# Parallel Compact Differential Evolution for Optimization Applied to Image Segmentation
## 1 Introduction  
Differential Evolution (DE) has prove to be an useful optimization algorithm applied in many areas [1; 2; 3]. In many practical application scenarios, it may be less likely to use high-performance computing equipment due to various reasons, but it is necessary to solve varieties of optimization problems. The traditional optimization algorithm often needs to store a lot of solutions, and to calculate each solution's corresponding value. The huge amount of calculation conflicts with the performance of the computing equipment. Whereas, the compact evolutionary algorithm (cEA) which belongs to the estimation of distribution algorithm is proposed to overcome this dilemma. The compact evolutionary algorithm uses only one individual solution with the statistical characteristics of the population to optimize the related problem. Therefore, the method demands less computing power and memory compared with traditional methods. Several versions of compact evolutionary algorithm have been proposed. The compact genetic algorithm (cGA) [4] is the first compact concept of the genetic algorithm (GA), which only processes one solution, but it gets the similar result when compared with the traditional genetic algorithm. The convergence of compact genetic algorithm is proved in [5] and an extended compact geneticalgorithm (ecGA) can be found in [6]. The study of the scalability for extended compact genetic algorithm can be found in [7] and the compact genetic algorithm is also applied to the training of natural network [8]. A compact differential evolution (cDE) algorithm is proposed in [9]. The principle of compact differential evolution algorithm is similar to that of compact genetic algorithm, but there are still two obvious differences. The first is survivor selection scheme. cDE adopts one-to-one generation logic and selects survivors by comparing the fitness of parents and offspring, which is different from the typical selection mechanism of the genetic algorithm. The second difference lies in that the number of DE search operations is limited, which will most likely result in failure when efforts are made to find the highest quality solution (see [10; 11; 12]). To solve this problem, randomness is added to the search logic of the basic DE algorithm, and cDE introduces certain randomness because it uses the statistical characteristics of the population. This feature not only makes it easier for the algorithm to find better solutions, but also reduces stability. In this paper, we propose an improved version of cDE, which is called parallel compact differential evolution algorithm (pcDE). In cDE, only one individual is generated in per iteration, so it is easy to cause a large experimental error. The stability of the cDE algorithm is not strong, and the experimental results fluctuate widely. In the pcDE algorithm, multiple groups are parallelized, and the results of different groups are fused through the communication strategies after fixed number of iterations so as to obtain a reliable solution. Hence, the stability and efficiency of the algorithm are enhanced. It is found that the performance of pcDE is better than that of cDE. Image segmentation is still a hot topic in image processing and computer vision research. The goal of image segmentation is to separate the target from its background, which is the basis of image classification and recognition. Frequently-used image segmentation methods include threshold segmentation, region tracking, and edge detection. The method of threshold segmentation is the most frequently-used image segmentation method. At present, there are many threshold selection methods, like maximum inter-class variance method (Otsu method) [13], best histogram entropy method (KSW entropy method) [14], and minimum error thresholding method [15] etc. Most existing methods use the one-dimensional gray histogram to select segmentation threshold. However, these segmentation methods will cause a lot of errors when the signal-to-noise ratio (SNR) of image decreases.