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A multilevel thresholding algorithm using Electromagnetism Optimization
Diego Oliva, Erik Cuevas, Gonzalo Pajares, Daniel Zaldivar, Valentin Osuna
TL;DR
Classical multilevel thresholding is computationally expensive because it exhaustively searches threshold values. The paper introduces MTEMO, which combines EMO with Otsu or Kapur objectives, and reports effective segmentation with reduced iterations and computational cost relative to compared evolutionary methods.
Problem
Classical multilevel thresholding becomes computationally expensive because Otsu’s and Kapur’s exhaustive searches grow exponentially with each additional threshold.
Method
MTEMO samples histogram-based candidate thresholds and evolves them with EMO attraction-repulsion operators using Otsu or Kapur objective functions.
Results
The experiments report that MTEMO provides effective segmentation, lower computational cost than compared evolutionary approaches, and better results with Otsu than Kapur.
Takeaways & Limitations
The results support EMO as an attractive alternative for multilevel image segmentation rather than as a method intended to outperform every existing technique.
Abstract
from arXiv · showhide
Segmentation is one of the most important tasks in image processing. It consist in classify the pixels into two or more groups depending on their intensity levels and a threshold value. The quality of the segmentation depends on the method applied to select the threshold. The use of the classical implementations for multilevel thresholding is computationally expensive since they exhaustively search the best values to optimize the objective function. Under such conditions, the use of optimization evolutionary approaches has been extended. The Electromagnetism Like algorithm (EMO) is an evolutionary method which mimics the attraction repulsion mechanism among charges to evolve the members of a population. Different to other algorithms, EMO exhibits interesting search capabilities whereas maintains a low computational overhead. In this paper, a multilevel thresholding (MT) algorithm based on the EMO is introduced. The approach combines the good search capabilities of EMO algorithm with objective functions proposed by the popular MT methods of Otsu and Kapur. The algorithm takes random samples from a feasible search space inside the image histogram. Such samples build each particle in the EMO context whereas its quality is evaluated considering the objective that is function employed by the Otsu or Kapur method. Guided by these objective values the set of candidate solutions are evolved through the EMO operators until an optimal solution is found. The approach generates a multilevel segmentation algorithm which can effectively identify the threshold values of a digital image in a reduced number of iterations. Experimental results show performance evidence of the implementation of EMO for digital image segmentation.
28040 Madrid, Spain
This passage block contains author affiliations, contact information, and a keyword list for the paper.
- The listed affiliations include Universidad de Guadalajara, CUCEI, and Centro de Investigación en Computación-IPN in Mexico.
- The contact information includes email addresses using the cucei.udg.mx domain.
- The paper’s keywords are image segmentation, evolutionary algorithms, and the electromagnetism-like algorithm.
1. Introduction
The introduction frames multilevel thresholding as a computationally difficult segmentation problem and presents MTEMO as an EMO-based alternative using Otsu and Kapur objectives.
- Multilevel thresholding requires selecting multiple intensity thresholds to divide image pixels into more than two classes, while classical methods become exponentially more complex as thresholds increase.
- The introduction describes EMO as a population-based global optimizer whose particles are guided by attraction and repulsion based on objective values.
- MTEMO samples candidate thresholds from the histogram-defined feasible space and evolves them with EMO attraction-repulsion operators.
- The method evaluates candidate solutions with objective functions from Otsu’s variance criterion or Kapur’s entropy criterion.
- The paper reports that MTEMO can identify image thresholds in fewer iterations while reducing the computational complexity of the original proposals.
2. Electromagnetism – Like Optimization Algorithm (EMO)
EMO optimizes a bound-constrained objective by assigning charge-like values to population points, moving them through collective forces, and refining them locally across iterations.
- EMO initializes uniformly sampled points in a feasible search region and iterates until a stopping condition such as a maximum iteration count is met.
- An iteration first moves points through the attraction-repulsion mechanism and then applies local search before forming the next population.
- Each point’s charge depends on its objective value, so better points attract other population members while lower-quality points repel them.
- The algorithm moves points along their total force, explores nearby locations, and selects the next population from the resulting candidates.
- A convergence analysis for bound-constrained problems reports a considerable probability that at least one particle moves closer to optimal solutions after one iteration.
3. Image Multilevel Thresholding (MT)
Multilevel thresholding selects several intensity thresholds to form image classes, with Otsu maximizing between-class variance and Kapur maximizing entropy.
- Multilevel thresholding selects multiple threshold values to divide an image into more than two intensity-based classes.
- Otsu’s method: Otsu’s method determines thresholds by maximizing between-class variance computed from the image histogram and class statistics.
- Otsu’s method: For multilevel Otsu thresholding, the objective uses a vector of thresholds and sums the between-class variance contributions across classes.
- Both Otsu’s and Kapur’s methods extend from bi-level to multilevel thresholding by computing class-specific statistics for multiple threshold values.
- Kapur’s method: Kapur’s method determines thresholds by maximizing the overall entropy derived from the histogram probability distributions of the resulting classes.
4. Multilevel Thresholding Using EMO (MTEMO)
MTEMO formulates multilevel thresholding as an optimization problem and uses EMO to search threshold values under Otsu or Kapur objectives. It represents candidate thresholds as particles, evolves them through attraction-repulsion and local-search steps, then applies the best thresholds to segment the image.
- Optimization formulation: MTEMO optimizes threshold vectors within the feasible intensity range 0–255 using either the Otsu or Kapur objective function.The threshold vector contains k decision variables, each representing a segmentation threshold.
- Particle representation: The population is initialized with N random particles whose k dimensions represent threshold points for the image.RGB images use three component populations, whereas grayscale images use one.
- EMO evolution: Each particle is evaluated with the selected objective, after which EMO computes particle charges and the total force vector.The objective is evaluated using either Otsu or Kapur before force-based population updates.
- EMO evolution: EMO moves the population along the total force vector, applies local search, and retains the best candidates according to objective values.Iterations continue until the maximum-iteration condition or another stopping criterion is reached.
- Final segmentation: The algorithm selects the particle with the best objective value and applies its threshold values to the image.This final particle supplies the thresholds used for segmentation.
5. Experimental Results
MTEMO is evaluated on benchmark images using Otsu’s and Kapur’s objectives, multiple threshold counts, noise conditions, and comparisons with other evolutionary methods. The reported results indicate rapid convergence, better performance for higher threshold counts, statistically stronger Otsu PSNR values, and lower iteration counts than competing methods.
- MTEMO stabilizes around the first 50 iterations, while its maximum iteration setting is 150 without affecting solution quality when increased.The stopping rule also considers whether the best fitness remains unchanged for 10% of the maximum iterations.
- 5.1 Otsu’s results: Using Otsu’s objective, segmentation outcomes are better with 4 or 5 thresholds, while 3 thresholds can suffice when extreme accuracy is unnecessary.The Otsu analysis reports PSNR, standard deviation, iterations, and threshold values across the benchmark images.
- For noisy images, MTEMO remains consistent with the outcomes on clean images under Gaussian noise and 2% salt-and-pepper noise.The noisy-image experiments apply both Otsu’s and Kapur’s objective functions to the Train image.
- 5.5 Comparisons: Wilcoxon tests report Otsu PSNR means as statistically better than Kapur’s, while MTEMO uses statistically fewer iterations than competing methods.The reported p-values are below the 0.05 significance level for both comparisons.
6. Conclusions
The paper presents MTEMO as a multilevel thresholding method combining EMO with Otsu or Kapur objective functions. Experiments indicate that MTEMO performs well against other evolutionary methods, with lower computational cost, while serving as an alternative rather than a universally superior method.
- MTEMO combines EMO with Otsu and Kapur objective functions for multilevel image thresholding.The method evaluates candidate solutions using these objective functions while exploiting EMO search capabilities.
- Otsu-based MTEMO produces better results than the Kapur-based version, with the difference statistically supported by the Wilcoxon test.The comparison evaluates PSNR performance between the two objective-function variants.
- Compared with GA, PSO, and BF, MTEMO shows evidence of strong performance, accuracy, convergence, and lower computational cost.The comparison uses PSNR and STD values to evaluate the algorithms.
- The paper positions EMO as an attractive alternative for multilevel thresholding rather than a method intended to outperform every existing approach.The stated aim is to demonstrate the effectiveness of electromagnetism systems for this purpose.