Computational Intelligence and Neuroscience

Volume 2016 (2016), Article ID 1476838, 16 pages

http://dx.doi.org/10.1155/2016/1476838

## Hybrid Artificial Root Foraging Optimizer Based Multilevel Threshold for Image Segmentation

^{1}Peking University, Beijing 100871, China^{2}Shenyang University, Shenyang 110044, China^{3}Northeastern University, Shenyang 110318, China

Received 18 March 2016; Revised 10 July 2016; Accepted 11 July 2016

Academic Editor: Carlos M. Travieso-González

Copyright © 2016 Yang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a new plant-inspired optimization algorithm for multilevel threshold image segmentation, namely, hybrid artificial root foraging optimizer (HARFO), which essentially mimics the iterative root foraging behaviors. In this algorithm the new growth operators of branching, regrowing, and shrinkage are initially designed to optimize continuous space search by combining root-to-root communication and coevolution mechanism. With the auxin-regulated scheme, various root growth operators are guided systematically. With root-to-root communication, individuals exchange information in different efficient topologies, which essentially improve the exploration ability. With coevolution mechanism, the hierarchical spatial population driven by evolutionary pressure of multiple subpopulations is structured, which ensure that the diversity of root population is well maintained. The comparative results on a suit of benchmarks show the superiority of the proposed algorithm. Finally, the proposed HARFO algorithm is applied to handle the complex image segmentation problem based on multilevel threshold. Computational results of this approach on a set of tested images show the outperformance of the proposed algorithm in terms of optimization accuracy computation efficiency.

#### 1. Introduction

Image segmentation is an important image preprocessing technique with primitive operations for image recognition [1, 2]. The goal of image segmentation is to partition an original image into a suit of disjoint sections or regions by gray values and texture structures [3]. Generally, there is a strong correlation between the objects of these disjoint regions in the image. Bithreshold or multilevel threshold based segmentation methods have been deeply developed and employed in various practical applications. The key issue to this segmentation method is the computational determination of the involved threshold. A broad variety of threshold based segmentation methods have been proposed, including conventional approaches [4] and intelligent approaches [5, 6]. Among them, the classical Otsu criterion shows significant merits of simplicity and high efficiency, which determines the appropriate thresholds according to intrinsic profile characteristic of histogram [7]. As a matter of fact, the Otsu transforms the multilevel threshold segmentation into an optimization problem, which tends to maximize intercluster variance of subpartition. However, due to the exhaustive property of this approach, the computational complexity will rise exponentially with the increasing of the threshold number [8, 9].

Recently, due to their excellent abilities of tackling complex NP-hard problems, metaheuristics such as artificial bee colony [10, 11], particle swarm optimization [12], artificial ant colony [13], differential evolution [14], firefly algorithm [15], wind driven optimization [16], and bacterial foraging algorithm [17] have been adopted widely in threshold image segmentation. It is worth noting that those metaheuristics are generally inspired form intelligent behaviors of animals that have foraging strategies. The survival wisdom of plants, as another typical species of foraging organisms, has received little attention due to their specific lifestyle [18]. However, terrestrial plants have prominent adaptability and sensing ability to use environmental information as a basis for governing their growth orientation and root system development [19]. Logically, such adaptive growth processes can provide novel insights into new computing paradigm for global optimization [20–22]. References [23, 24] have proposed and developed the novel and effective EA variants by using a hybridization of life-cycle and optimal search strategies and obtain significant performance improvement, which shows a novel and effective computation framework for related scientists. How to deliberately design novel evolutionary computation model and algorithm is increasingly becoming an area of active research; taking a promising example, a representative ARFO algorithm is proposed by Ma et al. in [22] and has received a surge of attention [23, 24]. Essentially, the ARFO provides an open and extensible biocomputation framework and model for scientists in the field of optimization theory to exploit new bioinspired algorithms.

Thus, this paper develops a novel hybrid artificial root foraging optimizer (HARFO) which synergizes the idea of coevolution and root-to-root communication strategy. In the proposed model, all roots can be generally divided into the main roots and lateral roots according to the auxin concentration. The main root as the strongest individuals can branch and regrow under effect of hydrotropism. The lateral root involves many branches derived from the main root, and its growth direction orients from corresponding main root [25, 26]. Furthermore, in the root-to-root communication, through different effective topology, individual roots share more information from the elite roots in the early exploration stage of the algorithm. With multipopulation coevolution mechanism, the hierarchical population of roots can be structured with enhanced interactions of individual behaviors from different subpopulations. By incorporating a set of hybrid strategies, the proposed HARFO can be claimed very effective and efficient because the exploitation and exploration can be elaborately balanced, which guarantees finding the optimal thresholds at a more reasonable time.

This paper is structured as follows: In Section 2, a brief overview of the proposed hybrid artificial root foraging optimizer model and algorithm is presented. Section 3 experimentally compares HARFO with other well-known algorithms on a set of benchmark functions. In Section 4 the implementation of HARFO for multilevel threshold for image segmentation is conducted. In Section 5 final conclusion is outlined.

#### 2. Hybrid Artificial Root Foraging Optimizer

##### 2.1. Artificial Root Foraging Optimization (ARFO) Model

This section briefly describes the classical ARFO proposed in [22], which simulates the intelligent foraging behaviors of plant roots. As depicted in [22], in order to idealize biological plant root growth behaviors, some criteria are presented as follows.

*Auxin Concentration* The root’s adaptive growth is conducted by auxin concentration, which significantly influences the information exchange among root tips. The auxin concentration regulates the roots’ spatial structure, after new roots germinate and grow, and it is dynamically reallocated instead of static.

*Growth Strategies* Regrowing: one root apex elongates forward (or sideways) in the substrate. Branching: one root apex produces daughter root apices.

*Root Classification* The whole root system generally consists of three categories sorted by the auxin concentration from high to low: the main roots, the lateral roots, and the dead roots

*Root Tropisms* The growth trajectory of plant roots is influenced by hydrotropism, which makes the growing direction of the root tips towards the optimal individual position.Generally, each root implements different growth strategies and operators according to the above criteria. Each main root regrows (i.e., elongates itself) while branching new individuals once some conditions are met. After each growth cycle, some deteriorated roots are selected as the dead roots to be eliminated from current population.

###### 2.1.1. Auxin Regulation

Supposing that as the auxin concentration is used to exhibit the nutrient distribution in artificial soil environment, then it can be stated mathematically as below:Thenwhere is the functional fitness value, is the normalization fitness value of the root , and are the maximum and minimum of the current population, respectively, and is the size of current population. In each cycle of root growth process, all root taps are sorted by auxin concentration values defined above. In our model, half of the sorted population are selected as main roots while the rest of roots are identified as lateral roots.

###### 2.1.2. Main Roots’ Growth: Regrowing and Branching

According to the growth strategy of main root in criterion for the plant root growth behaviors, a main root with high value has strong growth ability of implementing both regrowing operator and branching operator.

*(i) Regrowing Operator*. In this regrowing process, the strong main root can sense environmental stimuli (i.e., nutrient distribution) and use this information to govern its growth orientation. Then, the formulation of this operator is given as below:where and are defined as the position of root at time step and , respectively, is a local learning inertia, rand is a random coefficient varying within , and is the local best individual in current population.

*(ii) Branching Operator*. The main roots with higher auxin concentration values have higher probability to branch more individuals. In this operator, for each main root, if its auxin concentration value is more than a branching threshold* T_Branch*, it will start generating a certain number of new individuals as follows:

In principle, the main root in nutrient-rich environment will forage for energy to obtain higher auxin concentration and then produces more branches. Thus, the branch number can be calculated aswhere is a random coefficient within the range , is the auxin concentration of root , and and are the maximal number and minimal number of the new branching individuals, respectively, which are usually preset to 4 and 1, respectively.

The position of a newly branching root is initialized from the parent main root with Gauss distribution , where can be defined aswhere is the current iteration index, is the maximum of iterations, the initial standard deviation is determined by the range of searching, and donates the final standard deviation.

###### 2.1.3. Lateral Roots Growth: Random Walking

At the iteration, each lateral root tip generates a random head angle and a random elongation length, given as follows: all lateral roots will conduct random searches at each feeding process; random search strategy is considered to be the most effective foraging strategy in nutrient distributed environment [27, 28]. Each lateral root generates a random growth angle and random elongated length, which is given bywhere is the maximum elongate length unit (i.e., objective function boundary range), rand is a random number with uniform distribution in , and is a growth angle computed by a random vector .

###### 2.1.4. Dead Roots’ Growth: Shrinkage

In the case that the root does not get enough nutrients from soil, its corresponding auxin concentration is intended to be weak. Once auxin concentration is lower than a certain threshold, the sustained growth probability will be stagnated. This enables the corresponding root to be simply removed from the current population. The branching criterion and dead roots eliminating criterion are listed as follows:where is the current population size, is the branching threshold, is the branching number defined by (5), and* T_Nmority* is the death threshold.

##### 2.2. Root-to-Root Communication

The intrinsic property of the “population” in swarm intelligence is collective intelligence emerging by a number of connected individuals exchanging information in some specific topologies [27–30]. This means that the spatial topological structure plays an important role in enhancing dynamic interaction between individuals and optimizing information propagation path across the structured population.

Accordingly, the population topology technique has been strongly recommended for potential improvement of swarm intelligence or evolutionary algorithms [30–33]. Particularly, by lucubrating on the relationship between population topologies structure and algorithmic performances in [29], Kennedy and Mendes conclude that the Von Neumann exhibits better convergence speed on a variety of test functions, as shown Figures 1(a) and 1(b).