A fast algorithm for multilevel thresholding

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A fast algorithm for multilevel thresholding

In general, thresholding methods can be divided into parametric and nonparametric methods. Using parametric methods, such as a novel image thresholding method based on Parzen window estimate [ 11 ], nonsupervised image segmentation based on multiobjective optimization [ 12 ], a multilevel thresholding approach using a hybrid optimal estimation algorithm [ 13 ], and optimal multithresholding using a hybrid optimization approach [ 14 ], may involve the solution of nonlinear equations which increases of the computational complexity.

Therefore, the nonparametric methods [ 15 ] are introduced for finding the thresholds by optimizing some discriminating criteria. Among the mentioned different thresholding criteria, the entropy is the most popular optimization method. Using the entropy of the histogram, Pun was the first to introduce a new method for gray level image thresholding [ 8 ].

Later, this method was corrected and improved by Kapur et al. Information about the gray value of each pixel and the average value of its immediate neighborhood are obtained by two-dimensional entropy which is calculated by two-dimensional histogram.

Another important group of methods based on discriminant analysis is the clustering-based methods [ 18 ]. In these methods, gray values are clustered into several classes, so that there is a similarity of gray values within the class and dissimilarity between classes.

To perform the separation of classes, Otsu has developed a thresholding method for computing the optimal thresholds by maximizing the between-class variance using an exhaustive search [ 7 ]. It has been shown that this method gives acceptable results when the number of pixels in each class is close to each other.

For bilevel image thresholding, the above-mentioned methods are effective.

A fast algorithm for multilevel thresholding (2001)

However, for the optimal multilevel thresholding, the existing conventional methods are being hindered by an exhaustive search when the number of thresholds is increased.

To overcome this problem, powerful metaheuristics are used to search for the optimal thresholds in order to achieve a fast convergence and reduce the computational time.

A fast algorithm for multilevel thresholding

Metaheuristics are optimization methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space [ 1920 ]. Several metaheuristic algorithms derived from the behavior of biological and physical systems in the nature have been proposed as powerful methods for searching the multilevel image thresholds.

Since magic algorithm that works for all problems does not exist [ 21 ], different approaches have been developed for different classes of problems such as combinatorial or continuous, with additions for constrained optimization problems [ 22 ].

Original versions of metaheuristic algorithms are often modified or hybridized in order to improve performance on some classes of problems. The most popular nature-inspired algorithms for optimization, with improvements, adjustments, and hybridizations, include particle swarm optimization PSO [ algorithm are able to function well to the image with low contrast level and high unclearness level.

Keywords: Multilevel Thresholding, Ultrafuzziness, Fuzzy Sets, Type II, Gaussian 1. In this paper, a novel improved particle swarm optimization (IPSO)-based multilevel thresholding algorithm is proposed to search the near-optimal MCET thresholds.

A study of some nature inspired metaheuristic algorithms for multilevel thresholding for image segmentation is conducted.


Here, we study about Particle swarm optimization (PSO) algorithm, artificial bee colony optimization (ABC), Ant colony optimization (ACO) algorithm and Cuckoo search (CS) algorithm.

The experimental results show that CPE is a good criterion of image thresholding and GA is a applicable fast algorithm for multi-level thresholding compared to the exhaustive searching method. Year: ensure the fast convergence of the algorithm to the best local maximum of the likelihood function.

Sequential EM based initialization procedure has been proposed [Farag, El-Baz Adaptive multilevel thresholding algorithm The steps in adaptive multilevel thresholding algorithm . Color image segmentation is a crucial preliminary task in robotic vision systems.

This paper presents a novel automatic multilevel color thresholding algorithm to address this task efficiently. The proposed algorithm consists of a learning process and a multi-threshold searching process.

World Academy of Science, Engineering and Technology