Elsevier

Measurement

Volume 58, December 2014, Pages 175-186
Measurement

A novel image thresholding algorithm based on neutrosophic similarity score

https://doi.org/10.1016/j.measurement.2014.08.039Get rights and content

Highlights

  • This study proposes a novel method to segment the objects on clear or noisy images.

  • The proposed approach performs well on images without noise or with different levels of noise.

  • Neutrosophic similarity score is defined and employed to deal with uncertain information on image segmentation.

Abstract

Image thresholding is an important field in image processing. It has been employed to segment the images and extract objects. A variety of algorithms have been proposed in this field. However, these methods perform well on the images without noise, and their results on the noisy images are not good. Neutrosophic set (NS) is a new general formal framework to study the neutralities’ origin, nature, and scope. It has an inherent ability to handle the indeterminant information. Noise is one kind of indeterminant information on images. Therefore, NS has been successfully applied into image processing and computer vision research fields. This paper proposed a novel algorithm based on neutrosophic similarity score to perform thresholding on image. We utilize the neutrosophic set in image processing field and define a new concept for image thresholding. At first, an image is represented in the neutrosophic set domain via three membership subsets T, I and F. Then, a neutrosophic similarity score (NSS) is defined and employed to measure the degree to the ideal object. Finally, an optimized value is selected on the NSS to complete the image thresholding task. Experiments have been conducted on a variety of artificial and real images. Several measurements are used to evaluate the proposed method’s performance. The experimental results demonstrate that the proposed method selects the threshold values effectively and properly. It can process both images without noise and noisy images having different levels of noises well. It will be helpful to applications in image processing and computer vision.

Introduction

Image thresholding, one of the simple image segmentation procedures, is a crucial step for several image-processing applications such as object detection, shape recognition, and optical character recognition [1]. In the image thresholding process, a threshold value is selected, and the pixels on the images are classified into background or objects according to their values. Image thresholding can convert the gray level images into binary ones [2]. Thresholding is quite efficient when the object pixels and background pixels have distinct gray level distributions. Furthermore, it is easy to be implemented and usually be run fast [3], [4].

A variety of algorithms have been proposed. Generally, image thresholding methods are classified into two groups based on the criteria to select the threshold value: global and local methods [5]. Global methods select the threshold values according to the characteristics of the entire images, and local ones adopt threshold values using the local information on the images. Threshold value selection method based on image histogram is a kind of the global methods [6]. For a high contrast image, the histogram has two distinguished peaks, and a wide valley between the two peaks. The threshold value is selected the value in the valley. However, the histogram based methods fail to find a proper value to segment the image on a low contrast image because the histogram does not have distinguished peaks and valleys. A variety of methods have been presented to select the thresholds based on histogram and fuzzy logic [7], [8], [9], [10], [11], [12], [13], [14].

A fuzzy based image thresholding scheme was proposed by Pal and Rosenfeld [7]. The authors used the fuzzy compactness by using the S-function for membership evaluation. Huang and Wang proposed an efficient fuzzy thresholding method based on Yager’s measure which is a measure of fuzziness depending on the relationship between the fuzzy set and its complement [8], [9]. Chaira and Ray [10] used the Gamma membership function to compute the membership values of the pixels, and proposed the fuzzy divergence for image thresholding. Ramar et al. proposed the neural networks for selecting the optimum threshold value using fuzzy measure [11]. Cheng and Chen used fuzzy homogeneity and fuzzy co-occurrence matrix for image thresholding [12]. The method [12] employed the homogeneity vectors and the fuzzy membership function, and extracted the feature of an image to determine fuzzy regions. The fuzzy entropy values were utilized to determine the thresholds for segmenting the input images. Tizhoosh proposed a thresholding technique based on ultra-fuzzy sets [13]. The ultra-fuzzy set was used to remove the vagueness in the image. Cheng et al. proposed a two dimensional fuzzy entropy method for obtaining the best threshold value [14]. The proposed method involved fuzzy partitioning on a two-dimensional histogram where fuzzy entropy was defined. Finally a genetic algorithm was employed to obtain the optimal threshold value.

In [15], Xiao et al. presented a thresholding method using an artificial bee colony (ABC) algorithm and entropy function. The ABC searched the maximum value of the entropy, and the optimal thresholds were determined based on the maximum. Xiong et al. proposed a threshold selection mechanism for the radar images thresholding which combines the characteristics of two different measures using the Markov random field model [16]. In [17], He et al. presented a threshold method using a two-dimensional histogram and multi-resolution analysis. The method determined the optimal threshold value using the spatial correlation of gray level and the flexibility, and searched the threshold value via multi-resolution way. Jun et al. proposed a two-dimensional Tsallis symmetric cross entropy for image thresholding [18]. The two-dimensional Tsallis symmetric cross entropy was defined, and a recursive algorithm was used to search the optimal threshold vector. A fuzzy entropy measure on a two-dimensional histogram method was proposed in [19]. The image was separated into several different grids with different densities. Then the intensity in the image and the average intensity of the local neighborhood were used to build a two-dimensional histogram. A multi-threshold method was presented based on the maximum fuzzy entropy principle and the two-dimensional histogram. The parameters of the entropy function were tuned via a genetic algorithm. In [20], Bustince et al. defined an ignorance function and used it to obtain a threshold value. Measurements were constructed using t-norms and auto morphism. The degree of ignorance was employed to describe the background and objects. Based on the ignorance degree, the threshold is obtained from the interval-valued fuzzy set having the lowest associated ignorance.

However, the above methods suffer from finding the optimal threshold value when the input images have noise. Especially, under the low SNR levels the above-mentioned methods’ achievements drop considerably. To overcome the limitations of the above methods, we proposed a neutrosophic set based image thresholding scheme for efficient bi-level segmentation. More specifically, the proposed method uses the neutrosophic similarity measures for determining the optimal threshold value.

Neutrosophy is a new kind of generalizations of dialectics, and it studies the neutralities’ origin, nature, and scope [21]. It represents every entity 〈A〉, the opposite 〈Anti-A〉, and the neutralities 〈Neut-A〉 that is neither 〈A〉 nor 〈Anti-A〉.

The traditional fuzzy set utilizes a membership to represent the degree belonging to a set. When the fuzzy membership value is uncertain and vague, it is challenging to be defined using a crisp value [22]. In some situations, we have to consider both the membership and the indeterminacy of the membership.

In the neutrosophic set (NS), each entity is depicted via three memberships: truth, indeterminacy and falsity memberships. This characteristic is essential to such applications as information fusion where data might have a degree of uncertainty.

The image thresholding methods based on the traditional fuzzy set can be affected by noise severely. This paper newly develops a neutrosphic set approach for image thresholding. First, an image is mapped into the NS domain. Then, a novel similarity measurement, neutrosophic similarity score, is defined to measure the pixels’ belonging degree to the object on the image. Finally, the image is performed thresholding using the neutrosophic similarity score. The experiments on synthetic images having different levels of noise and noisy real world images are conducted to evaluate the proposed approach’s performance.

The paper is organized as follows. Section 2 describes the proposed method, Section 3 discusses the experimental results and comparisons, and the conclusions are drawn in Section 4.

Section snippets

Neutrosophic similarity score

A neutrosophic set can be defined under different criteria as: let A={A1,A2,,Am} be a set of alternatives in neutrosophic set, and C={C1,C2,Cn} be a set of criteria. The alternative Ai at Cj criterion is denoted as TCj(Ai),ICj(Ai),FCj(Ai)/Ai, where TCj(Ai), ICj(Ai) and FCj(Ai) are the membership values to the true, indeterminacy and false set at the Cj criterion.

A similarity measurement is proposed to evaluate the similarity degree between two elements in neutrosophic set under

Experimental results and discussions

We have tested the proposed algorithm using different images, and compared its performance with those of newly developed algorithms. In the experiments, we compare the NSS method with a newly published thresholding method based on neutrosophic set (NS) [25] which performed better thresholding results than those of Otsu method [24], Parzen window technique [26], the minimal error thresholding (MET) algorithm [27] and a entropy based approach [28].

Conclusions

This paper presents a new image thresholding algorithm using neutrosophic similarity score. The image is depicted in neutrosophic set via three subsets. Then, a neutrosophic similarity score is defined to measure the degree to the object pixels on the image. Finally, an optimized value is selected on the NSS to perform image thresholding. The experimental results show that the NSS method can obtain the thresholds properly and effectively. It is able to process both images without noise and

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