixel is now reconsidered by the influence from the neighborhood patterns. This improvement tends to smooth out the isolated noise or image artifacts and produces more homogeneous segmentation results.

Most of these improved methods were developed in the last decade. The major contribution to the modifications of the FCM algorithm through the incorporation of the spatial information can be tracked back to 1998. Mohamed et al. [9] used a modified FCM algorithm for medical image segmentation. They introduced the spatial information into the similarity measure. The similarity measure is modified such that the pixel can be dragged closer to the cluster center if it is in homogenous regions. Although there is no more model assumption in the FCM algorithm, the drawbacks of the FCM algorithm [8] are its sensitivity to the non-descriptive initial centers and its massive computational load. Therefore, Ahmed et al. [10] used another similarity measure in a Bias-Corrected FCM (BCFCM) algorithm for bias field estimation and segmentation, which achieved a better performance when an additional term is added to the new objective function. Many researchers subsequently modified the objective functions and developed several robust FCM variants for image segmentation [11], [12], [13], [14], [15]. These algorithms were shown to have better performance than the standard FCM algorithm. However, some of these methods [11], [13], [14] depend on a fixed spatial factor which needs to be adjusted according to the real applications. The shortcoming of using a fixed spatial parameter is evident. It makes the segmentation algorithm less robust to various images and causes the problem of over-smoothed edges. In order to overcome this, clustering algorithms that have an adaptive selection mechanism of the spatial parameters have been proposed recently [16], [15]. The new similarity measure makes use of local and spatial intensity information, and so it performs better and is able to reduce the blurring effect. However, the need for experimentally adjusted parameter and the blurring problems still exist.

In this paper, we propose a new adaptive spatial fuzzy clustering algorithm, called the Adaptive Spatial Information-Theoretic Fuzzy Clustering Algorithm (ASIFC), to address the noise problem and the lack of spatial information for the conventional FCM algorithms with two-level robustness enhancements. We extend the idea in [17] to specifically enhance the robustness of FCM algorithms. The lack of spatial information problem is taken into consideration by using a novel adaptive similarity measure, while the noise and outliers are to be identified through the mutual information (MI) maximization. This new information framework allows us to add robust capability to the basic FCM algorithm while inheriting its advantages such as fast processing time and less sensitive to the density of clusters.