Segmentation method based on multiobjective optimization for very high spatial resolution satellite images
 Saleh El Joumani^{1},
 Salah Eddine Mechkouri^{1}Email author,
 Rachid Zennouhi^{1},
 Omar El Kadmiri^{1} and
 Lhoussaine Masmoudi^{1}
DOI: 10.1186/s1364001601612
© The Author(s). 2017
Received: 31 July 2016
Accepted: 27 December 2016
Published: 31 March 2017
Abstract
In this paper, a new multicriterion segmentation method has been proposed to be applied to satellite image of very high spatial resolution (VHSR). It is consisted of the following process: For each region of the grayscale image, a center of gravity has been calculated and it has been also selected a threshold for its histogram. According to a certain criteria, this approach has been based on the separation of the different classes of grayscale in an optimal way. The proposed approach has been tested on synthetic images, and then has applied to an urban environment for the classification of data in Quickbird images. The selected zone of study has been laid in SkhirateTémara province, northwest of Morocco. Which is based on the Levine and Nazif criterion, this segmentation technique has given promising results compared those obtained using OTSU and Kmeans methods.
Keywords
Segmentation Multicriterion Entropy Otsu Kmeans Satellite image VHSR (Quickbird) Levine and Nazif criterion1 Introduction
Segmentation is the technique and procedure used to divide the image into different nonoverlapping regions according to their characteristics. The pixel values in the same region have similar attributes while the pixel values from diverse regions have various features. Various methods have been developed and used with a relative success. They can be roughly classified into several categories according to the dominant features they employ, such as edgebased method [1], regiongrowing method [2], neural networks method, physicsbased method [3–5], and histogram thresholds method [6].
However, in some practical situations, solving segmentation problems need more information than what is contained in onesingle image band. In these cases, the use of several image color components or a multispectral image is necessary [7–9]. In practice, the application of such method, on a VHSR image, leads to inaccurate results. In certain specific cases, variant region of interest are classified to be homogenous, this is due to two main critical issues in color image segmentation: (1) what's the way segmentation method should be used?; and (2) what's the way color space should be adopted? [10]. It demonstrated that, for unsupervised classification problems, histogram thresholding is a suitable method for achieving good segmentation results with a low computation complexity for a wide class of images [4, 10].
In this case, a number of classification algorithms, based on 2D histogram analysis, are obtained by multidimensional histogram projection which are focused on two color procedures. These algorithms have been elaborated and used successfully [7–9, 11].
This work proposes a method that focuses on the separation of different classes of grayscale in an optimal way according to some criterion, using typical techniques of image segmentation. We calculate the center of gravity for each region of the grayscale image and the threshold of its histogram [7–9]. In order to show the feasibility of the proposed method, firstly, we will compare our approach with OTSU and Kmeans methods by testing and applying them on synthetic images. Secondly, we will evaluate our algorithm on land cover and land use classification using a satellite image of a selected urban zone.
This task confirm that the segmentation technique provides better results when it is established on a combination of criteria. Thus, the diversity of images to which it could be applied successfully. At the same time, it reveals the weakness of the criteria when it' s used separately, without being combined.
The first chapter of this article presents the proposed multicriteria segmentation approach. The second one describes the multiobjective function. The third one presents the VHSR satellite image we used in this study. The fourth chapter introduces the criterion of Levine and Nazif, and the last one reveals the experimental outcomes and the discussion.
2 Description of the method
Multiobjective optimization extends from the theory of optimization by allowing several design goals to optimize simultaneously. A multiobjective optimization problem is solved in a way similar to the simple objective classic problem. The goal is to find a set of values for the design variables that simultaneously optimize several objective functions (or costs). In general, the solution obtained by the separated optimization of each objective (simple objective optimization) does not represent a possible solution for the multiobjective problem.
 1.
The modified withinclass variance criterion,
 2.
The overall probability of error criterion, and
 3.
The entropy criterion.
The identification of these three criteria in the thresholding algorithm requires the introduction of three parameters: w _{1} , w _{2} , and w _{3}, see eq. (7) and the detail of which we shall see later.
Our aim is to increase the information about the position of the optimal threshold that allows us to obtain the correct segmentation.
In this subsection, we present the different criteria that we will minimize later for the process of multilevel image thresholding. Functions (criteria) that we chose are the modified withinclass variance, the overall probability of error and the entropy.
2.1 Modified withinclass variance criterion
And we assume that the number NR of regions is two.
α is given by \( \frac{1}{10000\mathbf{XM}}\sqrt{\mathbf{NR}} \) where M is the image size.
\( {\boldsymbol{\beta}}_{\boldsymbol{j}}=\frac{1}{1+\mathrm{Log}\left({\boldsymbol{N}}_{\boldsymbol{j}}\right)} \), N _{ j } denotes the number of pixels in the region j.
\( {\boldsymbol{\gamma}}_{\boldsymbol{j}}={\left(\frac{\boldsymbol{R}\left({\boldsymbol{N}}_{\boldsymbol{j}}\right)}{{\boldsymbol{N}}_{\boldsymbol{j}}}\right)}^2 \), and R(N _{ j }) is the number of the regions of which cardinal is equal to N _{ j }.
2.2 Overall probability of error criterion
i = 1; 2;…; d−1 with respect to the threshold T _{ i },
Where T is the vector of thresholds: 0 < T1 < T2 < … < Td−1 < 255.
2.3 Entropy criterion
2.4 Objective function
Obviously, this function has certainly been successful but it showed its limits. For that reason, we thought about introducing another factor such as entropy.
Where T is the vector of thresholds: 0 < T_{1} < T_{2} < … < T_{d1} < 255.

○ For the function MOBJ1 (6): w _{1} = 1 − w _{2}

○ For the function MOBJ2 (7): w _{1} = 1 − w _{2} − w _{3}
Where d is the number of the Gaussians; σ _{ i } is the standard deviation of the ith Gaussian probability density function; and σ _{Histogram} is the standard deviation of the original histogram. The weighting parameters (w _{1} , w _{2} , and w _{3}) allow touching the boundary of the feasible domain. This operation was used when the goal of the segmentation is to extract the target from the original image.
3 Quickbird image data
Quickbird MS image specification
Band  Wavelength (nm)  Spatial resolution (m^{2}) 

Blue  450–520 (485)  2.4 × 2.4 
Green  520–600 (560)  
Red  630–690 (660)  
Nearinfrared  760–900 (830)  
Panchromatic  445–900  0.61 × 0.61 
4 Levine and Nazif evaluation of criteria
 (I).
I _{ R } corresponds to the segmentation result of the image in a set of regions R = {R _{1},…,R _{NR}} having N _{ R } regions,
 (II).
Card(I) corresponds to the number of pixels of the image I,
 (III).
g _{ I }(s) corresponds to the graylevel intensity of the pixels of the image I and can be generalized to any other characteristic (color, texture …).
Sezgin and Sankur [17] proposed a standardized uniformity measure. Based on the same principle, the measurement of homogeneity of Cochran [18] gives a confidence measure on the homogeneity of a region. However, this method requires a threshold selection that is often arbitrarily is done, limiting thus the proposed method. Another criterion to measure the intraregion uniformity is developed by Pal and Pal [19]. It is based on a thresholding that maximizes the local secondorder entropy of regions in the segmentation result. In the case of slightly textured images, these criteria of intraregion uniformity prove to be effective and very simple to use. However, the presence of textures in an image often generates improper results due to the over influence of small regions.
This criterion [20] combines intra and interregion disparities. Intraregion disparity is computed by the normalized standard deviation of gray levels in each region. The interregion disparity computes the dissimilarity of the average gray level of two regions in the segmentation result.
 (I).
The regions must be uniform and homogeneous,
 (II).
The interior of the regions must be simple without too many small holes,
 (III).
The adjacent regions must present significantly different values for the uniform characteristics, and
 (IV).
Boundaries should be smoothed and accurate.
5 Contribution of the new multiobjective function
The improvement of the objective function requires on the way to identify the contribution of our method. We precede by a comparison between two eqs. (6) and (7).
Values of Levine and Nazif evaluation of criteria for various functions (MOBJ1 and MOBJ2)
Imagery  Threshold  Filter  Criterion intraregion of Levine and Nazif  Criterion interregion of Levine and Nazif  Criterion intrainter region of Levine and Nazif  

Multiobjective1  Multiobjective2  Multiobjective1  Multiobjective2  Multiobjective1  Multiobjective2  
Image_synt [22]  2  2.5  0.0120  0.0372  0.2943  0.1834  0.5542  0.5310 
Image_panchr  2  2.5  0.1129  0.1240  0.2635  0.2424  0.5350  0.5341 
6 Experimental results and discussion
Thresholding based on withinclass variance tends to classify an image as the object. The experiments presented here concern the pixel classification of both a synthetic image and the classification of our Quickbird image in the different land cover and land use classes.
Values of Levine and Nazif evaluation of criteria for various methods
Imagery  Threshold  Filter  Intraregion criterion of Levine and Nazif  Interregion criterion of Levine and Nazif  Intrainter criterion region of Levine and Nazif  

Otsu  Kmeans  Multiobjective  Otsu  Kmeans  Multiobjective  Otsu  Kmeans  Multiobjective  
ImagSynt1  1.3  1  0.0105  0.0263  0.0335  0.2473  0.2217  0.1826  0.5503  0.5509  0.5397 
ImagSynt2  1.3  1.5  0.0231  0.0246  0.0306  0.1936  0.2142  0.1789  0.5442  0.5490  0.5334 
ImagSynt3  0.5  1.5  0.0265  0.0292  0.0331  0.1623  0.1725  0.1469  0.5447  0.5517  0.5328 
ImagSynt4  0.23  0.5  0.0425  0.0412  0.0467  0.1718  0.1892  0.1706  0.5500  0.5597  0.5374 
ImagSynt5  0.5  1  0.0221  0.0051  0.0461  0.2486  0.2574  0.2495  0.6121  0.5915  0.5803 
ImagSat1  1.66  1.5  0.0612  0.0704  0.0709  0.3747  0.2952  0.2912  0.5556  0.5443  0.5437 
ImagSat2  4  3  0.0898  0.0858  0.1286  0.2940  0.3158  0.2901  0.5865  0.5957  0.5789 
ImagSat3  4  3  0.1015  0.1002  0.1246  0.3059  0.3355  0.3111  0.5860  0.5975  0.5856 
ImagSat4  2.6  1  0.1026  0.0996  0.1338  0.2900  0.3054  0.2826  0.5853  0.5914  0.5796 
Forêt_T  0.5  1  0.0695  0.0704  0.1145  0.2156  0.2253  0.2259  0.5810  0.5919  0.5398 
Plage_T  1.25  1  0.0675  0.0735  0.1064  0.3271  0.3360  0.3533  0.5837  0.5883  0.5503 
The second phase of experimentation was conducted on a set of summary images with a VHSR (panchromatic image with a spatial resolution of 0.61m × 0.61m). While adjusting the threshold and the filter coefficients to segment each image, we also calculated their centers of gravity as well as their uniformity criterion of intraregion and intrainter region of Levine and Nazif. This was done for the multicriteria method and the Otsu method.
To evaluate quality of segmentation results in the case of real images, which usually contains several unknown degradations, the second phase of this comparative experimental study conducted as a result and evaluated using a real gray level image and a set of VHSR satellite images. We could infer from obtained evaluation criterion values (Table 3), which remains constantly inferior to those obtained when using Otsu’s algorithm, that the multiobjective optimization method provides more stable and reliable results especially in the case of highresolution satellite images.
7 Conclusions
In this work, we proposed a new multicriterion segmentation method based on the separation of different classes of gray levels in an optimal way according to certain criteria and applied it to VHSR satellite images. Therefore, we implemented a segmentation method based on multiobjective optimization function MOBJ2 developed and take account of entropy. We tested the function with respect to that of Nakib MOBJ1 while appealing to Levine and Nazif evaluation criteria and gave good results.
We applied the MOBJ2 according to the segmentation of multiclass images such as synthetic images and samples of panchromatic image of VHSR in order to assess the MOBJ2 function compared to that of the OTSU and the Kmeans available MATHLAB. The evaluation of the segmentation by introducing Levine and Nazif assessment criteria shows that the multiobjective function developed is better than the OTSU method and the Kmeans.
Abbreviations
 LEV1:

The formula that calculates the uniformity of intraregion based on the variance of this characteristic
 LEV2:

The formula that calculates the interregion disparity total
 LEV3:

The formula that calculates the combination of the intraregion uniformity and the interregion disparity
 MOBJ1:

The multiobjective function applied to two threshold images by Nakib
 MOBJ2:

Our multiobjective function applied to images with at least two thresholds
 VHSR:

Very high spatial resolution
Declarations
Acknowledgements
Since 2007, this satellite image has been used for several research projects. Consequently, all LETS/Geomatic PhD students who use this satellite image in their research work always express their thanks to the Spanish Agency for International Cooperation which has financed the acquisition of this image in 2007.
Funding
We do not have any funding for this work.
Authors’ contributions
The authors’ contributions for this work are as follows: OE suggests the multiobjective function idea and participates at the automatization program. SE and SEM carried out the development of image segmentation algorithm based on the revised multiobjective function (MOBJ1 and MOBJ2) and participated in the design of the study, and performed the experimentation of this algorithm for the assessment of the multiobjective function. RZ carried out the algorithm of thresholding program and helped for the choice of the evaluation criteria. SEM conceived of the study and participated in its design and coordination, and helped to draft the manuscript. Moreover, of course, the work conducted under the direction of our Professor LM. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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 The sample images are taken from the website: http://pages.upf.pf/Sebastien.Chabrier/ressources.php, http://pages.upf.pf/Sebastien.Chabrier/download/ImSynth.zip