# Segmentation of Articular Cartilage and Early Osteoarthritis based on the Fuzzy Soft Thresholding Approach Driven by Modified Evolutionary ABC Optimization and Local Statistical Aggregation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Recent Methods of Cartilage Segmentation

## 3. Materials and Methods

#### 3.1. Soft Segmentation of Intensity Spectrum

^{th}segmentation class is given as ${\mu}_{n}\left(k\right)$. When using the triangular function, a membership satisfies a condition:

- Complete division: $\forall k,\exists {\mu}_{l}\left(k\right),1\le l\le p$, so that ${\mu}_{l}\left(k\right)>0$.
- Consistency: if ${\mu}_{n}\left({k}_{0}\right)=1$, then ${\mu}_{m}\left({k}_{0}\right)=0,\forall n\ne m$.
- Normality: $\mathrm{max}\left({\mu}_{n}\left(k\right)\right)=1$.
- Intersection between adjacent fuzzy sets: ${\mu}_{n}\left({k}_{0}\right)={\mu}_{n+1}\left({k}_{0}\right)=0.5\left|\right|{\mu}_{n-1}\left({k}_{0}\right)={\mu}_{n}\left({k}_{0}\right)=0.5$.

#### 3.2. Process of Centroids Extraction

#### 3.3. Modified ABC Algorithm

^{th}solution in the bee swarm, where p stands for a size of the dimension, and in other words these are the number of optimized centroids of the multiregional soft segmentation model.

_{p}represents 100 p% quantile and n represents the range of sample data (we analyzed 200 MR image records).

^{th}solution and L denotes a vector of segmentation classes: $L=\left\{1,2,\dots ,p\right\}$. Vector ${C}_{L}$ stands for the i

^{th}sequence of the centroids generated by the K-means clustering in the form: ${C}_{L}=\left\{{C}_{1},{C}_{2},\dots {C}_{p}\right\}$. In each ${C}_{L}$, we have to identify and replace centroid representing the cartilage area. In order to do this task, we use the following formulation:$\underset{\forall k\in L}{{C}_{i,cartilage}=\mathrm{min}}\left|{C}_{i,k}-{I}_{c}^{{R}_{i}}\right|$. ${C}_{cartilage}$ replaces a respective centroid from ${C}_{L}$ for each solution in the swarm based on the minimal distance where ${I}_{c}^{{R}_{i}}$ stands for randomly chosen value from I

_{c}.

_{Vi}> fit

_{Xi}, V

_{i}is stored in the memory. Otherwise, a new ${V}_{i}$ is generated. The maximal number of such repetitions is controlled by the choice limit ${L}_{v}$ (we use: ${L}_{v}$=10). When the ${L}_{v}$ is exhausted, the ${X}_{i}$ is perceived as an exhausted food source.

#### 3.4. Features Extraction Based on Fitness Function

#### 3.5. Local Statistical Aggregation

## 4. Results

## 5. Quantitative Comparison and Segmentation Performance

**Otsu thresholding (Otsu-N):**Hard thresholding segmentation utilizing image partitioning into N regions.**Fuzzy C means (FCM):**Represents clustering. An algorithm generates clusters into c parts, attempts to find centroids of natural clusters in the data. For this task, a minimization of the inner clustering variance based on error function is used.**Iterative thresholding (ITS):**The initial thresholding is iteratively adjusted based on the local information and the resulting threshold is less sensitive against the noise.**Maximal Spatial Probability (MASP):**It is a segmentation, considering the spatial information. A probability of pixel’s belonging to respective class, in a frame of spatial restrictions, is defined as spatial probability.

**Rand Index (RI):**Measures a similarity between two segmentation regions. RI compares the compatibility of an assignment between pairs of elements in two regions. The RI formulation is as follows:

**Variation Information (VI):**measures distance between two segmentations in a sense of their conditional entropy, which is defined:

_{i}and I is a mutual information between ${C}_{1}$ and ${C}_{2}$.

**Segmentation Overlapping:**overlapping ${C}_{1}$ by ${C}_{2}$ is defined as follows:

## 6. Discussion

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Hayashi, D.; Roemer, F.W.; Jarraya, M.; Guermazi, A. Imaging of osteoarthritis. In Geriatric Imaging; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar] [CrossRef]
- Felson, D.T.; Niu, J.; Gross, K.D.; Englund, M.; Sharma, L.; Cooke, T.D.V.; Guermazi, A.; Roemer, F.W.; Segal, N.; Nevitt, M.C. Valgus malalignment is a risk factor for lateral knee osteoarthritis incidence and progression: Findings from the multicenter osteoarthritis study and the osteoarthritis initiative. Arthritis Rheum.
**2013**, 65, 355–362. [Google Scholar] [CrossRef] [PubMed] - Link, T.M. MR imaging in osteoarthritis: Hardware, coils, and sequences. Radiol. Clin.
**2009**, 474, 617–632. [Google Scholar] [CrossRef] [PubMed] - Guermazi, A.; Hayashi, D.; Roemer, F.W.; Felson, D.T. Osteoarthritis: A review of strengths and weaknesses of different imaging options. Rheum. Dis. Clin.
**2013**, 39, 567–591. [Google Scholar] [CrossRef] [PubMed] - Park, H.J.; Kim, S.S.; Lee, S.Y.; Park, N.H.; Park, J.Y.; Choi, Y.J.; Jeon, H.J. A practical MRI grading system for osteoarthritis of the knee: Association with Kellgren-Lawrence radiographic scores. Eur. J. Radiol.
**2013**, 82, 112–117. [Google Scholar] [CrossRef] [PubMed] - Li, X.; Pedoia, V.; Kumar, D.; Rivoire, J.; Wyatt, C.; Lansdown, D.; Amano, K.; Okazaki, N.; Savic, D.; Koff, M.F.; et al. Cartilage T 1ρ and T 2 relaxation times: Longitudinal reproducibility and variations using different coils, MR systems and sites. Osteoarthr. Cartil.
**2015**, 23, 2214–2223. [Google Scholar] [CrossRef] [PubMed] - Shelbourne, K.D.; Urch, S.E.; Gray, T.; Freeman, H. Loss of normal knee motion after anterior cruciate ligament reconstruction is associated with radiographic arthritic changes after surgery. Am. J. Sports Med.
**2012**, 40, 108–113. [Google Scholar] [CrossRef] [PubMed] - Hunter, D.J.; Arden, N.; Conaghan, P.G.; Eckstein, F.; Gold, G.; Grainger, A.; Zhang, W. Definition of osteoarthritis on MRI: Results of a Delphi exercise. Osteoarthr. Cartil.
**2011**, 19, 863–969. [Google Scholar] [CrossRef] - Sheehy, L.; Culham, E.; McLean, L.; Niu, J.; Lynch, J.; Segal, N.A.; Cooke, T.D.V. Validity and sensitivity to change of three scales for the radiographic assessment of knee osteoarthritis using images from the Multicenter Osteoarthritis Study (MOST). Osteoarthr. Cartil.
**2015**, 23, 1491–1498. [Google Scholar] [CrossRef] [PubMed][Green Version] - Stefanik, J.J.; Guermazi, A.; Zhu, Y.; Zumwalt, A.C.; Gross, K.D.; Clancy, M.; Felson, D.T. Quadriceps weakness, patella alta, and structural features of patellofemoral osteoarthritis. Arthr. Care Res.
**2011**, 63, 1391–1397. [Google Scholar] [CrossRef] [PubMed] - Braun, H.J.; Gold, G.E. Diagnosis of osteoarthritis: Imaging. Bone
**2012**, 51, 278–288. [Google Scholar] [CrossRef] - Boesen, M.; Ellegaard, K.; Henriksen, M.; Gudbergsen, H.; Hansen, P.; Bliddal, H.; Riis, R.G. Osteoarthritis year in review 2016: Imaging. Osteoarthr. Cartil.
**2017**, 25, 216–226. [Google Scholar] [CrossRef] [PubMed] - Wenham, C.Y.J.; Grainger, A.J.; Conaghan, P.G. The role of imaging modalities in the diagnosis, differential diagnosis and clinical assessment of peripheral joint osteoarthritis. Osteoarthr. Cartil.
**2014**, 22, 1692–1702. [Google Scholar] [CrossRef] [PubMed][Green Version] - Trattnig, S.; Winalski, C.S.; Marlovits, S.; Jurvelin, J.S.; Welsch, G.H.; Potter, H.G. Magnetic resonance imaging of cartilage repair: A review. Cartilage
**2011**, 2, 5–26. [Google Scholar] [CrossRef] [PubMed] - Kijowski, R.; Blankenbaker, D.G.; Munoz del Rio, A.; Baer, G.S.; Graf, B.K. Evaluation of the Articular Cartilage of the Knee Joint: Value of adding a T2 mapping sequence to a routine mr imaging protocol. Radiology
**2013**, 267, 503–513. [Google Scholar] [CrossRef] [PubMed] - Guermazi, A.; Roemer, F.W.; Alizai, H.; Winalski, C.S.; Welsch, G.; Brittberg, M.; Trattnig, S. State of the art: MR imaging after knee cartilage repair surgery. Radiology
**2015**, 277, 23–43. [Google Scholar] [CrossRef] - Ho-Fung, V.M.; Jaramillo, D. Cartilage imaging in children. Current indications, magnetic resonance imaging techniques, and imaging findings. Radiol. Clin. N. Am.
**2013**. [Google Scholar] [CrossRef] - Jungmann, P.M.; Baum, T.; Bauer, J.S.; Karampinos, D.C.; Erdle, B.; Link, T.M.; Welsch, G.H. Cartilage repair surgery: Outcome evaluation by using noninvasive cartilage biomarkers based on quantitative mri techniques? BioMed Res. Int.
**2014**. [Google Scholar] [CrossRef] - Suppanee, R.; Yazdifar, M.; Chizari, M.; Esat, I.; Bardakos, N.V.; Field, R.E. Simulating osteoarthritis: The effect of the changing thickness of articular cartilage on the kinematics and pathological bone-to-bone contact in a hip joint with femoroacetabular impingement. Eur. Orthop. Traumatol.
**2014**, 5, 65–73. [Google Scholar] [CrossRef] - Wu, Y.; Krishnan, S.; Rangayyan, R.M. Computer-aided diagnosis of knee-joint disorders via vibroarthrographic signal analysis: A review. Crit. Rev. TM Biomed. Eng.
**2012**, 38. [Google Scholar] [CrossRef] - Eckstein, F.; Glaser, C. Measuring cartilage morphology with quantitative magnetic resonance imaging. Semin. Musculoskelet. Radiol.
**2004**. [Google Scholar] [CrossRef] - Lee, K.Y.; Dunn, T.C.; Steinbach, L.S.; Ozhinsky, E.; Ries, M.D.; Majumdar, S. Computer-aided quantification of focal cartilage lesions of osteoarthritic knee using MRI. Magn. Reson. Imaging
**2004**, 22, 1105–1115. [Google Scholar] [CrossRef] [PubMed] - Dam, E.B.; Folkesson, J.; Pettersen, P.C.; Christiansen, C. Semi-automatic knee cartilage segmentation. Prog. Biomed. Opt. Imaging—Proc. SPIE
**2006**, 6144, 614441. [Google Scholar] - Görres, J.; Brehler, M.; Franke, J.; Vetter, S.Y.; Grützner, P.A.; Meinzer, H.-P.; Wolf, I. Articular surface segmentation using active shape models for intraoperative implant assessment. Int. J. Comput. Assist. Radiol. Surg.
**2016**, 11, 1661–1672. [Google Scholar] [CrossRef] [PubMed] - Tabrizi, P.R.; Zoroofi, R.A.; Yokota, F.; Nishii, T.; Sato, Y. Shape-based acetabular cartilage segmentation: Application to CT and MRI datasets. Int. J. Comput. Assist. Radiol. Surg.
**2016**, 11, 1247–1265. [Google Scholar] [CrossRef] [PubMed] - Tabrizi, P.R.; Zoroofi, R.A.; Yokota, F.; Tamura, S.; Nishii, T.; Sato, Y. Acetabular cartilage segmentation in CT arthrography based on a bone-normalized probabilistic atlas. Int. J. Comput. Assist. Radiol. Surg.
**2015**, 10, 433–446. [Google Scholar] [CrossRef] [PubMed] - Fripp, J.; Crozier, S.; Warfield, S.K.; Ourselin, S. Automatic segmentation and quantitative analysis of the articular cartilages from magnetic resonance images of the knee. IEEE Trans. Med. Imaging
**2010**, 29, 55–64. [Google Scholar] [CrossRef] [PubMed] - Kumarv, A.; Jayanthy, A.K. Classification of MRI images in 2D coronal view and measurement of articular cartilage thickness for early detection of knee osteoarthritis. In Proceedings of the 2016 IEEE International Conference on Recent Trends in Electronics, Information and Communication Technology (RTEICT 2016), Bangalore, India, 20–21 May 2016; pp. 1907–1911. [Google Scholar]
- Kubicek, J.; Penhaker, M.; Augustynek, M.; Bryjova, I.; Cerny, M. Segmentation of Knee Cartilage: A Comprehensive Review. J. Med. Imaging Health Inform.
**2018**, 8, 401–418. [Google Scholar] [CrossRef] - Gougoutas, A.J.; Wheaton, A.J.; Borthakur, A.; Shapiro, E.M.; Kneeland, J.B.; Udupa, J.K.; Reddy, R. Cartilage volume quantification via Live Wire segmentation. Acad. Radiol.
**2004**, 11, 1389–1395. [Google Scholar] [CrossRef] - Mikulka, J.; Gescheidtova, E.; Bartusek, K. Modern edge-based and region-based segmentation methods. In Proceedings of the TSP 2009—32nd International Conference on Telecommunications and Signal Processing, Dunakiliti, Hungary, 26 August 2009; pp. 89–91. [Google Scholar]
- Kubicek, J.; Vicianova, V.; Penhaker, M.; Augustynek, M. Time deformable segmentation model based on the active contour driven by Gaussian energy distribution: Extraction and modeling of early articular cartilage pathological interuptions. Front. Artif. Intell. Appl.
**2017**, 297, 242–255. [Google Scholar] - Aja-Fernández, S.; Curiale, A.H.; Vegas-Sánchez-Ferrero, G. A local fuzzy thresholding methodology for multiregion image segmentation. Knowl.-Based Syst.
**2015**, 83, 1–12. [Google Scholar] [CrossRef] - Ma, M.; Liang, J.; Guo, M.; Fan, Y.; Yin, Y. SAR image segmentation based on artificial bee colony algorithm. Appl. Soft Comput. J.
**2011**, 11, 5205–5214. [Google Scholar] [CrossRef] - Horng, M.H. Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation. Expert Syst. Appl.
**2011**, 38, 13785–13791. [Google Scholar] [CrossRef] - Sağ, T.; Çunkaş, M. Color image segmentation based on multiobjective artificial bee colony optimization. Appl. Soft Comput. J.
**2015**, 34, 389–401. [Google Scholar] [CrossRef] - Osuna-Enciso, V.; Cuevas, E.; Sossa, H. A comparison of nature inspired algorithms for multi-threshold image segmentation. Expert Syst. Appl.
**2013**, 40, 1213–1219. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Clinical cases of the MR knee cartilage visualization, including the early cartilage loss, indicated as red marked circles.

**Figure 4.**Native MR knee image with active contour model detecting the physiological femoral cartilage (left), energy map of the active contour (middle), and a binary model of the physiological cartilage (right).

**Figure 6.**A complex structure for soft methodology optimization based on the modified artificial bee colony (ABC) algorithm.

**Figure 7.**Convergence characteristics for the fitness function evolution within 100 iterations: (

**a**) 100 food sources and (

**b**) 50 food sources.

**Figure 8.**Extract of native MR image, containing the articular cartilage, with the osteoarthritis change, indicated by the blue RoI. A sequence of individual segmentation models of the articular cartilage by using 6 segmentation classes is represented by (

**a**–

**f**). The color spectrum differentiates a level of individual tissue membership. Yellow color represents presence of individual tissue, while blue color identifies the background (non-presence) of the respective tissue.

**Figure 9.**Neighborhood of analyzed pixel, indicated as red where: (

**a**) it is not supposed a presence of the noisy pixels and (

**b**) analyzed centered pixel represents the image noise.

**Figure 10.**Application of the local median aggregation for: (

**a**) pixels not containing the image noise and (

**b**) noisy centered pixel.

**Figure 11.**Example of cartilage segmentation model: (

**a**) Native MR knee images, containing the early cartilage loss where the cartilage area is indicated as red, (

**b**) proposed soft segmentation model with 8 classes—cartilage is shown by yellow contour, and (

**c**) extraction of the articular cartilage where the violet RoI indicate the cartilage interruptions caused by the early cartilage loss.

**Figure 12.**Time-inverse knee image (

**a**), indicating the full chondral defect (arrows), with marked RoI for segmentation, and segmentation model (eight segmentation classes) of the time-inverse knee image after region of articular cartilage extraction (

**b**), where the focal defect is sharply indicated in red RoI. Artificial colors represent segmentation classes in the cartilage, according to the MR signal strength and other knee tissues are suppressed.

**Figure 13.**The native data of the knee area (

**a**), obtained by 2D SE imaging. The native image gives a better contrast between the cartilage surface and synovial fluid. A high contrast well differentiate cartilage defect (arrows), where the blue RoI indicates the area of the interest for segmentation. The segmentation model (

**b**) identifies a part of the cartilage region, where the cartilage defect is sharply indicated by yellow contour in the red RoI.

**Figure 14.**T2 weighted image with fat suppression (

**a**) reflects locations of the complete cartilage loss in medial tibia-femoral area with degenerative lesions in the subchondral bone (arrows), where red RoI indicates area of the interest for segmentation procedure. The segmentation model (

**b**) of the articular cartilage, reflecting the highest signal intensity (yellow contours), contrarily model detects the locations of the cartilage loss (red areas of interest), degenerative lesions are sharply indicated by yellow contour in the blue RoI.

**Figure 15.**Sagittal 3.0T MR image of knee area of healthy volunteer, not exhibiting significant differences in manifestation of the articular cartilage (

**a**) and cartilage segmentation model (

**b**), identifying the morphological structure homogeneity (yellow contour).

**Figure 16.**Sagittal 7.0T MR image of the knee area of healthy volunteer, not exhibiting significant differences in manifestation of the articular cartilage (

**a**). The native data contain artefacts, caused by the magnetic susceptibility (arrows). The segmentation model of the articular cartilage (

**b**) identifies the morphological structure compactness (yellow contour).

**Figure 17.**Example of the gold standard definition by tracing the articular cartilage by clinical expert: (

**a**) manual tracing of the femoral cartilage and (

**b**) binary model of the cartilage.

**Figure 18.**A comparison of the cartilage segmentation applied on image region of the interest (RoI) 250 × 200 px: (

**a**) 3, (

**b**) 5, (

**c**) 8, and (

**d**) 12 classes.

**Figure 19.**Native results corrupted by the additive salt and pepper noise (up row) and segmentation results (down row) for noise density (d): (

**a**) ${d}_{1}=0.05$, (

**b**) ${d}_{2}=0.1$, (

**c**) ${d}_{3}=0.5,$ and (

**d**) ${d}_{4}=0.8$.

**Figure 20.**Native results corrupted by the additive Gaussian noise (up row) and segmentation results (down row) for average value ($\mu $) and dispersion (${\sigma}^{2}$): (

**a**) μ = 0, ${\sigma}_{1}{}^{2}$ = 0.01, (

**b**) μ = 0, ${\sigma}_{2}{}^{2}$ = 0.08, (

**c**) μ = 0, ${\sigma}_{3}{}^{2}$ = 0.1, and (

**d**) μ = 0, ${\sigma}_{4}{}^{2}$ = 0.8.

**Figure 21.**Native results corrupted by the multiplicative Rayleight noise (up row) and segmentation results (down row) for average value ($\mu $) and dispersion (${\sigma}^{2}$): (

**a**) μ = 0, ${\sigma}_{1}{}^{2}$ = 0.01, (

**b**) μ = 0, ${\sigma}_{2}{}^{2}$ = 0.08, (

**c**) μ = 0, ${\sigma}_{3}{}^{2}$ = 0.1, and (

**d**) μ = 0, ${\sigma}_{4}{}^{2}$ = 0.8.

**Figure 22.**A comparison of different settings of median aggregation procedure on RoI 500 × 400 pixels, with square kernel: (

**a**) 3, (

**b**) 5, (

**c**) 8, and (

**d**) 15 pixels.

**Figure 23.**Median aggregation procedure with 23-square kernel where reduction of the cartilage structure is indicated by the red RoI.

Interval median estimation | $\langle 209.54;212.37\rangle $ |

Gastwirth median estimation | 〈209.12; 211.95〉 |

Testing Image | Number of Classes | $\mathbf{f}\mathbf{i}{\mathbf{t}}_{\mathbf{b}\mathbf{e}\mathbf{s}\mathbf{t}}$ | $\mathbf{f}\mathbf{i}{\mathbf{t}}_{\mathbf{w}\mathbf{o}\mathbf{r}\mathbf{s}\mathbf{t}}$ | $\mathbf{f}\mathbf{i}{\mathbf{t}}_{\mathbf{m}\mathbf{e}\mathbf{d}\mathbf{i}\mathbf{a}\mathbf{n}}$ | ${f}\mathbf{i}{\mathbf{t}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{n}}$ | ${f}\mathbf{i}{\mathbf{t}}_{\mathbf{S}\mathbf{D}}$ |
---|---|---|---|---|---|---|

1 | 6 | 21.43 | 21.11 | 21.43 | 21.41 | 0.11 |

2 | 6 | 22.65 | 22.14 | 22.33 | 22.29 | 0.14 |

3 | 6 | 22.44 | 21.99 | 22.12 | 22.11 | 0.12 |

4 | 6 | 22.12 | 21.44 | 21.99 | 21.97 | 0.11 |

5 | 6 | 21.99 | 21.54 | 21.68 | 21.72 | 0.21 |

Testing Image [px] | Image Order | Number of Classes | Time Complexity [s] |
---|---|---|---|

(800 × 800) | 1 | 6 | 8.92 |

2 | 6 | 10.54 | |

3 | 6 | 10.12 | |

(300 × 300) | 1 | 6 | 9.91 |

2 | 6 | 9.11 | |

3 | 6 | 8.59 | |

(150 × 150) | 1 | 6 | 5.45 |

2 | 6 | 5.22 | |

3 | 6 | 6.12 |

**Table 4.**Comparative analysis of quantitative evaluation of proposed of regional segmentation. (The bold font highlights the best results in the table.).

MedAg | AvAg | FCM | Otsu-N | ITS | MASP | ||
---|---|---|---|---|---|---|---|

RI | Nat. | 0.791 | 0.728 | 0.723 | 0.723 | 0.739 | 0.698 |

Gauss. | 0.697 | 0.669 | 0.601 | 0.683 | 0.681 | 0.667 | |

Mult. | 0.681 | 0.697 | 0.665 | 0.654 | 0.612 | 0.571 | |

VI | Nat. | 2.956 | 2.611 | 2.979 | 2.675 | 2.922 | 3.459 |

Gauss. | 3.122 | 3.788 | 3.312 | 3.367 | 3.122 | 3.998 | |

Mult. | 3.233 | 3.811 | 3.711 | 3.568 | 3.679 | 3.799 | |

$\mathit{C}\left({\mathit{S}}_{\mathbf{2}}\to {\mathit{S}}_{\mathbf{1}}\right)$ | Nat. | 0.366 | 0.343 | 0.354 | 0.343 | 0.371 | 0.219 |

Gauss. | 0.298 | 0.322 | 0.291 | 0.262 | 0.312 | 0.242 | |

Mult. | 0.345 | 0.289 | 0.271 | 0.233 | 0.327 | 0.236 | |

$\mathit{C}\left({\mathit{S}}_{\mathbf{1}}\to {\mathit{S}}_{\mathbf{2}}\right)$ | Nat. | 0.498 | 0.448 | 0.455 | 0.411 | 0.467 | 0.341 |

Gauss. | 0.499 | 0.295 | 0.353 | 0.412 | 0.399 | 0.277 | |

Mult. | 0.391 | 0.365 | 0.343 | 0.367 | 0.389 | 0.311 |

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**MDPI and ACS Style**

Kubicek, J.; Penhaker, M.; Augustynek, M.; Cerny, M.; Oczka, D.
Segmentation of Articular Cartilage and Early Osteoarthritis based on the Fuzzy Soft Thresholding Approach Driven by Modified Evolutionary ABC Optimization and Local Statistical Aggregation. *Symmetry* **2019**, *11*, 861.
https://doi.org/10.3390/sym11070861

**AMA Style**

Kubicek J, Penhaker M, Augustynek M, Cerny M, Oczka D.
Segmentation of Articular Cartilage and Early Osteoarthritis based on the Fuzzy Soft Thresholding Approach Driven by Modified Evolutionary ABC Optimization and Local Statistical Aggregation. *Symmetry*. 2019; 11(7):861.
https://doi.org/10.3390/sym11070861

**Chicago/Turabian Style**

Kubicek, Jan, Marek Penhaker, Martin Augustynek, Martin Cerny, and David Oczka.
2019. "Segmentation of Articular Cartilage and Early Osteoarthritis based on the Fuzzy Soft Thresholding Approach Driven by Modified Evolutionary ABC Optimization and Local Statistical Aggregation" *Symmetry* 11, no. 7: 861.
https://doi.org/10.3390/sym11070861