Minimum Cross Entropy Thresholding Research Articles

Improving Prostate Image Segmentation Based on Equilibrium Optimizer and Cross-Entropy

Over the past decade, the development of computer-aided detection tools for medical image analysis has seen significant advancements. However, tasks such as the automatic differentiation of tissues or regions in medical images remain challenging. Magnetic resonance imaging (MRI) has proven valuable for early diagnosis, particularly in conditions like prostate cancer, yet it often struggles to produce high-resolution images with clearly defined boundaries. In this article, we propose a novel segmentation approach based on minimum cross-entropy thresholding using the equilibrium optimizer (MCE-EO) to enhance the visual differentiation of tissues in prostate MRI scans. To validate our method, we conducted two experiments. The first evaluated the overall performance of MCE-EO using standard grayscale benchmark images, while the second focused on a set of transaxial-cut prostate MRI scans. MCE-EO’s performance was compared against six stochastic optimization techniques. Statistical analysis of the results demonstrates that MCE-EO offers superior performance for prostate MRI segmentation, providing a more effective tool for distinguishing between various tissue types.

Multi-strategy learning-based particle swarm optimization algorithm for COVID-19 threshold segmentation

With advancements in science and technology, the depth of human research on COVID-19 is increasing, making the investigation of medical images a focal point. Image segmentation, a crucial step preceding image processing, holds significance in the realm of medical image analysis. Traditional threshold image segmentation proves to be less efficient, posing challenges in selecting an appropriate threshold value. In response to these issues, this paper introduces Inner-based multi-strategy particle swarm optimization (IPSOsono) for conducting numerical experiments and enhancing threshold image segmentation in COVID-19 medical images. A novel dynamic oscillatory weight, derived from the PSO variant for single-objective numerical optimization (PSOsono) is incorporated. Simultaneously, the historical optimal positions of individuals in the particle swarm undergo random updates, diminishing the likelihood of algorithm stagnation and local optima. Moreover, an inner selection learning mechanism is proposed in the update of optimal positions, dynamically refining the global optimal solution. In the CEC 2013 benchmark test, PSOsono demonstrates a certain advantage in optimization capability compared to algorithms proposed in recent years, proving the effectiveness and feasibility of PSOsono. In the Minimum Cross Entropy threshold segmentation experiments for COVID-19, PSOsono exhibits a more prominent segmentation capability compared to other algorithms, showing good generalization across 6 CT images and further validating the practicality of the algorithm.

Gumbel (EVI)-Based Minimum Cross-Entropy Thresholding for the Segmentation of Images with Skewed Histograms

In this study, we delve into the realm of image segmentation, a field characterized by a multitude of approaches; one frequently used technique is thresholding-based image segmentation. This process divides intensity levels into different regions based on a specified threshold value. Minimum Cross-Entropy Thresholding (MCET) stands out as an independent objective function that can be applied with any distribution and is regarded as a mean-based thresholding method. In certain cases, images exhibit diverse structures that result in different histogram distributions. Some images possess symmetric histograms, while others feature asymmetric ones. Traditional mean-based thresholding methods are well-suited for symmetric image histograms, relying on Gaussian distribution definitions for mean estimations. However, in situations involving asymmetric distributions, such as left and right-skewed histograms, a different approach is required. In this paper, we propose the utilization of a Maximum Likelihood Estimation (MLE) of Gumbel’s distribution or Extreme Value Type I (EVI) distribution for the objective function of an MCET. Our goal is to introduce a dedicated image-thresholding model designed to enhance the accuracy and efficiency of image-segmentation tasks. This model determines optimal thresholds for image segmentation, facilitating precise data analysis for specific image types and yielding improved segmentation results by considering the impact of mean values on thresholding objective functions. We compare our proposed model with original methods and related studies in the literature. Our model demonstrates better performance in terms of segmentation accuracy, as assessed through both unsupervised and supervised evaluations for image segmentation.

DTP-Net: A convolutional neural network model to predict threshold for localizing the lesions on dermatological macro-images

Highly focused images of skin captured with ordinary cameras, called macro-images, are extensively used in dermatology. Being highly focused views, the macro-images contain only lesions and background regions. Hence, the localization of lesions on the macro-images is a simple thresholding problem. However, algorithms that offer an accurate estimate of threshold and retain consistent performance on different dermatological macro-images are rare. A deep learning model, termed ‘Deep Threshold Prediction Network (DTP-Net)’, is proposed in this paper to address this issue. For training the model, grayscale versions of the macro-images are fed as input to the model, and the corresponding gray-level threshold values at which the Dice similarity index (DSI) between the segmented and the ground-truth images are maximized are defined as the targets. The DTP-Net exhibited the least value of root mean square error for the predicted threshold, compared with 11 state-of-the-art threshold estimation algorithms (such as Otsu’s thresholding, Valley emphasized otsu’s thresholding, Isodata thresholding, Histogram slope difference distribution-based thresholding, Minimum error thresholding, Poisson’s distribution-based minimum error thresholding, Kapur’s maximum entropy thresholding, Entropy-weighted otsu’s thresholding, Minimum cross-entropy thresholding, Type-2 fuzzy-based thresholding, and Fuzzy entropy thresholding). The DTP-Net could learn the difference between the lesion and background in the intensity space and accurately predict the threshold that separates the lesion from the background. The proposed DTP-Net can be integrated into the segmentation module in automated tools that detect skin cancer from dermatological macro-images.

Energy curve and histogram thresholding implementation and evaluation with Aquila Cross-entropy optimization algorithm

This work proposes the implementation of minimum cross-entropy thresholding based on the aquila optimizer (MCE-AO) for the segmentation of base images and support to visually differentiate the different tissues present in the region. As an alternative to segmentation, the energy curve of the images was used, the energy curve has interesting properties, since it considers the spatial contextual information of each image and not only the intensity of the pixel as the histogram does, and in contrast to the histogram, the energy curve seems to be smoother by preserving the valleys and peaks. A comparison was made between the results calculated by the Aquila optimizer algorithm histograms of each image and the energy curve calculated for each image, showing considerable improvements in mean fitness. The quality of the segmented images was evaluated with the PSNR, SSIM and FSIM metrics, with the histogram and the energy curve, and a comparison of each of the results was made, showing improvement in the quality of the images segmented with the energy curve.

Apple image segmentation using teacher learner based optimization based minimum cross entropy thresholding

Apple image segmentation using teacher learner based optimization based minimum cross entropy thresholding

A Boosted Minimum Cross Entropy Thresholding for Medical Images Segmentation Based on Heterogeneous Mean Filters Approaches.

Computer vision plays an important role in the accurate foreground detection of medical images. Diagnosing diseases in their early stages has effective life-saving potential, and this is every physician’s goal. There is a positive relationship between improving image segmentation methods and precise diagnosis in medical images. This relation provides a profound indication for feature extraction in a segmented image, such that an accurate separation occurs between the foreground and the background. There are many thresholding-based segmentation methods found under the pure image processing approach. Minimum cross entropy thresholding (MCET) is one of the frequently used mean-based thresholding methods for medical image segmentation. In this paper, the aim was to boost the efficiency of MCET, based on heterogeneous mean filter approaches. The proposed model estimates an optimized mean by excluding the negative influence of noise, local outliers, and gray intensity levels; thus, obtaining new mean values for the MCET’s objective function. The proposed model was examined compared to the original and related methods, using three types of medical image dataset. It was able to show accurate results based on the performance measures, using the benchmark of unsupervised and supervised evaluation.

Improving Minimum Cross-Entropy Thresholding for Segmentation of Infected Foregrounds in Medical Images Based on Mean Filters Approaches.

Mean-based thresholding methods are among the most popular techniques that are used for images segmentation. Thresholding is a fundamental process for many applications since it provides a good degree of intensity separation of given images. Minimum cross-entropy thresholding (MCET) is one of the widely used mean-based methods for images segmentation; it is based on a classical mean that remains steady and limited value. In this paper, to improve the efficiency of MCET, dedicated mean estimation approaches are proposed to be used with MCET, instead of using the classical mean. The proposed mean estimation approaches, for example, alpha trim, harmonic, contraharmonic, and geometric, tend to exclude the negative impact of the undesired parts from the mean computation process, such as noises, local outliers, and gray intensity levels, and then provide an improvement for the thresholding process that can reflect good segmentation results. The proposed technique adds a profound impact on accurate images segmentation. It can be extended to other applications in object detection. Three data sets of medical images were applied for segmentation in this paper, including magnetic resonance imaging (MRI) Alzheimer's, MRI brain tumor, and skin lesion. The unsupervised and supervised evaluations were used to conduct the efficiency of the proposed method.

Precise and parallel segmentation model (PPSM) via MCET using hybrid distributions

Purpose Image segmentation is one of the most essential tasks in image processing applications. It is a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc. However, an accurate segmentation is a critical task since finding a correct model that fits a different type of image processing application is a persistent problem. This paper develops a novel segmentation model that aims to be a unified model using any kind of image processing application. The proposed precise and parallel segmentation model (PPSM) combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions. Moreover, a parallel boosting algorithm is proposed to improve the performance of the developed segmentation algorithm and minimize its computational cost. To evaluate the effectiveness of the proposed PPSM, different benchmark data sets for image segmentation are used such as Planet Hunters 2 (PH2), the International Skin Imaging Collaboration (ISIC), Microsoft Research in Cambridge (MSRC), the Berkley Segmentation Benchmark Data set (BSDS) and Common Objects in COntext (COCO). The obtained results indicate the efficacy of the proposed model in achieving high accuracy with significant processing time reduction compared to other segmentation models and using different types and fields of benchmarking data sets. Design/methodology/approach The proposed PPSM combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions. Findings On the basis of the achieved results, it can be observed that the proposed PPSM–minimum cross-entropy thresholding (PPSM–MCET)-based segmentation model is a robust, accurate and highly consistent method with high-performance ability. Originality/value A novel hybrid segmentation model is constructed exploiting a combination of Gaussian, gamma and lognormal distributions using MCET. Moreover, and to provide an accurate and high-performance thresholding with minimum computational cost, the proposed PPSM uses a parallel processing method to minimize the computational effort in MCET computing. The proposed model might be used as a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc.

Trading strategies for image segmentation using multilevel thresholding aided with minimum cross entropy

Multilevel thresholding (MLT) is one of the most widely used methods in image segmentation. However, the exhaustive search method is computationally time consuming for selecting the optimal thresholds. Consequently, heuristic algorithms are extensively used to reduce the complexity of the MLT problem. In this paper, an efficient Exchange Market Algorithm (EMA) is proposed to segment images using minimum cross entropy thresholding method. In the EMA, a market risk variable is used to balance the exploration and exploitation capabilities of the algorithm. Moreover, the local search capability is strengthened by the search and absorbent operators of EMA. Meanwhile, the most competent shareholders of EMA retain their best rank without undergoing any changes in their shares. These help in reducing the computational time. The proposed EMA based MLT is tested on benchmark and brain images with different threshold levels. Additionally, EMA approach is compared with other well-known algorithms such as, genetic algorithm, particle swarm optimization, bacterial foraging algorithm, firefly algorithm, honey bee mating optimization and teaching–learning based optimization. The experimental results show that the proposed EMA approach provides better outcomes than other algorithms.

Multilevel minimum cross entropy thresholding: A comparative study

Multilevel thresholding method is one of the most popular techniques in image segmentation. However, the multilevel thresholding method is time-consuming, its time complexity increases exponentially with the number of threshold levels. In this paper, in order to improve the computation efficiency of the multilevel minimum cross entropy thresholding, the iterative formula of the multilevel cross entropy thresholding algorithm is proposed and compared with the modern meta-heuristic optimization algorithms. The iterative multilevel cross entropy thresholding algorithm can find the thresholds close to the global optimums with less time. The computation cost of the iterative multilevel cross entropy thresholding algorithm is linear in the number of the threshold levels. We prove the convergence of the iterative algorithm and compare the iterative multilevel cross entropy thresholding algorithm with multilevel cross entropy thresholding methods combined with the state-of-the-art meta-heuristic optimization techniques including particle swarm optimization (PSO), cuckoo search algorithm (CS), differential evolution (DE), crow search algorithm (CSA) and genetic algorithm (GA). Experimental results show that the iterative multilevel cross entropy thresholding algorithm is efficient and effective. Therefore, iterative algorithm for the multilevel cross entropy thresholding is an effective method to improve the computation efficiency.

A Parallel Multi-Verse Optimizer for Application in Multilevel Image Segmentation

Multi-version optimizer (MVO) inspired by the multi-verse theory is a new optimization algorithm for challenging multiple parameter optimization problems in the real world. In this paper, a novel parallel multi-verse optimizer (PMVO) with the communication strategy is proposed. The parallel mechanism is implemented to randomly divide the initial solutions into several groups, and share the information of different groups after each fixed iteration. This can significantly promote the cooperation individual of MVO algorithm, and reduce the deficiencies that the original MVO is premature convergence, search stagnation and easily trap into local optimal search space. To confirm the performance of the proposed scheme, the PMVO algorithm was compared with the other well-known optimization algorithms, such as gray wolf optimizer (GWO), particle swarm optimization (PSO), multi-version optimizer (MVO), and parallel particle swarm optimization (PPSO) under CEC2013 test suite. The experimental results prove that the PMVO is superior to the other compared algorithms. In addition, PMVO is also applied to solve complex multilevel image segmentation problems based on minimum cross entropy thresholding. The application results appear that the proposed PMVO algorithm can achieve higher quality image segmentation compared to other similar algorithms.

Cloud Detection in High-Resolution Remote Sensing Images Using Multi-features of Ground Objects

The existence of clouds in high-resolution remote sensing images influences target recognition and feature classification. Therefore, finding areas covered with clouds is an important preprocessing step in remote sensing image applications. This paper proposes a cloud detection method for satellite images with high resolution using ground objects’ multi-features, such as color, texture, and shape. First, the highly reflective areas are extracted from the image using the minimum cross entropy threshold method. Second, the multi-scale image decomposition based on domain transform filter extracts the texture features of ground objects. Finally, based on the shape features, regular-shaped artificial ground objects are removed to further improve cloud detection accuracy. The experimental results show that the proposed method not only improves the overall accuracy rate but also reduces the false positive rate compared to the classical traditional cloud detection methods. The method is suitable for cloud detection in high-resolution remote sensing images with complex ground objects.

An Improved PSO-Based Multilevel Image Segmentation Technique Using Minimum Cross-Entropy Thresholding

Entropy-based thresholding techniques are quite popular and effective for image segmentation. Among different entropy-based techniques, minimum cross-entropy thresholding (MCET) has received wide attention in the field of image segmentation. Considering the high time complexity of MCET technique for multilevel thresholding, recursive approach to reducing its computational cost is highly desired. To reduce the complexity, further optimization techniques can be applied to find optimal multilevel threshold values. In this paper, a novel improved particle swarm optimization (IPSO)-based multilevel thresholding algorithm is proposed to search the near-optimal MCET thresholds. The general PSO algorithm often suffers from premature convergence problem which has been addressed in the IPSO by decomposing a high-dimensional swarm into several one-dimensional swarms, and then premature convergence is removed from each one-dimensional swarm. The proposed technique is applied to the set of grayscale images, and the experimental results infer that it produces better MCET optimal threshold values at a higher and faster convergence rate. The qualitative and quantitative results are compared with existing optimization techniques like modified artificial bee colony, Cuckoo search, Firefly, particle swarm optimization, and genetic algorithm. It has been observed that the proposed technique performs better in terms of producing better fitness value, less CPU time as quantitative measurements, and effective misclassification error, peak signal-to-noise ratio, feature similarity index measurement, complex wavelet structural similarity index measurement values as qualitative measurements compared to other considered state-of-the-art methods.

Histogram Based Multimodal Minimum Cross Entropy Thresholding Method for Magnetic Resonance Brain Tissue Segmentation

Histogram Based Multimodal Minimum Cross Entropy Thresholding Method for Magnetic Resonance Brain Tissue Segmentation

Teaching-learning-based optimization algorithm to minimize cross entropy for Selecting multilevel threshold values

Image thresholding is one of the most important approaches for image segmentation. Among multilevel thresholding techniques, cross entropy has been widely used by researchers to find multilevel threshold values. In multilevel cross entropy thresholding techniques, main target is to find an optimal combination of threshold values at different levels for minimizing the cross entropy. In this paper, Teaching-Learning-based Optimization (TLBO) algorithm is used to find an optimal combination of threshold values at different levels for minimizing the cross entropy. TLBO algorithm is inspired by passing on knowledge within a classroom environment where students first gain knowledge from a teacher and then through mutual interaction. This new proposed approach is called the TLBO-based minimum cross entropy thresholding (TLBO-based MCET) algorithm. The performance of the proposed algorithm is tested on a number of standard test images. For comparative analysis, the results of TLBO-based MCET algorithm are compared with the results of Firefly-based minimum cross entropy thresholding (FF-based MCET), Honey Bee Mating Optimization-based minimum cross entropy thresholding (HBMO-based MCET) and Quantum Particle Swarm Optimization-based minimum cross entropy thresholding (Quantam PSO-based MCET). Comparative analysis is done based on two most popular objective performance measures, Peak Signal to Noise Ratio (PSNR) and Uniformity. From experimental results, it is observed that the proposed method is an efficient and feasible method to search an optimal combination of threshold values at 2nd, 3rd, 4th and 5th levels.

Multi-Level Thresholding for Image Segmentation With Swarm Optimization Algorithms

Image segmentation is an important problem for image processing. The image processing applications are generally affectedfromthe segmentation success. There is noany image segmentation method which gives good results for all sorts of images. That’s why there are many approaches and methods forimage segmentationin the literature. And one of the most used is the thresholding technique. Thresholding techniques can be categorized into two topics: bi-level and multi-level thresholding. Bi-level thresholding technique has one threshold value which separates the image into two groups. However, multi-level thresholding technique uses n threshold values where n greater than one. In this paper, two swarm optimization algorithms (Particle Swarm Optimization, PSO and Cat Swarm Optimization, CSO) are applied on finding the optimum threshold values for the multi-level thresholding. In literature, there are some minimization or maximization functions to find the best threshold values for thresholding problem. Some of these methods are: Tsalli’s Entropy, Kapur’s Entropy, Renyi’s Entropy, Otsu’s Method (within class variance/between class variance), the Minimum Cross Entropy Thresholding (MCET) etc.In this work, Otsu’s (within class variance) method, which is one of these popular functions,is used as the fitness function of algorithms.In the experiments, five real images are segmented by usingParticle Swarm Algorithm and Cat Swarm Optimization Algorithms. The performances of the swarm algorithms on multi-level thresholding problem arecompared with Peak Signal-to-Noise Ratio (PSNR) and fitness function (FS) values. As a result, the PSO yields better performance than CSO.

Thresholding schemes for visible light communications with CMOS camera using entropy-based algorithms.

Recent visible light communication (VLC) studies mainly used positive-intrinsic-negative (PIN) and avalanche photodiode (APD). VLC using embedded complementary-metal-oxide-semiconductor (CMOS) camera is attractive. Using the rolling shutter effect of CMOS camera can increase the VLC data rate; and different techniques have been proposed for improving the demodulation of the rolling shutter pattern. Important steps to demodulate the rolling shutter pattern are the smoothing and the application of efficient thresholding to distinguish data logic. Here, we propose and demonstrate for the first time two entropy thresholding algorithms, including maximum entropy thresholding and minimum cross entropy thresholding. Experimental evaluation to compare their bit-error-rate (BER) performances and efficiencies are also performed.

Multilevel Minimum Cross Entropy Image Thresholding using Artificial Bee Colony Algorithm

The minimum cross entropy thresholding (MCET) has been widely applied in image processing. In this paper, a new multilevel MCET algorithm based on the artificial bee colony (ABC) algorithm is proposed. The proposed thresholding algorithm is called ABC-based MCET algorithm. Four different methods including the exhaustive search, the honey bee mating optimization (HBMO), the particle swarm optimization (PSO) and the quantum particle swarm optimization (QPSO) methods are also implemented for comparison with the results of the proposed method. The experimental results demonstrate that the proposed ABC-based MCET algorithm can efficiently search for multiple thresholds that are very close to the optimal ones selected by using the exhaustive search method. Compared with the other three thresholding methods, the segmentation results using the ABC-based MCET algorithm is the best. It is promising to encourage further research for applying the HBMO algorithm to complex problems of image processing and pattern recognition. DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.3273

Multilevel Image Thresholding with Glowworm Swam Optimization Algorithm based on the Minimum Cross Entropy

The measure of cross entropy is a widely used index applied to many areas of computer science. In this article, we proposed a new multilevel thresholding algorithm for image segmentation using the glowworm swarm optimization based on the criterion of minimum cross entropy (MCE). In this paper, a new multilevel MCE thresholding (MCET) algorithm using the glowworm swam optimization (GSO) algorithm is proposed. The proposed image thresholding algorithm is called the GSO-based MCET algorithm. The five different methods including the exhaustive search, the honey bee mating optimization (HBMO), the firefly (FF) algorithm, the artificial bee colony algorithm (ABC) and the particle swarm optimization (PSO) are also implemented for performance comparison. The experimental results demonstrate that the proposed GSO-based MCET algorithm can efficiently search for multiple thresholds that are very close to the optimal ones examined by the exhaustive search method. Compared with the other five thresholding methods, the needs of computation time using the FF-based MCET algorithm is the smallest. Furthermore, the segmentation performance of GSO-based MCET algorithm is better than the PSO-based MCET algorithm, while the results of GSO-based MCET algorithm are not significant different to the other three bio-inspired computing algorithms.