# An Efficient SAR Image Segmentation Framework Using Transformed Nonlocal Mean and Multi-Objective Clustering in Kernel Space

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## Abstract

**:**

## 1. Introduction

## 2. Methodology of Mkcis

#### 2.1. Nonlocal Means Filter in PCA

_{i}, v(NB

_{i}) is the vector of neighboring pixel around i, a is the standard deviation of the Gaussian kernel, and h controls the decay of the exponential function.

_{1}, e

_{2}, …, e

_{N}} and eigenvalues Φ = {λ

_{1}, λ

_{2}, …, λ

_{N}} by de-compositing above matrix. If the d larger eigenvectors are selected to span d-dimensional space, the original neighboring vector in (2) can be denoted in the low dimensional space.

_{i}) in Equation (2). ˂v(NB

_{i}), e˃ denotes the inner product of the two vectors. The meaning of Equation (1) can be updated by non-local mean estimator in low-dimensional space.

#### 2.2. Multi-Objective Kernel Clustering in AIS

_{i}, i = 1, 2, …, N is a sample in a clustering problem and z

_{p}, p = 1, 2, …, K is the cluster center, n is the total number of samples, K is the number of categories, U

_{K × n}is the fuzzy membership matrix and L is the parameter to determine the number of neighbors that contribute to the connectivity measure. It is clear that XB

^{kernel}is formulated by calculating the ratio of the summation of variation to the minimum separation, and the lower values of the index can provide better partition of image. Conn

^{kernel}is defined by dividing Euclidian distance of datum i to its j-th nearest neighbor by gradually decreasing penalty factor. Note that K is the number of clusters and n is the total pixels.

_{i}and x

_{j}can be calculated through the kernel function $\wp ({x}_{i},{x}_{j})=\mathrm{exp}\left(-{\Vert ({x}_{i})-({x}_{j})\Vert}^{2}/(2{\sigma}^{2})\right)$ in the input space, where σ > 0, and it can be represented in the following equation, φ(x

_{i}) is the value of the features of the pixel x

_{i}.

## 3. Experimental Study

#### 3.1. Experimental Results Presentation and Discussion

**X**-band of Swabian Jura, Germany by Terra-SAR. The image with 280 × 280 pixels consists of four distinct typical land covers: urban villages and four types of crops.

#### 3.2. Sensitivity to Different Looks of Speckle Noise

#### 3.3. Influence of the Number of Eigenvectors in PCA

#### 3.4. Running Times Comparison and Analysis

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Oliver, C.; Quegan, S. Understanding Synthetic Aperture Radar Images; Artech House: Boston, MA, USA, 1988. [Google Scholar]
- Ahmed, M.N.; Yamany, S.M.; Mohamed, N.; Farag, A.A.; Moriarty, T. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans. Med. Image.
**2002**, 21, 193–199. [Google Scholar] - Chen, S.C.; Zhang, D.Q. Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Trans. Syet. Man Cybern. Part B Cybern.
**2004**, 34, 1907–1916. [Google Scholar] - Cai, W.L.; Chen, S.C.; Zhang, D.Q. Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation. Pattern Recognit.
**2007**, 40, 825–838. [Google Scholar] - Krinidis, S.; Chatzis, V. A robust fuzzy local information c-means clustering algorithm. IEEE Trans. Image Process.
**2010**, 19, 1328–1337. [Google Scholar] - Gong, M.G.; Liang, Y.; Shi, J.; Ma, W.P.; Ma, J.J. Fuzzy c-means clustering with local information and kernel metric for image segmentation. IEEE Trans. Image Process.
**2013**, 22, 573–584. [Google Scholar] - Hill, P.R.; Canagarajah, C.N.; Bull, D.R. image segmentation using a texture gradi-ent based watershed transform. IEEE Trans. Image Process.
**2003**, 12, 1618–1633. [Google Scholar] - Zhou, H.Y.; Li, X.L.; Schaefer, G.; Celebi, M.E.; Miller, P. Mean shift based gradient vector flow for image segmentation. Comput. Vis. Image Underst.
**2013**, 117, 1004–1016. [Google Scholar] [Green Version] - Zhou, H.; Schaefer, G.; Celebi, M.E.; Lin, F.; Liu, T. Gradient vector flow with mean shift for skin lesion segmentation. Comput. Med. Imaging Graph.
**2013**, 35, 121–127. [Google Scholar] - Zhou, H.Y.; Schaefer, G.; Sadka, A.H.; Celebi, M.E. Anisotropic mean shift based fuzzy c-means segmentation of dermoscopy images. IEEE J. Sel. Top. Signal Process.
**2009**, 3, 26–34. [Google Scholar] - Tasdizen, T. Principal neighborhood dictionaries for nonlocal means image denoising. IEEE Trans. Image Process.
**2009**, 18, 2649–2660. [Google Scholar] - Yang, D.D.; Jiao, L.C.; Gong, M.G.; Feng, J. Adaptive rank clone and k-nearest neighbour list based immune multi-objective optimization. Comput. Intell.
**2010**, 26, 359–385. [Google Scholar] - Handl, J.; Knowles, J. An evolutionary approach to multiobjective clustering. IEEE Trans. Evol. Comput.
**2007**, 11, 56–76. [Google Scholar] - Salah, M.B.; Mitiche, A.; Ayed, I.B. Multiregion image segmentation by parametric kernel graph cuts. IEEE Trans. Image Process.
**2011**, 20, 545–557. [Google Scholar] - Deledalle, C.; Denis, L.; Tupin, F. Iterative weighted maximum likelihood denoising with probabilistic patch-based weights. IEEE Trans. Image Process.
**2009**, 18, 2661–2672. [Google Scholar] - Parrilli, S.; Poderico, M.; Angelino, C.V.; Verdoliva, L. A nonlocal SAR image denoising algorithm based on LLMMSE wavelet shrinkage. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 606–616. [Google Scholar] - Su, X.; Deledalle, C.A.; Tupin, F.; Sun, H. Two-step multitemporal nonlocal means for synthetic aperture radar images. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 6181–6196. [Google Scholar] - Rachmawati, L.; Srinivasan, D. Multiobjective evolutionary algorithm with controllable focus on the knees of the Pareto front. IEEE Trans. Evol. Comput.
**2009**, 13, 810–824. [Google Scholar] - De Castro, L.N.; von Zuben, F.J. learning and optimization using the clonal selection principle. IEEE Trans. Evol. Comput.
**2002**, 6, 239–251. [Google Scholar] - Zhong, Y.; Zhang, L.; Huang, B.; Li, P. An unsupervised artificial immune classifier for multi/hyperspectral remote sensing imagery. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 420–431. [Google Scholar] - Bandyopadhyay, S.; Maulik, U.; Mukhopadhyay, A. Multi-objective genetic clustering for pixel classification in remote sensing imagery. IEEE Trans. Geosci. Remote Sens.
**2007**, 45, 1506–1511. [Google Scholar] - Deb, K.; Ratap, A.; Agarwal, S.; eyarivan, T.M. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] - Yang, D.D.; Jiao, L.C.; Gong, M.G.; Liu, F. Artificial immune multi-objective SAR image segmentation with fused complementary features. Inf. Sci.
**2011**, 181, 2797–2812. [Google Scholar] - Goodman, J. Some fundamental properties of speckle. J. Optic. Soc. Am.
**1976**, 66, 1145–1150. [Google Scholar]

**Figure 1.**The procedure of the synthetic aperture radar (SAR) image segmentation algorithm by using the nonlocal means filter in principal component analysis (PCA) and multi-objective kernel clustering in artificial immune system (AIS).

**Figure 3.**The segmentation results of the synthetic SAR image. (a) Original image; (b–f) segmentation results by KWFLICM, FLICM, FGFCM, KGC, and MKCIS, respectively.

**Figure 4.**The segmentation results of the real SAR image. (

**a**) Original image; (

**b–f**) segmentation results by KWFLICM, FLICM, FGFCM, KGC, and MKCIS, respectively.

**Figure 5.**Mean values of partitioning accuracy of five algorithms in segmenting the synthetic SAR image by adding simulated speckle from 1-look to 10-look.

**Figure 6.**Mean values of partitioning accuracy of five algorithms in segmenting the synthetic SAR image by adding simulated speckle from 1-look to 10-look.

**Figure 7.**Error-bar graphs of running times of KWFLICM, FLICM, FGFCM, KGC and MKCIS in segmenting the two SAR images. (

**a**) The right figure is CPU times for the synthetic SAR image; (

**b**) the left one is that of real SAR image.

**Figure 8.**Boxplot of running times of KWFLICM in segmenting the synthetic SAR images with size of 130 × 130, 260 × 260, 520 × 520, 1040 × 1040.

Input: SAR image X = {x_{1}, x_{2}, …, x_{n}}, number of clusters K, size of searching window in NLM w, number of population N; size of clonal pool C; |
---|

Step1. Perform NLM-PCA(w) filter on the input SAR image X. |

Step2. Implement the watershed transformation on the filted image and the raw segmentation results of can be denoted by X._{1} |

Step3. i=0, X is the input local image patches, initialize population _{1}P(i) randomly and compute its two objective functions F(i) in kernel method defined in equation. (5)–(6). |

[Minmal(i)] = FindBestSolution(F(i), P(i)); |

Label = 0; |

Step4. while Label < M |

[A(i), AF(i)] = FindSmallBestIndividuals(P(i), F(i), C); %find C the better solutions |

[NP(i)] = ProportionalClone(A(i), AF(i), N); %perform the clone on above selected solutions |

[NP(i)] = Crossover(NP(i), A(i)); %perform gene crossover on the above new solutions |

[NP(i)] = Mutation([NP(i)]); %perform gene perturbation (local search) on the above new solutions |

[NF(i)] = FitnessCalculation(NP(i)); %judge the above new created solutions |

TotalP = NP(i) ∪ P(i); %merge the two-consecutive-steps solution sets at variable space |

TotalF = NF(i) ∪ F(i); % merge the two-consecutive-steps solution sets at objective space |

[P(i), F(i)] = UpdatePopulation(TotalP, TotalF); % update the current solutions |

I = i+1; |

[Minmal(i)] = FindBestSolution(F(i), P(i)); % find the current best solution |

if |Minmal(i) − Minmal(I + 1)| < α |

Label = Label + 1; |

end-if |

end-while. |

Step5. find the best soltion among the final non-dominated front. Output k clusters of X. |

**Table 2.**Statistical segmentation results of accurate rate (AR) and entropy (E) of the synthesized SAR image over 30 independent runs.

T | KWFLICM | FLICM | FGFCM | KGC | MKCIS |
---|---|---|---|---|---|

AR | 85.12 (0) | 65.28 (0.52) | 78.15(0) | 78.95(24.5) | 98.14(0.01) |

E | 2.58(0.01) | 2.59 (0.01) | 2.59(0) | 2.59(0.15) | 2.55(0.2) |

**Table 3.**Statistical segmentation results of entropy (E) of the real SAR image over 30 independent runs.

Index | KWFLICM | FLICM | FGFCM | KGC | MKCIS |
---|---|---|---|---|---|

E | 2.57(0.01) | 2.78 (0.01) | 2.57(0) | 2.55(0.03) | 2.55(0.01) |

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**MDPI and ACS Style**

Yang, D.; Yang, H.; Fei, R.
An Efficient SAR Image Segmentation Framework Using Transformed Nonlocal Mean and Multi-Objective Clustering in Kernel Space. *Algorithms* **2015**, *8*, 32-45.
https://doi.org/10.3390/a8010032

**AMA Style**

Yang D, Yang H, Fei R.
An Efficient SAR Image Segmentation Framework Using Transformed Nonlocal Mean and Multi-Objective Clustering in Kernel Space. *Algorithms*. 2015; 8(1):32-45.
https://doi.org/10.3390/a8010032

**Chicago/Turabian Style**

Yang, Dongdong, Hui Yang, and Rong Fei.
2015. "An Efficient SAR Image Segmentation Framework Using Transformed Nonlocal Mean and Multi-Objective Clustering in Kernel Space" *Algorithms* 8, no. 1: 32-45.
https://doi.org/10.3390/a8010032