Performance and robustness of regional image segmentation driven by selected evolutionary and genetic algorithms: Study on MR articular cartilage images

Citation: Kubicek, J.; Varysova, A.; Cerny, M.; Hancarova, K.; Oczka, D.; Augustynek, M.; Penhaker, M.; Prokop, O.; Scurek, R. Performance and Robustness of Regional Image Segmentation Driven by Selected Evolutionary and Genetic Algorithms: Study on MR Articular Cartilage Images. Sensors 2022,22, 6335. https://doi.org/10.3390/ s22176335 Academic Editor: Pawel Strumillo Received: 6 July 2022 Accepted: 18 August 2022 Published: 23 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). sensors Article Performance and Robustness of Regional Image Segmentation Driven by Selected Evolutionary and Genetic Algorithms: Study on MR Articular Cartilage Images Jan Kubicek 1,*, Alice Varysova 1, Martin Cerny 1, Kristyna Hancarova 1, David Oczka 1, Martin Augustynek 1, Marek Penhaker 1, Ondrej Prokop 2and Radomir Scurek 3 1 Department of Cybernetics and Biomedical Engineering, VŠB—Technical University of Ostrava, 17.listopadu 2172/15, Poruba, 708 00 Ostrava, Czech Republic 2MEDIN, a.s., Vlachovicka 619, 592 31 Nove Mesto na Morave, Czech Republic 3Department of Security Services, Faculty of Safety Engineering, VŠB—Technical University of Ostrava, ul. Lumirova 3, 700 30 Ostrava, Czech Republic *Correspondence: [email protected] Abstract: The analysis and segmentation of articular cartilage magnetic resonance (MR) images belongs to one of the most commonly routine tasks in diagnostics of the musculoskeletal system of the knee area. Conventional regional segmentation methods, which are based either on the histogram partitioning (e.g., Otsu method) or clustering methods (e.g., K-means), have been frequently used for the task of regional segmentation. Such methods are well known as fast and well working in the environment, where cartilage image features are reliably recognizable. The well-known fact is that the performance of these methods is prone to the image noise and artefacts. In this context, regional segmentation strategies, driven by either genetic algorithms or selected evolutionary computing strategies, have the potential to overcome these traditional methods such as Otsu thresholding or K-means in the context of their performance. These optimization strategies consecutively generate a pyramid of a possible set of histogram thresholds, of which the quality is evaluated by using the fitness function based on Kapur’s entropy maximization to find the most optimal combination of thresholds for articular cartilage segmentation. On the other hand, such optimization strategies are often computationally demanding, which is a limitation of using such methods for a stack of MR images. In this study, we publish a comprehensive analysis of the optimization methods based on fuzzy soft segmentation, driven by artificial bee colony (ABC), particle swarm optimization (PSO), Darwinian particle swarm optimization (DPSO), and a genetic algorithm for an optimal thresholding selection against the routine segmentations Otsu and K-means for analysis and the features extraction of articular cartilage from MR images. This study objectively analyzes the performance of the segmentation strategies upon variable noise with dynamic intensities to report a segmentation’s robustness in various image conditions for a various number of segmentation classes (4, 7, and 10), cartilage features (area, perimeter, and skeleton) extraction preciseness against the routine segmentation strategies, and lastly the computing time, which represents an important factor of segmentation performance. We use the same settings on individual optimization strategies: 100 iterations and 50 population. This study suggests that the combination of fuzzy thresholding with an ABC algorithm gives the best performance in the comparison with other methods as from the view of the segmentation influence of additive dynamic noise influence, also for cartilage features extraction. On the other hand, using genetic algorithms for cartilage segmentation in some cases does not give a good performance. In most cases, the analyzed optimization strategies significantly overcome the routine segmentation methods except for the computing time, which is normally lower for the routine algorithms. We also publish statistical tests of significance, showing differences in the performance of individual optimization strategies against Otsu and K-means method. Lastly, as a part of this study, we publish a software environment, integrating all the methods from this study. Keywords: medical image segmentation; articular cartilage; regional segmentation; ABC; PSO; DPSO; Otsu thresholding; K-means clustering Sensors 2022,22, 6335. https://doi.org/10.3390/s22176335 https://www.mdpi.com/journal/sensors Sensors 2022,22, 6335 2 of 38 1. Introduction Medical image segmentation represents one of the essential procedures in medical image analysis. The methods, belonging in the area of medical image segmentation, play an important role for the image area decomposition with the focus image understanding. Such methods enable two important issues: (1) the extraction of morphological features of objects of interest and (2) the consequent extraction of various features of such objects with the aim of the quantification of biological tissues [ 1 – 7 ]. In this context, we are routinely focused on either geometrical parameters of image regions such as the area, perimeter, diameter, or curvature parameters or intensity parameters, including a statistic estimation of the intensity spectrum to quantify the image surface [ 8 , 9 ]. Not having automated image segmentation methods, clinical experts would have to perform medical tissues segmentation manually by contouring objects of interest. Such a procedure would be surely linked with subjective error depended on the skills of the individual physician. On the other hand, manual contouring plays an important role in the objectivization of automated image segmentation methods, where manual annotation normally serves as a gold standard to objectively evaluate the segmentation performance based on selected evaluation parameters such as the index of correlation, the mean squared error (MSE), the structural similarity index (SSIM), and many others [10–14]. Image segmentation includes a lot of methods varying in their mathematical strategy and the aim of the segmentation. Edge detection represents one of the most conventional methods for the automatic contouring of objects of interest. Here, we recognize multiple principles such as the maximum of the first derivative, or the zero crossing detectors [ 15 – 17 ]. These methods are normally linked with two main limitations. Firstly, they perform the segmentation of the whole image regardless of the focus on a particular object of interest and mainly they are prone to intensity variations as the impact of image noise, which may significantly influence the segmentation quality. Therefore, these methods are often completed with smoothing filters to improve the segmentation quality. More sophisticated segmentation techniques represent active shape models such as active contours or level set methods, which are capable of focusing on a particular object of interest and within a predefined number of iterations perform the gradual detection of geometrical features of objects of interest. One of the major limitations of these methods is its computing time, because they use a higher number of iterations, and the computing time is also depended on image resolution [18,19]. The most extensive area of the medical image segmentation is regional image segmentation. These methods normally enable medical image decomposition into a predefined number of regions [ 20 , 21 ]. Such a region is perceived as a finite number of image points (pixels or voxels) that mutually share similar features. This predetermines that such regionally oriented methods are able to well recognize biological tissues of interest within individual regions. Regarding the nature of regional segmentation, we recognize so called noninterpreted methods, which normally utilize conventional segmentation strategies and only enable a decomposition of the image points into individual regions without interpreting the content of individual regions [ 22 – 24 ]. Nowadays, the recent trends in medical image regional segmentation are mainly focused on so called interpreted methods, enabling the interpretation of individual detected objects. Such methods normally use semantic segmentation [ 25 , 26 ]. Among the benefits of such methods, it is important to mention that these methods require training on huge datasets, which may be a limitation in the context of medical image availability [27–30]. In this paper, we provide a comprehensive insight in the form of a comparative analysis of selected evolutionary optimization algorithms and genetic algorithms performances, which are used for the tuning of conventional segmentation strategies to achieve a maximal performance under various image conditions and deterioration by image noise. In this study, we compare the performance of optimized segmentation strategies with the elements Sensors 2022,22, 6335 3 of 38 of artificial intelligence (evolutionary and genetic algorithms) with conventional strategies based on the hard thresholding (Otsu method) and nonhierarchical clustering (K-means). This analysis should objectively point out on the performance and impact of modern optimization methods with artificial intelligence as from the view of segmentation performance and robustness under additive noise and also computing time, which is an important factor of each segmentation procedure regarding complex effectivity. This objectivization analysis investigates the robustness and computing requirements of individual segmentation strategies provided under the influence of various types of additive deterministic noise with dynamical intensity. That enables the study of the performance of individual optimization techniques and its determining parameters along gradually deteriorated conditions and shows the dynamical features of robustness of individual methods. Besides the analysis of performance, we also publish the application of regional segmentation for cartilage features extraction. As a part of our research, we publish a testing software environment, integrating individual methods of regional segmentation with the possibilities to select individual steering segmentation parameters. The software application enables the application of various deterministic noise generators with the settings of the noise parameters, which control noise intensity to simulate image degradation for the testing of individual segmentation strategies robustness. This application also enables the segmentation accuracy evaluation based on selected objectivization parameters, which are also used in this study to evaluate the segmentation performance. The organization of the paper is following. In Section 2, we provide recent notes and advances in the area of medical image segmentation. In Section 3, we introduce individual segmentation strategies, guidelines for testing of these methods, and datasets of MR images of articular cartilage used in this study. Section 4is aimed on quantitative results, providing a comprehensive insight on the effectivity, robustness, and limitations of segmentation methods. Section 5is aimed on complex conclusions, discussion, and future trends of this study. 2. Recent Work In this section, we outline the conventional procedures, serving for a spatial image domain decomposition, which is routinely used as a fundamental tool for medical tissues identification. There are various mathematical approaches, which may be used for the aforementioned image decomposition, including mainly techniques based on histogram partitioning, edge detectors, contours tracing, analysis pixel’s relationships, methods of artificial intelligence, and others [30–38]. One of the most popular techniques, and it is also the aim of this paper, is the regional image segmentation bases on the histogram thresholding. These methods normally allow for a histogram decomposition bases on either one, or multiple thresholds, defining individual image regions [ 37 , 38 ]. Here, one of the most popular methods is historically Otsu segmentation, which defines individual thresholds based on the minimization of intra-class intensity variance and the maximization of inter-class variance [39–41]. Other popular areas for regional medical image segmentation is clustering analysis. Here, the most popular methods are based on the nonhierarchical clustering such as Kmeans or fuzzy C-means (FCM) segmentation [ 42 , 43 ]. These methods usually measure distance-based parameters between individual pixels and cluster (region) centroids for the pixel’s classification [ 44 , 45 ]. Such methods are capable of performing image decomposition into various isolated classes based on their features as a level of similarity between the pixel intensity and the centroid [ 46 – 50 ]. Of course, apart from the mentioned approaches, there are plenty of others, which are normally used for medical image segmentation, including edge detectors, outlining image boarders, the methods for consecutive regions forming, such as region growing, or splitting methods, watershed or wavelet transformation, and others [ 51 – 53 ]. Of course, in recent times, one of the most popular segmentation methods deals with various applications of machine and deep learning, enabling semantic segmenta- Sensors 2022,22, 6335 4 of 38 tion instead of the segmentation without interpretation as it is typical in many conventional approaches [54–68]. These routine approaches, as we outlined earlier, are usually easily implemented with a reasonable computing time, on the other hand they normally suffer from certain limitations, which may have a significant influence on their effectivity and robustness as well. In the comparison with conventional segmentation methods such as Otsu thresholding, which is based on the hard selection of individual thresholds in histograms, we proposed schemes on thresholding strategies utilizing optimization techniques for optimal thresholds selection from various thresholds combinations. This is supposed to be a more effective approach, which better reflects a pixel’s distribution inside defined regions. Furthermore, we provide analysis of robustness of each tested method upon dynamic various noise influence to objectively show dynamic features of performance when an image domain is gradually deteriorated by additive noise. On the other hand, we are aware that evolution strategies and a genetic algorithm may have a significant influence on the computing time. Therefore, we also publish time complexity analysis, showing their complexity. All the optimized methods we put in a contrast with the conventional approaches such as Otsu thresholding and the K-means method to objectively point out differences in segmentation performance in the context benefits and limitations of using evolutionary and genetic algorithms for various numbers of thresholds and other steering optimization parameters of these optimization techniques. 3. Materials and Methods Recently, various implementations of evolutionary and genetic optimization strategies have increased in popularity for solving various engineering problems in the area of optimal settings of steering parameters of various procedures. The main aim of this paper is to objectively point out on the effectivity and robustness (a level of stability in various image environment) of selected thresholding-based regional segmentation strategies, being optimized with evolutionary computing methods (ABC and PSO with its variants: FPSO (fuzzy particle swarm optimization) and DPSO (Darwinian particle swarm optimization)) and genetic algorithms as from the view of their effectivity of segmentation, features extraction, and also time complexity. On the other hand, ABC algorithm is used in the combination with fuzzy thresholding, which forms individual segmentation regions based on the membership functions for each region, where pixels are classified into regions based on the membership values as we describe further. This is also an important issue of this study as shows the impact of fuzzy thresholding besides conventional hard thresholding histogram partitioning. In the contrast of the optimized methods, we put two selected conventional segmentation approaches, which have been considered for a long time as standards for medical image segmentation, as they were used in plenty of research studies, dealing with various object detections from medical images. The first one is Otsu thresholding, which is the implementation of so-called hard histogram thresholding, and the second method is K-means, which defines segmented regions based on the nonhierarchical clustering. Implementation of these routine segmentation strategies, which utilize various principles for image segmentation, point out on differences in performance between non-hierarchical clustering and thresholding for regional image segmentation. In a general way, we define the optimization problem of a set of thresholds: T={T1,T2, . . . , Tn}(1) In such configuration, we search for an optimal combination of individual thresholds ( T1 , T2 , . . . , Tn ), defining individual segmented regions, which the best satisfies optimization criteria, which in evolutionary and genetic algorithms is given by fitness function, which is described further. As the definition of fitness function, we use a measure of entropy (Kapur entropy), which well defines pixel’s distributions in segmented regions. Sensors 2022,22, 6335 5 of 38 3.1. Segmentation Methods In this section, we introduce individual segmentation strategies. Here, we describe the evolutionary strategies based on the ABC and PSO (and its variants) and genetic algorithms for histogram-based thresholding. In contrast with these strategies, we put the conventional methods based on the hard thresholding (Otsu thresholding) and K-means, which classifies pixels into regions based on a similarity (Euclidean distance) with region’s centroid. These conventional methods do not contain any optimization elements, so it would be interesting to compare the performance of optimization strategies with these segmentation routines. In order to objectively report the effectivity and robustness of individual methods, we employ selected deterministic noise generators with dynamic noise intensity (controlled by their steering parameters). Dynamical noise impact is manifested by gradual deterioration and modification of pixel’s intensity distribution, which supposedly should have impact on the segmentation robustness as we provide modeling in the section results. In order to provide such analysis, we employ Gaussian, salt and pepper, speckle, and Rician noise generators with dynamical range of their noise impact. In order to objectively measure the noise impact of the segmentation performance of individual studied methods, we employ selected evaluation parameters, which are focused on measuring a level of similarity or difference between the native segmentation (with a zero level of added noise) and respective noise level. This approach enables objective performance evaluation of studied segmentation strategies. For this analysis we use the following objectivization parameters: structural similarity (SSIM), mean squared error (MSE), correlation coefficient (CORR), and signal noise ratio (SNR). Figure 1represents a whole testing environment, which is the main aim of this paper, including application of noise generators, segmentation strategies, and parameters for evaluation. 3.1.1. Otsu Thresholding Otsu method [ 66 ] is one of the sophisticated thresholding methods, which is based on the number of regions selected, Otsu method algorithm determines the optimal thresholds according to the histogram. Image segmentation uses the classification of pixels into segmentation regions. The basis of the method is the statistical parameter of variance, which characterizes the variability of individual pixels in the image. The criteria for this classification include minimizing the intra-class variance or maximizing the inter-class variance. Otsu method uses histogram thresholding to define the number of regions. It searches for the segmentation class with the smallest variance, i.e., the optimally chosen threshold. This technique is classified as a statistical method because it works based on the statistical parameter of variance, which characterizes the variability of the distribution of individual pixels in the image. The equation for calculation of the within-class variance at any threshold is: σ2(t)=ωbg(T)σ2 bg(T)+ωfg(T)σ2 fg(T), (2) where ωbg(t) and ωfg(t) are the probability of number of pixels for each class at threshold T and σ2is variance of color values (pixels). The variance is represented by equation: σ2(t)=∑(xi−x)2 N−1, (3) where xi presents pixel value in group of bg or fg and x presents the mean pixel value in group of bg or fg and N represents the number of pixels. Sensors 2022,22, 6335 6 of 38 Figure 1. Complex general flowchart of testing environment for segmentation evaluation. Sensors 2022,22, 6335 7 of 38 ωbg and ωfg are calculated by: ωbg =PBG(T) Pall , (4) ωfg =PFG(T) Pall , (5) where P BG is count of background pixels at threshold T, P FG is count of foreground pixels at threshold T, and Pall is the total count of pixels in image. Otsu method can be extended for a multiregional segmentation scheme [ 67 ], where more thresholds are defined. In this configuration, the image histogram is divided into equal areas, and for each such area the own threshold is defined. Finally, the original image is segmented by using all these thresholds. Supposing we have Limage intensities in the range: [0, 1, 2, . . . , L] and the parameter pstands for the number of thresholds. A width of one area is defined as the ratio: a=L p(6) Optimal thresholds (P) for individual areas are defined as the maximization of interclass variance: Pp=maxpσ2(t)(7) 3.1.2. K-Means K-means method [ 68 ] is classified as a non-hierarchical clustering method. K-means method allows assigning individual pixels into segmentation classes to which they belong based on distance. It uses nonhierarchical clustering for pixels assignment and searches for the minimum distance between the pixel and the selected center of gravity (centroid). A given pixel is then assigned to the region to which it has the smallest distance. The most commonly used metric is Euclidean, which measures the distance of pixels in the feature space according to the following equation: D(→ x,→ y) = q∑n i=1(xi−yi)2, (8) where → x , → y are the feature vectors, D(→ x,→ y) is the resulting distance, nis the dimension of the space, xand yare the pixel coordinates. Pixel xiis assigned to class yiaccording to the following relation: yi=argminj xi−µj (9) The following vector recalculation calculates the new values of the vectors µj as the mean values from the pixels x i that were classified into the class determined by the vector µj. The new value of µjis calculated according to equation: µj=1 nj∑n i=1,y1=j(xi), (10) where n j denotes the number of pixels and x i classified in the second step into the class determined by the vector µj . The vector classification and recalculation steps are repeated until at least one vector x i is classified into a different class than it was classified in the previous step. The pixel in each class that possesses the maximum frequency is determined as the centroid. The disadvantage of this method is that by assigning objects to each class, it can only determine whether the object belongs to the cluster or not. Therefore, K-means is classified as a hard approach technique. Sensors 2022,22, 6335 8 of 38 3.1.3. ABC Evolutionary Optimization ABC algorithm or artificial bee colony is an algorithm that belongs to the algorithms based on the swarming behavior of animals. Specifically, it is the behavior of bees looking for food. The principle of the algorithm is that it tries to provide the best approximate solution with low computational requirements. The bees function as a whole in a certain way and the allocation of the different roles in the community is automatic. These are the employed bees (EB), the onlooker bees (OB), and the scouts (SB) whose task is to improve the overall food resources. The basic parameters of ABC include the number of food sources, the limit, and the number of iterations. The limit determines after how many iterations a worker will abandon their solution if they have not been able to improve it. Thetotalpopulation(SN)consistsofanequalnumberofEBsandOBs,witheachEBhavingone temporary solution R i adjacent to the solution X i . Parameter X i = {X i , 1, X i , 2, . . . ,X i ,p} represents the i-th solution in the swarm of bees, where p represents the number of parameters that are optimized. In the first stage of the algorithm, these two solutions are compared using the fitness function and if the solution of the fitness function R i is better, it is kept as the new solution from this pair. Otherwise, no change occurs. This is done for each of the pairs X i and R i . It is necessary to apply a selection limit L v specifying the maximum number of attempts in selecting a solution Xiin case an optimal solution Ricannot be found. However, if an optimal solution cannot be found even after exhausting L v , we consider it as a burnt-out solution. The second stage is essentially an extension of EB. It works with OB in which the existing individual solutions are tested from different perspectives. The more optimal solution should have a higher value of P i . After selecting the food source X i , a neighboring food source R i is determined and their fitness values are compared. The last part is the scouts searching for new food sources instead of depleted sources. The process of evaluating solutions is iterative, in most cases 100 cycles are applied. The output of this optimization method is the set of all admissible solutions, where in the final step the solution possessing the maximum value of Piis selected. 3.1.4. PSO Evolutionary Optimization PSO, or particle swarm optimization, is an evolutionary optimization computing technique inspired by the social behavior of birds and fish swarms. This method uses a population of particles that fly in an irregular motion through a given space at a certain speed. The position of each agent is given by the vector x i , and its movement corresponds to the velocity vi. The particle velocity is determined as follows: vi(t) = vi(t−1) + c1∗rand1(pi−xi(t−1)) + c2∗rand2(pg−xi(t−1)), (11) where c 1 and c 2 are positive numbers, rand 1 and rand 2 denote random numbers from the range 0 to 1. Equation is composed of three parts. The inertia and attraction to the best-found position of a given particle p i , and we denote the value of the fitness function at this position by p best . This attraction is multiplied by a random weight c 1∗ rand 1 and is called the memory of the particle. The third part of the equation is the attraction to the best-found position of the particle p g , and we denote the corresponding fitness value by g best . The aforementioned attraction is again multiplied by a random weight c 2∗ rand 2 and is called shared information, or also shared knowledge. Each individual remembers their previous best value and the best value of their neighbors. The agents therefore use the information from the best particle, and therefore this algorithm is more memory efficient than the genetic algorithm. 3.1.5. FPSO Evolutionary Optimization FPSO stands for fuzzy particle swarm optimization. It is a modified PSO algorithm using fuzzy logic theory. The position and velocity of the particles in this algorithm are defined to represent the relationship between the fuzzy and the variables. Fuzzy logic controller with two inputs and one output improves the performance of PSO. The two Sensors 2022,22, 6335 9 of 38 input variables represent current best performance evaluation (CBPE) and current inertia weight. The output variable is change in inertia weight. CBPE needs to be normalized according to the following formula: NCBPE =CBPE −CBPEmin CBPEmax −CBPEmin , (12) where CBPE min is the true minimum and CBPE max represents the suboptimal CBPE. CBPE normalization is used to make the algorithm applicable to a wide range of optimization processes. A non-optimal CBPE is considered to be any solution with a CBPE greater than or equal to CBPE max . These fuzzy variables are defined as fuzzy sets with nine rules for a fuzzy system. 3.1.6. DPSO Evolutionary Optimization DPSO is a Darwinian algorithm extending the PSO algorithm by natural selection and survival of the fittest to increase the ability to escape from local optima. Darwinian particle swarm optimization (DPSO) allows many swarms of test solutions to exist at any point in time. Each swarm works like a regular PSO algorithm, except that it uses natural selection (Darwinian survival of the fittest) to enhance the ability to escape from a local optimum. The principle of the solution search is that if it is heading towards a local optimum, then the search for a solution in that region is terminated, and the search for another area begins. Each swarm is monitored at every step. If swarms improve, they are rewarded. The reward is to extend the lifetime of the particles or to produce offspring. If swarms stagnate, they are punished. The punishment consists of shortening the lifetime of the swarm or removing particles. After the removing the particle, instead of being set to zero, the counter is reset to a value approaching the threshold number, according to: SCC(Nkill)=SCmax C1−1 Nkill+1, (13) where N kill represents a number of deleted particles from the swarm, SCmax C represents that the maximum number of swarms must not be exceeded. Whereas the new swarm is created with a probability based on the equation: p=f NS, (14) where pis the probability, fis a random number in the interval 0 to 1, NS represents the number of swarms. Each swarm is evaluated using the fitness function of all particles. In this way, it is possible to analyze the overall state of the swarms separately and thus update the neighborhood and individual best positions of each particle. New particles are created if a new global solution is found. Conversely, particle extinction occurs if the swarm does not find a more suitable state in a defined number of steps. 3.1.7. Genetic Algorithms-Based Optimization Genetic algorithms are based on natural processes with gradual elimination and subsequent selection of the most suitable solutions. It is a combination between biology and mathematics. Patterns from living nature are used, which initially work by chance and gradually produce better solutions. These patterns are then applied using a mathematical model to a variety of technical applications, including image processing using segmentation techniques. Genetic algorithms use special procedures to find the optimal solution using selection, crossover, and mutation operations. They start with random selection and search for new, better solutions; the most optimal solution is then selected from the results. All algorithms include a fitness function that provides information about the quality of the solution. Each approach has specific parameters that must be set. Examples are the number of regions, the Sensors 2022,22, 6335 16 of 38 Figure 5. Example of proton-dense sequence for investigation of articular cartilage with early cartilage loss. The first row shows a sequence of three native images from the MR dataset and the second row represents image RoIs, focusing on cartilage area, where the red squares point out MR signal change in cartilage structure that indicate the early cartilage loss. 3.3. Deterministic Artificial Noise Generators In order to provide the analysis of robustness of individual segmentation techniques, we employ various image noise generators, which simulate gradual deterioration of spatial image area by using their steering parameters, as we describe further. For our analysis, we use the following noise generators: Gaussian noise, speckle noise, salt and pepper noise, and Rician noise. 3.3.1. Gaussian Noise Gaussian noise represents white statistical noise. This type of noise is due to natural sources such as ambient temperature. The distribution of Gaussian noise is uniform in the image and affects all pixels with the same intensity. It is a normal distribution of noise distribution in the image. Gaussian noise can be defined using the following formula: G(x) = 1 σ√2π e (x−µ)2 2σ2, (24) where xrepresents the luminance of the noise, σ2 is the variance, and µ represents the mean. 3.3.2. Speckle Noise Speckle noise is a common noise that occurs in all coherent imaging systems (lasers, acoustic systems, ultrasound). The cause of this noise is the interference of a signal that has a different phase when returning from the target. This noise is displayed in the image as dark pixels with a higher brightness value. The input parameter is the speckle noise variance. Speckle noise can be described by the formulation: J=I+n∗I, (25) where Ipresents the input image, Jis the noise distribution in the input image, and n presents unified zero mean value of the noise in input image. Sensors 2022,22, 6335 17 of 38 3.3.3. Salt and Pepper Noise Salt and pepper represents impulse noise. The image degradation takes place at several pixels in the image, with the pixel carrying no information about the original value. The pixel values in the image are replaced by values of 255 or 0. Thus, this noise is represented in the image as white and black dots resembling salt and pepper. The input parameter for setting the noise is the density. This noise is most often noticeable during data transmission. 3.3.4. Rician Noise Rician noise represents the most typical noise in images taken by magnetic resonance. Rician noise is based on Gaussian noise in that the real and imaginary parts of the signal are corrupted by an uncorrelated zero mean. The magnitude of Rician noise can be expressed using the following formula: M=q(I+n1)2+n2 2, (26) where Mrepresents the signal magnitude, Irepresents the original image with negligible noise intensity, and n1 and n2 are Gaussian noise variables with zero mean and equal variance σ2 n . Here, we can define the probability density function (PDF) for an image, which is corrupted by Rician distribution by the following way: pM|I,σ2 n=M σ2 n exp−M2+I2 2σ2 nI0IM σ2 nu(M)(27) In this definition, I0(.) depicts the 0th order of modified Bessel function of the first kind, and the parameter u(.) stands for Heaviside step function [56]. 3.4. Application and Settings of Noise Generators Firstly, we introduce the settings of noise deterministic generators, which are used in this study. Each of the noise generators is determined by its steering parameters, which determine the noise intensity. We use a gradual ascended sequence of the noise intensities to effectively simulate the segmentation performance degradation upon increasing the level of the noise-based image deterioration. In the Gaussian noise (G), we use a constant dispersion ( σ2= 0.01) and variable mean value of the noise ( µ ), in the salt and pepper (SaP) noise we provide testing for variable noise density (d) and for speckle (Sp) and Rician noise (Ric), we control the noise intensity via the parameter variance ( σ2 ). For the purposes of testing, we use 20 noise levels to simulate the segmentation performance (Table 2). Table 2. Definition of noise generators for segmentation performance analysis. Noise Generator Number of Regions G: (σ2= 0.01 ), (µ)SaP: (d)Sp: (σ2) Ric: (σ2) 4 0.01–0.2 0.17–0.33 0.01–0.2 0.02–0.4 7 0.01–0.2 0.17–0.33 0.01–0.2 0.02–0.4 10 0.01–0.2 0.17–0.33 0.01–0.2 0.02–0.4 We gradually applied the noise generators with the range of the noise intensity parameters to artificially simulate the noise impact on the pixel’s distribution. As we stated earlier, for each noise, we set 20 levels on the noise intensity. That means each native MR image contains in total 21 images for testing of segmentation algorithms (1 native image + 20 noise levels). For each image, we defined a multidimensional array, where all these noisy images are stored. In the following outputs: Figures 6–9, we provide the examples of gradual deterioration of individual noise generators, which we used for the testing. Sensors 2022,22, 6335 18 of 38 Figure 6. Application of Gaussian noise on native MR cartilage image with intensities (from left): native image, σ2=0.01, µ= {0.005, 0.01}. Figure 7. Application of Rician noise on native MR cartilage image with intensities (from left): native image, σ2={0.2, 0.4}. Figure 8. Application of salt and pepper noise on native MR cartilage image with intensities (from left): native image, d={0.2, 0.4}. Sensors 2022,22, 6335 19 of 38 Figure 9. Application of speckle noise on native MR cartilage image with intensities (from left): native image, σ2={0.2, 0.4}. 3.5. Evaluation Parameters All the performance characteristics are constructed by the way we use the segmentation of native MR images as a gold standard against individual segmentation in individual noise levels. This approach enables objective measurement of the noise influence for each noise level. This finally shows dynamical features of performance within continuous degradation by image noise with variable intensity. The following parameters are considered for this study. SSIM or structural similarity index [ 59 ] is a parameter that allows us to objectively express the similarity of two images xand yusing a metric. This parameter is defined by the following formula: SSIM (x,y)=2µxµy+C12σxy +C2 µ2 x+µ2 y+C1σ2 xσ2 yC2, (28) where C i = (k,l)2 , where lrepresents the dynamic range of pixel values, k<< 1 are small constants with values usually 0.02, µ represents the weighted average of the xand y images, and σ represents the covariance of xand y. These components in the formula allow to compare between xand yimages: brightness (l), contrast (c), and texture (s). The comparison method extracts structural information from the scene. This parameter takes values from − 1 to 1, with 1 representing the absolute match between the xand yimages. Here, we consider that xrepresents the segmentation with zero level of additive noise and yrepresents the segmentation output with respective level of the noise. Correlation coefficient represents the linear correlation between two images xand y. The correlation coefficient is defined as the ratio of the covariance of the variables xand y multiplied by their standard deviations. The Pearson pairwise correlation coefficient rcan be expressed using the following equation: r=∑(xi−x)·(yi−y) (n−1)sxsy, (29) where s x and s y represent standard deviations and x and y represent the arithmetic mean for each of the variables xand y. The correlation coefficient takes values from − 1 to +1, and the closer the absolute value of the correlation coefficient ris to one, the closer the relationship between the variables x,y. The higher the value, the better the segmentation performance. Sensors 2022,22, 6335 20 of 38 SNR or signal to noise ratio is a parameter that allows us to express the ratio of useful power to useless power of a signal (image). This parameter is defined by the following equation: SNR =10log10 · ∑M i=1∑N j=1g2 i,j −f2 i,j ∑M i=1∑N j=1gi,j −fi,j2(30) SNR or signal to noise ratio is a pair where gi,j represents the original (gold standard) segmentation (without additive noise) and fi,j is the segmented image with respective additive noise level. The SNR quantity is decibels (dB). SNR values can be interpreted in the form the higher SNR values we achieve for respective segmentation, the better agreement with the gold standard we have, and better segmentation performance we achieve. MSE, or mean squared error, is a parameter that can be used to objectively evaluate image quality. This parameter expresses the degree of mean squared error between the original image and the segmented image. This parameter is defined by the following formula: MSE =1 MN M ∑ i=1 N ∑ j=1xi,j −yi,j2, (31) where Mrepresents the image size in the horizontal direction, Nrepresents the image size in the vertical direction, xi,j corresponds to a pixel in the segmented image at coordinates i and j, and yi,j corresponds to a pixel in the original image at coordinates i and j. For this parameter, the lower the value, the greater the similarity between the images. Practically, we compute the squared differences between the pixels, having the same coordinates in the segmentation matrixes. Consequently, these differences are summed up, and lastly, its mean value is computed. By this way, we compute the mean quadratic difference between the gold standard segmentation and respective noise level segmentation. The segmentation results (multiregional segmentation) are evaluated via labeling matrix, where each region has a unique number. This number represents an interval of intensity values, which are classified into a specific region. Thus, this can be interpreted as a transformation of a set of intensity values from the image spatial area into the region index. The evaluation parameters reflect pixel reclassification among individual such regions by the influence of additive noise. By adding additive noise with gradually increasing intensity, a respective pixel will have significantly different intensity value when comparing with the situation without additive noise. Therefore, such pixels may be reclassified in a different region. The evaluation of pixel-wise parameters such as SNR or MSE, reflect the impact of change of pixels assignment among individual regions. The main aim of these parameters is reflecting the impact between change of pixel’s assignment in adjacent regions (this is only small change on noise impact) and the shift between more regions, where we can suppose a higher noise impact. This situation firstly reflects the change of pixel region reassignment, but also the shift of pixel intensity by additive noise. Finally, the evaluation parameters quantify the impact of a pixel’s assignment change and thus objectively evaluate a robustness of a respective pixel’s classification upon the image noise with gradual intensity. The higher shift between regions is registrable, the bigger impact on evaluation parameters is, which quantify the performance and robustness of the regional segmentation upon dynamic noise intensity. 4. Results In this section, we introduce quantitative results of testing analyzed thresholdingbased segmentation strategies. Here, we provide several types of characteristics to provide an objective view of the segmentation performance and limitations. We provide examples of graphical comparisons of the segmentation methods, which show the influence of the variable image noise of segmentation maps. For the generation of the segmentation maps, we use an artificial color coding. Where each single color represents one region of the Sensors 2022,22, 6335 21 of 38 segmentation model. To provide a complex view on the segmentation performance, we provide this testing for a variable number of segmentation classes because this parameter has a substantial effect on the segmentation performance. One of the important performance features is the time complexity, thus we provide time requirements of individual segmentation methods. This aspect is substantially important when performing a simultaneous segmentation of a stack of MR images. In order to show a statistical significance between the routine methods and optimized segmentation models, we provide the statistical testing of significance of p-values for median tests. The last quantitative analysis deals with the extraction of clinically important cartilage features including the area, perimeter, and cartilage skeleton. Here, we show differences of automatic segmentation and the gold standards. Lastly, we provide a presentation of the software environment, which integrates individual reported segmentation strategies with the possibility of selecting steering parameters of segmentation. 4.1. Quantitative Segmentation Evaluation Gradual noise dynamics has a substantial effect on the pixel’s distribution as we mention in the previous examples. In our study, we utilize this fact to test the robustness of segmentation strategies to justify the impact of optimization elements for the performance of regional segmentation as we describe further. The first analysis, which we provide is aimed on the graphical evaluation of the analyzed segmentation methods under gradual increasing noise influence. Based on such results, we can subjectively observe clearly visible notable differences in individual methods in segmentation maps. As the example, we provide the comparison (Figures 10 and 11) for all the methods for salt and pepper noise with three levels of density: 0.1, 0.5, and 0.7 and Rician noise with three settings: σ2={0.1, 0.5, 0.7}. The segmentation results are interpreted in the form of segmentation maps in the color spectrum (Figures 10 and 11). The interpretation of these color maps is that each segmentation region in the segmentation map is represented by a single value. Thus, the number of colors corresponds with the number of regions. Each such regional model can be interpreted as a transformation of the scale of intensity values to the number of regions. For instance, 8-bit images (256 intensity values) are transformed into four intensities (segmentation model with four regions). The main aim of this analysis is to objectively report how the distribution of a pixel’s assignment into individual regions are modified under the influence of additive noise against the gold standard (segmentation without additive noise influence). Based on such experimental results, it is noticeable that an increasing noise intensity can significantly impair the quality of the segmentation results. For lower noise levels the segmentation results point out on a good performance, for example the ABC algorithm does not exhibit more significant signs of the noise. On the other hand, higher levels of noise cause significant impairment of the segmentation model consistency. In order to objectively justify this fact, we further provide a robust testing of these segmentation methods based on the mentioned evaluation parameters, to objectively show the change of segmentation performance among individual methods, and also how the number of regions influence the dynamic of segmentation performance. To better justify the testing scheme, we provide testing on routine approaches of Otsu thresholding and K-means clustering. Here, we only set the number of the segmentation regions. Contrarily, in the evolutionary strategies, including ABC, PSO, DPSO, and FPSO, we use a unified number of iterations, 100 (PSO 1 , GA 1 and ABC 1 ) and 500 (PSO 2 , GA 2 and ABC 2 ), and a population size of 50 (PSO 1 , GA 1 and ABC1) and 200 (PSO2, GA2and ABC2). Sensors 2022,22, 6335 22 of 38 Figure 10. Comparison of regional segmentation models with four regions, which are interpreted by four various single colors for three levels of salt and pepper noise: from left native image and noise density d={0.1, 0.5, 0.7} . All the evolution strategies (ABC, PSO, DPSO, and FPSO) have the same settings: 100 iterations and 50 populations. Sensors 2022,22, 6335 23 of 38 Figure 11. Comparison of regional segmentation models with four regions, which are interpreted by four various single colors for three levels of Rician noise: from left native image and noise density σ2={0.1, 0.5, 0.7} . All the evolution strategies (ABC, PSO, DPSO, and FPSO) have the same settings: 100 iterations and 50 populations. Here, we provide the quantitative comparison of individual optimization techniques for image thresholding-based regional segmentation against selected conventional segmentation approaches, including Otsu hard thresholding and K-means nonhierarchical clustering for regional segmentation. We provide dynamical feature extractions of these methods, reporting effectivity for each noise level and robustness in the form of the trend of the evaluation parameters upon additive noise with dynamic intensity, measured by the mean squared error (MSE), the index of correlation (CORR), the structural similarity index (SSIM), and the signal to noise ratio (SNR). As the example, we provide these characteristics (Figures 12–15) for the segmentation models with four regions. The provided characteristics are constructed for 1000 images, where the results for each level of each noise are averaged. Sensors 2022,22, 6335 24 of 38 Figure 12. Dynamical features of Gaussian noise influence for regional segmentation effectivity and robustness based on the MSE, SSIM, CORR, and SNR. Figure 13. Dynamical features of Rician noise influence for regional segmentation effectivity and robustness based on the MSE, SSIM, CORR, and SNR. Sensors 2022,22, 6335 25 of 38 Figure 14. Dynamical features of salt and pepper noise influence for regional segmentation effectivity and robustness based on the MSE, SSIM, CORR, and SNR. Figure 15. Dynamical features of speckle noise influence for regional segmentation effectivity and robustness based on the MSE, SSIM, CORR, and SNR. Judging by the experimental results, significant differences in effectivity among individual methods are notable. The trends of the parameters of similarity (SSIM, CORR, and SNR) for Otsu and K-means exhibit significantly lower values when comparing with the evolutionary algorithms. That indicates the notable worse results of these routine algorithms in the comparison with the optimization techniques. The higher these parameters are, the better the performance of respective segmentation is achieved. On the other hand, these routine approaches from the view of MSE exhibit the most rapid increasing trend when comparing with optimization techniques. This is also a sign of the much worse effectivity of Otsu and K-means against the elements of artificial intelligence. Sensors 2022,22, 6335 32 of 38 Figure 19. Example of report from the SW for regional segmentation testing. This report contains the segmentation results of all the integrated segmentation techniques under salt and pepper noise with density 0.1. 4.3. Clinical Important Features Extraction of Articular Cartilage Based on the reported analysis of the segmentation performance, mostly the combination of fuzzy thresholding with the ABC evolutionary algorithms appeared as the best segmentation strategy, judging by reported objectivization parameters and mainly provided statistical tests of significance. In this subsection, we would like to provide the last analysis of selected features extraction of articular cartilage from MR images based on the fuzzy thresholding with the ABC algorithm. The aim of this analysis is firstly computing a multiregional segmentation model, allowing for a decomposition of the MR image into a finite number (in this case five) segmentation regions. Consequently, a region, representing the articular cartilage, is selected (Figure 20) as the region of interest, while the rest of the segmentation regions are suppressed from the segmentation model (Figure 20). By this selection scheme, we obtain a binary segmentation model, exclusively classifying the articular cartilage from the rest of the tissues in the MR images. Figure 20 also presents a multiregional segmentation of a part of articular cartilage (femoral cartilage) affected by osteoarthritis of I. grade, which is notable by two segmented lobes of the articular cartilage, and between them is a gap, where the cartilage is missing. To objectize the quality of the articular cartilage extraction and the preciseness of the reported features, we extracted the same features for the gold standard manual segmentation of articular cartilage. Consequently, the feature differences are compared to quantify the segmentation effectivity of articular cartilage detection. Note that we used the following settings for the ABC algorithm: 100 iterations and population size 50. The following cartilage features are considered for evaluation: •Cartilage area —a total count of the pixels, belonging to the model of articular cartilage. Sensors 2022,22, 6335 33 of 38 •Cartilage perimeter —a perimeter of the cartilage model. Here, we used Sobel edge operator for the detection of cartilage borders, and consequently counted the border pixels. •Skeleton of cartilage—the detection of cartilage skeleton and computing its length. Figure 20. Example of segmentation results for articular cartilage and its features extraction based on fuzzy thresholding with ABC optimization: ( a ) gold standards by manual annotation, ( b ) binary segmentation, ( c ) native MR image with area of interest indicated by the green square (top) and multiregional segmentation with 4 regions (bottom), where yellow contours reflect two lobes of articular cartilage from region of interest, and ( d ) binary extraction of articular cartilage fused with the gold standard (red contour). Based on the segmentation form as binary images, representing extracted articular cartilage and its respective features, we compute descriptive statistics, pointing out on individual distribution’s error functions, which show percentual differences of individual features, and a distribution of values for the individual parameters of segmentation performance (SSIM and index of correlation). Here, the evaluation parameters were computed between the gold standard binary image and the results of the fuzzy thresholding with the ABC algorithm. Figure 21 provides a graphical representation of the distributions of differences for cartilage features and the distribution of values for performance parameters for fuzzy soft thresholding with ABC optimization. Based on the results of the quantitative analysis of difference function for the extracted features, we did not achieve significant differences between the gold standard images and fuzzy soft thresholding with the ABC algorithm. Mostly the distributions of difference function are kept under 6% of difference. Based on this analysis, we provide the descriptive characteristics (Table 13), which reports the median and standard deviation for each parameter. Based on these results, the best result in median difference is achieved for the feature of skeleton length (2.42%); contrarily, the worst median difference is achieved for the area (4.12%). From the view of measuring variability (standard deviation) of the difference function, the lowest difference is achieved for the skeleton (1.38%) in the contrast with the parameter area, where the difference was the worst (2.44%). The second studied aspect is the performance parameters: the index of correlation and the SSIM. Here, we achieved a higher median for correlation (0.94), where the median for the SSIM was 0.89. Furthermore, from the view of standard deviation, representing the concentration of values is better than the index of correlation (0.017), while in SSIM we achieved 0.028. Sensors 2022,22, 6335 34 of 38 Figure 21. Evaluation of percentage difference distributions for fuzzy soft thresholding with ABC algorithm (against manual segmentation) for cartilage features: area, perimeter, and skeleton and distributions of performance parameters: index of correlation and SSIM. Table 13. Descriptive statistic of difference functions for extracted features, where the best results are indicated as green and the worst as red. Cartilage Features Median Diff (%) Standard Deviation Diff (%) Area 4.12 2.44 Perimeter 3.51 1.85 Skeleton 2.42 1.38 5. Discussion and Conclusions Based on the provided results, significant differences among individual methods can be observed. In such comparisons, routine methods show significantly worse results when comparing with the evolutionary algorithms. Along these characteristics, we also provide the average values for all the noise levels to provide a global view on all the studied methods. By this statistical comparison, in most cases the ABC algorithm seems to be the most effective. On the other hand, the use of the genetic algorithm for medical image segmentation strategies does not give satisfactory results. Furthermore, this strategy is enough time demanding. We also studied the time complexity for all the studied methods for three different number of segmentation regions. Here, we can conclude that the increasing number of regions increases the time complexity. These comparisons also bring notable differences among routine methods and optimization strategies. The routine methods are less time demanding in the contrast with the optimization strategies, which is predictable because the evolution strategies usually represent complex procedures. The interesting notable fact from this study is the comparison between the hard thresholdingbased approaches with PSO and its variants and soft thresholding with the ABC algorithm. Mostly, soft thresholding overcame the concept of hard thresholding. In this view, the soft thresholding appears as more efficient. On the other hand, the hard thresholding strategies in this study are less time demanding. It is important to mention that the quantitative Sensors 2022,22, 6335 35 of 38 characteristics of the segmentation performance are represented by the trend characteristics (Figures 14–17) of the evaluation parameters, including the index of correlation, SSIM, MSE, and SNR. Ideally, these characteristics would be represented by a monotonous trend clearly defining a progress of the segmentation performance upon dynamic noise. The real results sometimes show certain variations in the form of local oscillations where the complex trends do not have to be always monotonous. This may be caused by the fact that upon various noise intensities, individual segmentation regions are differently affected by additive noise, which contributes to the total effectivity. This phenomenon is connected with the fact that the noise generators work on the principle of random definition of noise. Although this study reveals a complex view of selected aspects of the employment of evolutionary computing methods and genetic algorithms for medical image segmentation, there are still open issues for further research in this area. In the future research, it would be worth studying in detail various settings of population size and the number of iterations in the context of their impact on the segmentation accuracy. The further important aspect is the definition of criteria for the evaluation of the most suitable threshold settings. Here, we use Kapur entropy as the fitness function. Nevertheless, other alternatives may be plausible. For instance, using a local statistic of variability of pixel’s distribution inside of regions appears to be a reasonable alternative. Based on these open issues we would like to build future research in this area. Author Contributions: Conceptualization, J.K., O.P. and A.V.; methodology, M.P. and M.C.; software, R.S. and D.O.; validation, K.H., M.P. and M.A.; formal analysis, K.H. and R.S.; investigation, K.H. and D.O.; resources, M.P. and M.A.; data curation, M.C. and O.P.; writing—original draft preparation, J.K. and A.V.; writing—review and editing, M.P.; visualization, M.C. and M.A.; supervision, R.S.; project administration, M.P. and M.C.; funding acquisition, M.P. All authors have read and agreed to the published version of the manuscript. Funding: This paper was supported by project No. CZ.02.1.01/0.0/0.0/17 049/0008441, Innovative Therapeutic Methods of Musculoskeletal System in Accident Surgery within the Operational Programme Research, Development and Education financed by the European Union and by the state budget of the Czech Republic. The work and the contributions were supported by the project SV4502261/SP2022/98 ‘Biomedical Engineering systems XVIII’. Project Research and development of the new MEDIMONITOR system for intelligent prognosis forecasting—CZ: Výzkum a vývoj nového systému MEDIMONITOR pro inteligentníprognózovánívývoje diagnóz-OPPIK–MPO: CZ.01.1.02/0.0/0.0/20_321/0024858. This publication has been produced with the support of the Integrated Infrastructure Operational Program for the project: Creation of a Digital Biobank to support the systemic public research infrastructure, ITMS: 313011AFG4, co-financed by the European Regional Development Fund. This study was supported by the research project The Czech Science Foundation (TACR) No. TL02000313 Development of intelligent neuro-rehabilitation system for patients with acquired brain damage in early stages of treatment. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. We used the MR images from publicly available database The Osteoarthritis Initiative. Data Availability Statement: Data are used from publicly open clinical database The Osteoarthritis Initiative. The published SW application for articular cartilage segmentation based on the analyzed segmentation strategies with optimization algorithms can be found via the link: https://www.dropbox. com/sh/mrhnilirfz1tccz/AAATYhbioFPHX9x3cd6gVyUNa?dl=0 (accessed on 20 June 2022). Conflicts of Interest: The authors declare no conflict of interest. Sensors 2022,22, 6335 36 of 38 References 1. Deng, X.; Zhang, H.; Yang, Y. Ultrasonic Image Segmentation Algorithm of Thyroid Nodules Based on DPCNN. In Proceedings of the 2021 International Conference on Medical Imaging and Computer-Aided Diagnosis (MICAD 2021), Birmingham, UK, 25–26 March 2022; Lecture Notes in Electrical Engineering; Volume 784, pp. 163–174. [CrossRef] 2. Yang, X.; Xu, G.; Zhou, T. An effective approach for CT lung segmentation using region growing. J. Phys. Conf. Ser. 2021 ,2082, 012001. [CrossRef] 3. Fang, L.; Wang, X.; Wang, M. Superpixel/voxel medical image segmentation algorithm based on the regional interlinked value. Pattern Anal. Appl. 2021,24, 1685–1698. [CrossRef] 4. Mangrulkar, A.; Rane, S.B.; Sunnapwar, V. Automated skull damage detection from assembled skull model using computer vision and machine learning. Int. J. Inf. Technol. 2021,13, 1785–1790. [CrossRef] 5. Le, N.; Bui, T.; Vo-Ho, V.-K.; Yamazaki, K.; Luu, K. Narrow Band Active Contour Attention Model for Medical Segmentation. Diagnostics 2021,11, 1393. [CrossRef] 6. Filali, I.; Belkadi, M.; Aoudjit, R.; Lalam, M. Graph weighting scheme for skin lesion segmentation in macroscopic images. Biomed. Signal Process. Control 2021,68, 102710. [CrossRef] 7. Rebouças, E.D.S.; de Medeiros, F.N.S.; Marques, R.C.P.; Chagas, J.V.S.; Guimarães, M.T.; Santos, L.O.; Medeiros, A.G.; Peixoto, S.A. Level set approach based on Parzen Window and floor of log for edge computing object segmentation in digital images. Appl. Soft Comput. 2021,105, 107273. [CrossRef] 8. Qi, Y.; Li, J.; Chen, H.; Guo, Y.; Yin, Y.; Gong, G.; Wang, L. Computer-aided diagnosis and regional segmentation of nasopharyngeal carcinoma based on multi-modality medical images. Int. J. Comput. Assist. Radiol. Surg. 2021,16, 871–882. [CrossRef] 9. Hu, Y.-C.; Mageras, G.; Grossberg, M. Multi-class medical image segmentation using one-vs-rest graph cuts and majority voting. J. Med. Imaging 2021,8, 034003. [CrossRef] 10. Song, M.; Kim, Y. Manipulating Retinal OCT data for Image Segmentation based on Encoder-Decoder Network. In Proceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021, Seoul, Korea, 4–6 January 2021. [CrossRef] 11. Zheng, Z.; Oda, M.; Mori, K. Graph Cuts Loss to Boost Model Accuracy and Generalizability for Medical Image Segmentation. In Proceedings of the 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW), Montreal, BC, Canada, 11–17 October 2021; pp. 3297–3306. [CrossRef] 12. Sheng, A.; Li, A.; Xia, J.; Ye, Y. Application of MRI Image Based on Computer Semiautomatic Segmentation Algorithm in the Classification Prediction of Breast Cancer Histology. J. Health Eng. 2021,2021, 6088322. [CrossRef] 13. Cai, L.T.; Baida, M.; Wren-Jarvis, J.; Bourla, I.; Mukherjee, P. Diffusion MRI Automated Region of Interest Analysis in Standard Atlas Space versus the Individual’s Native Space. In Proceedings of the Computational Diffusion MRI: 12th International Workshop, CDMRI 2021, Strasbourg, France, 1 October 2021; Volume 13006, pp. 109–120. [CrossRef] 14. Wang, L.; Song, T.; Katayama, T.; Jiang, X.; Shimamoto, T.; Leu, J.-S. Deep Regional Metastases Segmentation for Patient-Level Lymph Node Status Classification. IEEE Access 2021,9, 129293–129302. [CrossRef] 15. Kaviani, S.; Han, K.J.; Sohn, I. Adversarial attacks and defenses on AI in medical imaging informatics: A survey. Expert Syst. Appl. 2022,198, 116815. [CrossRef] 16. Esengönül, M.; Marta, A.; Beirão, J.; Pires, I.M.; Cunha, A. A Systematic Review of Artificial Intelligence Applications Used for Inherited Retinal Disease Management. Medicina 2022,58, 504. [CrossRef] 17. Loddo, A.; Putzu, L. On the Reliability of CNNs in Clinical Practice: A Computer-Aided Diagnosis System Case Study. Appl. Sci. 2022,12, 3269. [CrossRef] 18. Avery, E.; Sanelli, P.C.; Aboian, M.; Payabvash, S. Radiomics: A Primer on Processing Workflow and Analysis. Semin. Ultrasound CT MRI 2022,43, 142–146. [CrossRef] 19. Gu, W.; Bai, S.; Kong, L. A review on 2D instance segmentation based on deep neural networks. Image Vis. Comput. 2022 ,120, 104401. [CrossRef] 20. Abdou, M.A. Literature review: Efficient deep neural networks techniques for medical image analysis. Neural Comput. Appl. 2022,34, 5791–5812. [CrossRef] 21. Jeong, J.J.; Tariq, A.; Adejumo, T.; Trivedi, H.; Gichoya, J.W.; Banerjee, I. Systematic Review of Generative Adversarial Networks (GANs) for Medical Image Classification and Segmentation. J. Digit. Imaging 2022,35, 137–152. [CrossRef] 22. Zhang, J.; Li, C.; Rahaman, M.; Yao, Y.; Ma, P.; Zhang, J.; Zhao, X.; Jiang, T.; Grzegorzek, M. A comprehensive review of image analysis methods for microorganism counting: From classical image processing to deep learning approaches. Artif. Intell. Rev. 2022,55, 2875–2944. [CrossRef] 23. Bhalodiya, J.M.; Keung, S.N.L.C.; Arvanitis, T.N. Magnetic resonance image-based brain tumour segmentation methods: A systematic review. Digit. Health 2022,8, 20552076221074122. [CrossRef] 24. Ahmed, S.M.; Mstafa, R.J. A Comprehensive Survey on Bone Segmentation Techniques in Knee Osteoarthritis Research: From Conventional Methods to Deep Learning. Diagnostics 2022,12, 611. [CrossRef] 25. Ebert, L.; Dobay, A.; Franckenberg, S.; Thali, M.; Decker, S.; Ford, J. Image segmentation of post-mortem computed tomography data in forensic imaging: Methods and applications. Forensic Imaging 2022,28, 200483. [CrossRef] 26. Guan, H.; Liu, M. Domain Adaptation for Medical Image Analysis: A Survey. IEEE Trans. Biomed. Eng. 2022 ,69, 1173–1185. [CrossRef] [PubMed] Sensors 2022,22, 6335 37 of 38 27. Spadarella, G.; Perillo, T.; Ugga, L.; Cuocolo, R. Radiomics in Cardiovascular Disease Imaging: From Pixels to the Heart of the Problem. Curr. Cardiovasc. Imaging Rep. 2022,15, 11–21. [CrossRef] 28. Muntarina, K.; Shorif, S.B.; Uddin, M.S. Notes on edge detection approaches. Evol. Syst. 2022,13, 169–182. [CrossRef] 29. Mishra, I.; Aravinda, K.; Kumar, J.A.; Keerthi, C.; Shree, R.D.; Srikumar, S. Medical Imaging using Signal Processing: A Comprehensive Review. In Proceedings of the 2022 Second International Conference on Artificial Intelligence and Smart Energy (ICAIS), Coimbatore, India, 23–25 February 2022; pp. 623–630. [CrossRef] 30. Rafi, A.; Khan, Z.; Aslam, F.; Jawed, S.; Shafique, A.; Ali, H. A Review: Recent Automatic Algorithms for the Segmentation of Brain Tumor MRI. In AI and IoT for Sustainable Development in Emerging Countries; Boulouard, Z., Ouaissa, M., Ouaissa, M., El Himer, S., Eds.; Lecture Notes on Data Engineering and Communications Technologies; Springer: Cham, Switzerland, 2022; Volume 105, p. 522. [CrossRef] 31. Mo, Y.; Wu, Y.; Yang, X.; Liu, F.; Liao, Y. Review the state-of-the-art technologies of semantic segmentation based on deep learning. Neurocomputing 2022,493, 626–646. [CrossRef] 32. Vizcarra, J.C.; Burlingame, E.A.; Hug, C.B.; Goltsev, Y.; White, B.S.; Tyson, D.R.; Sokolov, A. A community-based approach to image analysis of cells, tissues and tumors. Comput. Med. Imaging Graph. 2022,95, 102013. [CrossRef] 33. Skupski, D.W.; Duzyj, C.M.; Scholl, J.; Perez-Delboy, A.; Ruhstaller, K.; Plante, L.A.; Hart, L.A.; Palomares, K.T.S.; Ajemian, B.; Rosen, T.; et al. Evaluation of classic and novel ultrasound signs of placenta accreta spectrum. Ultrasound Obstet. Gynecol. 2022,59, 465–473. [CrossRef] 34. Radhika, R.; Mahajan, R. Medical Image Enhancement: A Review. Proc. Int. Conf. Data Sci. Appl. 2022,288, 105–118. [CrossRef] 35. Zaki, M.Z.A.A.; Som, M.H.M.; Yazid, H.; Basaruddin, K.S.; Basah, S.N.; Ali, M.S.A.M. A Review on Edge Detection on Osteogenesis Imperfecta (OI) Image using Fuzzy Logic. J. Phys. Conf. Ser. 2021,2071, 012040. [CrossRef] 36. Biswas, S.; Hazra, R. State-of-the-Art Level Set Models and Their Performances in Image Segmentation: A Decade Review. Arch. Comput. Methods Eng. 2021,29, 2019–2042. [CrossRef] 37. Gaddam, V.K.; Boddapati, R.; Kumar, T.; Kulkarni, A.V.; Bjornsson, H. Application of “OTSU”—An image segmentation method for differentiation of snow and ice regions of glaciers and assessment of mass budget in Chandra basin, Western Himalaya using Remote Sensing and GIS techniques. Environ. Monit. Assess. 2022,194, 337. [CrossRef] 38. Chen, M.; Zhang, Z.; Wu, H.; Xie, S.; Wang, H. Otsu-Kmeans gravity-based multi-spots center extraction method for microlens array imaging system. Opt. Lasers Eng. 2022,152, 106968. [CrossRef] 39. Deng, Q.; Shi, Z.; Ou, C. Self-Adaptive Image Thresholding within Nonextensive Entropy and the Variance of the Gray-Level Distribution. Entropy 2022,24, 319. [CrossRef] 40. Uplaonkar, D.S.; Virupakshappa; Patil, N. Modified Otsu thresholding based level set and local directional ternary pattern technique for liver tumor segmentation. Int. J. Syst. Assur. Eng. Manag. 2022, 1–11. [CrossRef] 41. Kanthavel, R.; Dhaya, R.; Venusamy, K. Detection of Osteoarthritis Based on EHO Thresholding. Comput. Mater. Contin. 2022 ,71, 5783–5798. [CrossRef] 42. Mattheus, J.; Grobler, H.; Abu-Mahfouz, A.M. A Review of Motion Segmentation: Approaches and Major Challenges. In Proceedings of the 2020 2nd International Multidisciplinary Information Technology and Engineering Conference, IMITEC 2020, Kimberley, South Africa, 25–27 November 2020; pp. 1–8. [CrossRef] 43. Jayalakshmi, D.; Dheeba, J. Border Detection in Skin Lesion Images Using an Improved Clustering Algorithm. Int. J. e-Collab. 2020,16, 15–29. [CrossRef] 44. Anilkumar, K.; Manoj, V.; Sagi, T. A survey on image segmentation of blood and bone marrow smear images with emphasis to automated detection of Leukemia. Biocybern. Biomed. Eng. 2020,40, 1406–1420. [CrossRef] 45. Chen, Z.; Guo, B.; Lib, C.; Liu, H. Review on Superpixel Generation Algorithms Based on Clustering. In Proceedings of the 2020 IEEE 3rd International Conference on Information Systems and Computer Aided Education (ICISCAE), Dalian, China, 27–29 September 2020; pp. 532–537. [CrossRef] 46. Hu, X.; Chen, Q.; Ye, X.; Zhang, D.; Tang, Y.; Ye, J. Research on the Region-Growing and Segmentation Technology of Micro-Particle Microscopic Images Based on Color Features. Symmetry 2021,13, 2325. [CrossRef] 47. Ali, N.H.; Abdullah, A.R.; Saad, N.M.; Muda, A.S.; Sutikno, T.; Jopri, M.H. Brain stroke computed tomography images analysis using image processing: A Review. IAES Int. J. Artif. Intell. (IJAI) 2021,10, 1048–1059. [CrossRef] 48. Kordt, J.; Brachmann, P.; Limberger, D.; Lippert, C. Interactive Volumetric Region Growing for Brain Tumor Segmentation on MRI using WebGL. In Proceedings of the Web3D 2021: 26th ACM International Conference on 3D Web Technology, Pisa, Italy, 8–12 November 2021. [CrossRef] 49. Habib, H.; Amin, R.; Ahmed, B.; Hannan, A. Hybrid algorithms for brain tumor segmentation, classification and feature extraction. J. Ambient Intell. Humaniz. Comput. 2022,13, 2763–2784. [CrossRef] 50. Rmili, M.; El Moutaouakkil, A.; Saleck, M.M. Hybrid Mammogram Segmentation Using Watershed and Region Growing. In Advances in Information, Communication and Cybersecurity; Maleh, Y., Alazab, M., Gherabi, N., Tawalbeh, L., Abd El-Latif, A.A., Eds.; Lecture Notes in Networks and Systems; Springer: Cham, Switzerland, 2022; Volume 357, pp. 23–32. [CrossRef] 51. Krishnammal, P.M.; Therase, L.M.; Devi, E.A.; Joany, R.M. Wavelets and Convolutional Neural Networks-Based Automatic Segmentation and Prediction of MRI Brain Images. IOT Smart Syst. 2022,251, 229–241. [CrossRef] 52. Su, M.; Shi, W.; Zhao, D.; Cheng, D.; Zhang, J. A High-Precision Method for Segmentation and Recognition of Shopping Mall Plans. Sensors 2022,22, 2510. [CrossRef] Sensors 2022,22, 6335 38 of 38 53. Luisi, J.D.; Lin, J.L.; Ameredes, B.T.; Motamedi, M. Spatial-Temporal Speckle Variance in the En-Face View as a Contrast for Optical Coherence Tomography Angiography (OCTA). Sensors 2022,22, 2447. [CrossRef] 54. Khan, A.-M.; Haque, F.; Hasan, K.R.; Alajmani, S.H.; Baz, M.; Masud, M.; Nahid, A.-A. LLDNet: A Lightweight Lane Detection Approach for Autonomous Cars Using Deep Learning. Sensors 2022,22, 5595. [CrossRef] 55. Bai, K.; Wang, J.; Wang, H. A Pupil Segmentation Algorithm Based on Fuzzy Clustering of Distributed Information. Sensors 2021,21, 4209. [CrossRef] 56. Shia, W.-C.; Hsu, F.-R.; Dai, S.-T.; Guo, S.-L.; Chen, D.-R. Semantic Segmentation of the Malignant Breast Imaging Reporting and Data System Lexicon on Breast Ultrasound Images by Using DeepLab v3+. Sensors 2022,22, 5352. [CrossRef] 57. Giang, T.T.H.; Khai, T.Q.; Im, D.-Y.; Ryoo, Y.-J. Fast Detection of Tomato Sucker Using Semantic Segmentation Neural Networks Based on RGB-D Images. Sensors 2022,22, 5140. [CrossRef] 58. Ciecholewski, M.; Kassja´nski, M. Computational Methods for Liver Vessel Segmentation in Medical Imaging: A Review. Sensors 2021,21, 2027. [CrossRef] [PubMed] 59. Zhu, Y.; Zhang, F.; Li, L.; Lin, Y.; Zhang, Z.; Shi, L.; Tao, H.; Qin, T. Research on Classification Model of Panax notoginseng Taproots Based on Machine Vision Feature Fusion. Sensors 2021,21, 7945. [CrossRef] [PubMed] 60. Liu, Y.; Zhu, M.; Wang, J.; Guo, X.; Yang, Y.; Wang, J. Multi-Scale Deep Neural Network Based on Dilated Convolution for Spacecraft Image Segmentation. Sensors 2022,22, 4222. [CrossRef] [PubMed] 61. Kweon, J.; Yoo, J.; Kim, S.; Won, J.; Kwon, S. A Novel Method Based on GAN Using a Segmentation Module for Oligodendroglioma Pathological Image Generation. Sensors 2022,22, 3960. [CrossRef] 62. Yamanakkanavar, N.; Choi, J.Y.; Lee, B. Multiscale and Hierarchical Feature-Aggregation Network for Segmenting Medical Images. Sensors 2022,22, 3440. [CrossRef] 63. Ali, R.; Hardie, R.C.; Narayanan, B.N.; Kebede, T.M. IMNets: Deep Learning Using an Incremental Modular Network Synthesis Approach for Medical Imaging Applications. Appl. Sci. 2022,12, 5500. [CrossRef] 64. Jimenez-Castaño, C.A.; Álvarez-Meza, A.M.; Aguirre-Ospina, O.D.; Cárdenas-Peña, D.A.; Orozco-Gutiérrez, A. Random Fourier Features-Based Deep Learning Improvement with Class Activation Interpretability for Nerve Structure Segmentation. Sensors 2021,21, 7741. [CrossRef] 65. Ali, R.; Hardie, R.C.; Ragb, H.K. Ensemble Lung Segmentation System Using Deep Neural Networks. In Proceedings of the 2020 IEEE Applied Imagery Pattern Recognition Workshop (AIPR), Washington, DC, USA, 13–15 October 2020; pp. 1–5. [CrossRef] 66. Otsu, N. A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 1979,9, 62–66. [CrossRef] 67. Kubicek, J.; Valosek, J.; Penhaker, M.; Bryjova, I.; Grepl, J. Extraction of Blood Vessels Using Multilevel Thresholding with Color Coding. In Advanced Computer and Communication Engineering Technology; Sulaiman, H., Othman, M., Othman, M., Rahim, Y., Pee, N., Eds.; Lecture Notes in Electrical Engineering; Springer: Cham, Switzerland, 2015; Volume 362, pp. 397–406. [CrossRef] 68. MacQueen, J. Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics; University of California Press: Berkeley, CA, USA, 1967; Volume 5.1, pp. 281–298. 69. Kapur, J.N.; Sahoo, P.K.; Wong, A.K.C. A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 1985,29, 273–285. [CrossRef] 70. Lang, C.; Jia, H. Kapur’s Entropy for Color Image Segmentation Based on a Hybrid Whale Optimization Algorithm. Entropy 2019,21, 318. [CrossRef] 71. NIMH Data Archive—OAI (The Osteoarthritis Initiative). National Institutes of Health. U.S. Department of Health and Human Services. Available online: https://nda.nih.gov/oai/ (accessed on 15 May 2022). 72. Xue, Y.-P.; Jang, H.; Byra, M.; Cai, Z.-Y.; Wu, M.; Chang, E.Y.; Ma, Y.-J.; Du, J. Automated cartilage segmentation and quantification using 3D ultrashort echo time (UTE) cones MR imaging with deep convolutional neural networks. Eur. Radiol. 2021 ,31, 7653–7663. [CrossRef]