04658475

1-4244-1355-9/07/$25.00 @2007 IEEE

International Conference on Intelligent and Advanced Systems 2007

~ 685

Abstract—Accurate registration of multitemporal remote sensing images is essential for various applications. Mutual information has been used as a similarity measure for registration of medical images because of its generality and high accuracy. However, its application in remote sensing is relatively new. In this paper, we introduce a registration algorithm that combines a powerful search strategy; named Simulated Annealing based Marquardt-Levenberg (SA-ML), with mutual information, together with a wavelet-based multiresolution pyramid due to Simoncelli. We consider images, which are misaligned by a three parameter rigid transformation, consisting of rotation and/or x- and y-translations. It is shown that the SA-ML search combined with mutual information produces accurate results and magnificently extends convergence region of Marquardt-Levenberg (ML) method, which previously has been developed for medical data, when applied to synthetic, as well as multitemporal sets of satellite data. We evaluate several hybrid Simoncelli pyramids (low-pass, high-pass) for the best results in terms of accuracy and convergence. It is found that 4-level pyramid SimIB1B2B3 (band-pass pyramid with the original image in the finest level) performs best for multitemporal images.

Keywords—Multiresolution image registration, mutual information, multitemporal images, Simulated Annealing based Marquardt-Levenberg optimization, Simoncelli pyramid.

I. INTRODUCTION

igital image registration is very important in many applications of image processing, such as medical

imagery, robotics, visual inspection, and remotely sensed data processing [1]. For all of these applications, image registration is defined as the process that determines the most accurate match between two images (reference and test) in different spectral ranges and/or at different resolutions, acquired from the same scene or objects, at the same or different times, by different or identical sensors, from the same or different viewpoints [4], [6]. The registration process determines the optimal transformation, which will align the two images. In this paper, we will only

Manuscript received October 1, 2007. This work was supported by Iran Telecommunication Research center.

H. Ghorbani was with the Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran. He is now with Iranian Space Agency. (e-mail: [email protected]).

A. A. Beheshti is with the Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran. (e-mail: [email protected]).

refer to remote sensing applications, for which automated image georegistration has become a highly desirable technique. Remote sensing data must be integrated to obtain a better understanding of the phenomenon under study, and image registration is the first step in this process. For prevalent applications, such as image fusion and changedetection, it is very important to reach sub-pixel accuracy, and automatic image registration offers a practical means of achieving this. For example, registration accuracy of less than 0.2 of a pixel is required to achieve a change detection error of less than 10% [2].

Cole-Rhodes et al. demonstrated many advantages of Mutual Information (MI) over Correlation as similarity metric of optimization in [6]. They showed that the MI optimum has an attraction region (radius of convergence) of about 16 pixels using a stochastic gradient optimization, that is, the MI converges if the starting distance is less than 16 pixels from the optimum point. The registration algorithm proposed by Thévenaz and Unser in [7], is based on a combination of MI together with a multiresolution gradient search for registration of medical images. By using the cubic B-spline data model both for image interpolation and for the probability density estimation with Parzen windows, smoothing was achieved and the gradient components of MI were computed exactly in a deterministic fashion. An optimizer similar to the Marquardt-Levenberg (ML) was then designed specifically for this criterion. Zavorin and Le Moigne in [5] evaluated several wavelet pyramids that may be used both for invariant feature extraction and for representing images at multiple spatial resolutions to accelerate registration. They found that the bandpass wavelets obtained from the steerable pyramid due to Simoncelli performs best in terms of accuracy and consistency, while the low-pass wavelets obtained from the same pyramid give the best results in terms of the radius of convergence. They suggested that in order to obtain best results, a hybrid method can be used, when low-pass Simoncelli wavelets (SimL) are applied at early stages of optimization (e.g., at coarse pyramid levels) followed by band-pass Simoncelli wavelets (SimB) applied for fine tuning. They also wanted to implement MI based on [7] in their future tasks.

In this paper, according to these results, we use optimization of MI by proposing a modification for ML method of [7] as SA-ML, in a multiresolution framework by

Multiresolution Registration of Multitemporal Remote Sensing Images by Optimization of Mutual Information Using a Simulated

Annealing based Marquardt-Levenberg Technique Hassan Ghorbani and Ali Asghar Beheshti

D


686 ~

the steerable Simoncelli pyramids suggested in [5], for registration of Multitemporal IRS PAN images. By our proposed Simulated Annealing based Marquardt-Levenberg (SA-ML) technique, we search in hybrid Simoncelli pyramids for best convergence and accuracy.

II. MULTIRESOLUTION REGISTRATION ALGORITHM

We adopt a multiresolution framework often used in registration [8]. It amounts to, first, representing the two images at several spatial resolutions using some sort of filtering and decimation framework, followed by progressive alignment of the image representations by going from the coarsest one to the finest. For all levels of decomposition, similarity metric between sub-band images of the reference image and test image is successively computed and optimized. The accuracy of this search increases when going from coarse resolution to fine resolution. Using this approach, compared to working solely with the original images, reduces computational costs, regularizes the registration and improves robustness [5], [6].

III. COMPONENTS OF REGISTRATION ALGORITHM

There are four components in registration methods [1]. The search space is the class of potential transformations

)( μ.;g that establish the correspondence between the reference and the test. The feature space determines the type of information extracted from the images that is used to find the best transformation. The similarity metric gives the meaning to the term “best match”. The search strategy describes how the features and the metric are used to find the best )( μ.;g [5]. Now, we describe different components used in this paper.

A. Search Space

Let fT(x) and fR(x) with coordinates 2),( ⊆∈= Vx yx ,where V is a region of interest, be a test and a reference image, respectively. These are registered by finding a transformation )( μx;g of a certain class such that )(xg

Rf

best matches fT(x), where )(μ21

...,,μμ= is a vector of

transform parameters. In this paper, we consider TP(.) to be the class of three-parameter transforms specified by a 2D rigid transformation in the plane. These can be represented by the 3-by-3 matrix shown below:

.1100

)(cos)(sin)(sin)(cos

);,(⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

−= yx

tytx

yx θθ

θθ

μg (1)

and we can write μ as the vector:μ = [tx, ty, ], indicating search space parameters. Note that these three parameters specify translation in x and y and rotation respectively, in the plane.

B. Feature Space There are many different types of information in the

images that can be used for registration, including original intensities, edges, contours, wavelet coefficients, moment invariants and higher level features [1]. Here, we have focused on wavelet features. Orthogonal wavelets are computationally efficient, but for the same reason, they also have poor invariance properties. As an image is shifted, energy shifts both within and across subbands [9]. Several approaches have been proposed that attempt to overcome the deficiencies of orthogonal wavelets. In [9], the steerable pyramid is proposed, that enables one to build translation and rotation-invariant filters by relaxing the critical sampling condition of the wavelet transforms. As a result, an overcomplete invertible wavelet representation is obtained. In this paper, both the reference and test images are decomposed via a Simoncelli steerable pyramid because it gives the best results for image registration [5].

C. Similarity Metric The concept of mutual information (MI) represents a

measure of relative entropy between two sets, which can also be described as a measure of information redundancy. The negative S of the mutual information between the test image A and the transformed reference image B is

.))()(

),((log),( 2 bpapbapbapS

BA

AB

a bAB ⋅−= ∑ ∑

(2)

with pA(a) and pB(b) defined as the marginal probability distributions, and pAB(a,b) defined as the joint probability distribution of A and B.

The MI registration criterion states that the transformed reference image )(xg

Rf is correctly aligned with the test

image by the parameter for which S is minimal. The MI surface is smooth when the interpolation kernel of transformed image and the parzen window are cubic B-spline. Also, in this work a histogram with 8 bins is used, since it produces a significantly smoother MI surface than the 256-bin histogram. The smoother surface works better with the optimization algorithm, and the reduced number of bins dramatically improves the runtime for MI registration [6], [7]. MI has been widely used to register medical images [7], and has recently been applied to the registration of remote sensing images [6].

D. Search Strategy The search for the optimum parameter transformation can

be done by an exhaustive search. This is computationally expensive as the number of parameters increases when sub-pixel accuracy is required, so an optimization scheme is implemented.


~ 687

1) Thévenaz-Unser Optimization Technique: Marquardt-Levenberg optimizer benefits from superlinear convergence, a regime in which the optimizer converges quadratically (or better) when the optimum is close enough. By selecting a B-spline as a Parzen window satisfying the partition of unity condition, Thévenaz and Unser computed closed form of MI gradient S∇ , and Hessian S2

∇ , in which, the Hessian comes at essentially no additional computational cost with respect to that of the gradient [7].

The Marquardt-Levenberg strategy is a convenient way to combine the advantages of the gradient method with those of the Newton method, preserving the efficiency of the latter when the conditions are nearly optimal, and the robustness of the former when they are not. For this method, a modified Hessian HS is introduced in which the off-diagonal entries of S2

∇ are retained and its diagonal entries are multiplied by some factor

)1()]([)]([ ,,2

, λδ jijiji SHS +∇= μμ (3)

where ji,δ is the Kronecker symbol, andλ is a tuning factor

that represents the compromise between the gradient method

and the Newton method. The new update 1ˆ+kμ of ML

method is determined as in

( ) ).(.) )(1)()()1( kkkk SHS μ(μμμ ∇−=

−

+ (4)

2) Proposed SA-ML Optimization Technique: Animportant consideration in the application of the optimization scheme is that the further away the initial guess is from the global maximum, the more local maxima the algorithm may need to overcome to reach the global maximum, and thus the more likely it is to fail. Note that the coarser the images (i.e., the deeper the level of the Simoncelli decomposition) the less smooth is the MI surface, and failure at this coarser level can be catastrophic to the optimization algorithm. Besides, the most infirmity of Thévenaz-Unser method is that algorithm convergence requires the distance between initial point and optimum parameters be at the region of attraction. Cole-Rhodes et al.[6] showed the MI optimum has an attraction region of about 16 pixels using a stochastic gradient optimization method. Thus, we need a global optimization at the coarsest

(a) (b) (c)

Fig. 1. RMS pixel error curves of ML optimization for MI with different initial distances over varying numbers of decomposition levels (band-pass). (a) Initial guess = 12 pixels and 5 degrees from correct result. (b) Initial guess = 16 pixels and 5 degrees from correct result. (c) Initial guess = 20 pixels and 5 degrees from correct result (Algorithm failure for all decomposition levels.).

(a) (b)

Fig. 2. RMS pixel error curves of SA-ML optimization for MI with 110-pixel and 5-degree initial distance (RMSE=111.5 pixels) over varying hybrid pyramids. (a) For dataset SYNTH1. (b) For dataset SYNTH2.


688 ~

level of multiresolution registration independent of initial guess.

The implemented optimization technique, is Simulated Annealing based Marquardt-Levenberg (SA-ML) algorithm that magnificently extends the convergence region of ML method. Spall [10] connected a simulated annealing concept to the stochastic approximation (SA) framework to achieve a global convergence from a local optimization method. We connect it to the Marquardt-Levenberg (ML) framework in the first (coarsest) level of multiresolution registration to achieve a global optimization.

Consider the equation of ML method (4). We inject a stochastic term to it for the first level of registration:

( ) .)(.) )(1)()()1(kk

kkkk bSHS wμ(μμμ +∇−=

−

+ (5)

where kw is a vector of zero mean Gaussian variables with variances related to pyramid size, image size, number of iterations and acceptable distance between initial guess and global maximum. This injected term decays to zero by the factor of bk in several iterations. Determination of desirable variances for each parameter, number of iterations and decay procedure of bk is the main task in this method. Moreover, because of the partial overlap defect of MI, maximum variation of translation from zero case must be limited. The effect of randomness is more in the initial iterations then the number of iterations be further, the probability of dropping in the local optimums be less. In the final iterations, the method goes toward ML. While the image size in the coarsest level is small, imposed computational cost is not considerable.

IV. EXPERIMENTS AND RESULTS

In this Section, multiresolution registration combining Simoncelli pyramids, MI, the ML and the SA-ML optimization schemes is thoroughly tested and compared using synthetic test data as well as multitemporal data. These experiments are conducted on a 512MB Pentium-IV 2*2.80GHz computer, and Matlab software.

A. Description of the Test Datasets In this study, four synthetic image sets (SYNTH1, 2, 3

and 4) created by a controlled process, that is designed to emulate real data, and two Multitemporal image sets of IRS-1C, 1D (MULTITIME: Quchan, Tehran) are used. The datasets are as follows:

1) SYNTH: First, we choose a subimage of size 1024*1024 from IRS-1D PAN scene of the city of Quchan as the source image and a subimage of size 512*512 is extracted from its center, which becomes the reference image. Second, the same source is geometrically warped by random translating and random rotating and then extracting the 512*512 centers of the transformed images. By creating 20 warped test images with random and known parameters, SYNTH1 dataset is made:

• Translation parameters are varied in the horizontal direction by amounts of -5 to 5 pixels;

• Rotation parameters are varied with angles ranging from -5° to 5°.

Third, SYNTH1 dataset is convolved with a simple point-spread function (PSF) introduced by [5] for simulating radiometric differences of multi-sensor satellite data. These 20 images make SYNTH2 dataset. Finally, to emulate imperfections of optical systems and of models used in preprocessing of satellite data, a controlled amount of (Gaussian) noise can be added to each image of SYNTH1 and SYNTH2 datasets to create SYNTH3 and SYNTH4datasets, respectively. This amount is specified in terms of signal-to-noise ratio (SNR).

2) MULTITIME: The first Multitemporal dataset consists of 15 pairs of images of size 512*512, each of which extracted from PAN Band of two scenes taken by IRS-1C (in 2003) and IRS-1D (in 2005) over the city of Quchan (Iran). These pairs of images are referred to as Quchan1 and Quchan2, respectively. Also, the second Multitemporal dataset consists of 15 pairs of images of size 512*512, each of which extracted from PAN Band of two scenes taken by IRS-1D in March, and July, 2005 over the eastern part of Tehran city (Iran). These pairs of images are referred to as Tehran1 and Tehran2, respectively.

(a) (b) (c) Fig. 3. Mean of converged results after 220 seconds with 110-pixel and 5-degree initial error over varying hybrid pyramids for (a) Datasets SYNTH1 and 2. (b) Dataset SYNTH3. (c) Dataset SYNTH4


~ 689

TABLE ISUMMARY OF SA-ML TEST RESULTS ON SYNTHETIC DATASETS

B. Measuring Accuracy When accurate ground truth is available, such as when

test images are created synthetically, a standard way of assessing registration accuracy is by using the RMS error [5]. Besides, in the absence of ground truth, registration Consistency may be used as a measure to evaluate the performance of different intensity-based image registration algorithms [3]. We use RMSE and Consistency measures for assessing registration accuracy of SYNTH and MULTITIME datasets, respectively.

C. Algorithm Implementation First, we conduct a series of experiments using the

synthetic images generated from the reference of SYNTH datasets, to test the sensitivity of ML and our algorithm (SA-ML) to several parameters. Then, we apply our algorithm to the MULTITIME datasets.

1) Sensitivity of ML to Initial Guess and Number of Decomposition Levels: In this subsection, we test the sensitivity of ML algorithm to the number of levels of decomposition, and the distance between the initial guess and the correct result. Plots of Fig. 1 correspond to MI optimization for the band-pass outputs of the Simoncelli decomposition for the images of dataset SYNTH1. They show the average of the final RMS errors measured in pixels, for the images of dataset SYNTH1 versus the time, for starting points (or initial guesses) at various horizontal distances from the correct result (or ground truth) and for different pyramid sizes. Each starting point has a rotational error of 5°, in addition to the indicated translational error.

For all the cases shown in Fig. 1, after 220 seconds the algorithm consistently converges to sub-pixel using 5 levels of decomposition, when the starting distance is 16 pixels or less in a single direction from the “ground truth” value, and fails at 20 pixels. Thus, the MI optimum has an attraction region of about 20 pixels. For one level of decomposition, a slow convergence is achieved for this size image by using

the original image, with no Simoncelli decomposition, while the algorithm does not converge using the band-pass output.

Similar plots were generated using the low-pass outputs of the Simoncelli decomposition while the low-pass being less sensitive than the band-pass to the distance of the initial guess from the correct result.

2) Implementation of SA-ML with SYNTH Datasets: Now,we apply proposed SA-ML optimization to datasets SYNTH1, 2, 3, and 4 while each starting point has a horizontal translational error of 110 pixels and a rotational error of 5° (RMSE0 = 111.5 pixels) within some 5-level hybrid pyramids. Fig. 2 shows the convergence rate to sub-pixel registration for datasets SYNTH1 and 2 and Fig. 3(a) shows the (mean for) final results of converged experiments after 220 seconds. Then, Figs. 3(b) and 3(c) correspond to the (mean for) final results of converged experiments for the images of datasets SYNTH3 and 4 after 220 seconds, respectively. The results of these experiments for different hybrid pyramids are summarized in Table I. This table shows that using low-pass wavelets in the first (coarsest) level of pyramid (SimL4) is necessary to obtain sub-pixel accuracy in 100% of all experiments (after 220 seconds). We can see that SimIL1L2L3L4 pyramid (including the original image in the finest level) led to sub-pixel accuracy in 100% of all experiments and to the best accuracy for images of datasets SYNTH1 and 2 and for low-noise images of datasets SYNTH3 and 4. For high-noise images, SimB0B1B2B3L4 (with no 100% convergence to sub-pixel) and SimL0L1L2L3L4 pyramids led to the best accuracy for datasets SYNTH3 and 4, respectively. It means that, the original image is sensitive to high noise, and in this case, desirable choice for finest level is band-pass output SimB0 and low-pass output SimL0 for datasets SYNTH3 and 4, respectively. It is because, the images of dataset SYNTH3 preserve edges and high contrast features of images of dataset SYNTH1. Moreover, the noise is filtered in the band-pass output SimB0. On the other hand, the edges of images of dataset SYNTH4 are smoothed by PSF and band-pass output SimB0 doesn’t lead to the best accuracy. Thus, low-pass output SimL0 with filtered noise lead to the best accuracy.

3) SA-ML Results on MULTITIME Datasets: Table II shows final results (registration consistency) of the SA-ML optimization algorithm applied to datasets Quchan and Tehran, for a maximum run-time of 250 seconds. The initial guesses for starting the optimization, are (tx0 = 0, ty0 = 0, 0

= 0) almost 75 (and 18) pixels away from the final registration value in the x-direction, and 85 (and 15) pixels in the y-direction for dataset Quchan (and Tehran). Since, information content of 32*32 sub-bands is not sufficient for registration of multitemporal images; 5-level pyramid SimIL1L2L3L4 does not lead to desirable results. Thus, for this type of images, we test 4-level pyramids SimIL1L2L3, SimIB1B2B3 and SimIB1B2L3, and the results are provided in Table II. SimIB1B2B3 yields the best results among these

Best Accuracy When ConvergedTest

Database

100% Converged (with 110 pixel-

and 5 degree-initial error) High Noise Low Noise

SYNTH4= Warping

+ PSF + Noise

SimIL1L2L3L4SimL0L1L2L3L4 SimL0L1L2L3L4 SimIL1L2L3L4

SYNTH3= Warping

+ Noise

SimIL1L2L3L4SimL0L1L2L3L4 SimB0B1B2B3L4 SimIL1L2L3L4

SYNTH2= Warping

+ PSF

SimIL1L2L3L4SimL0L1L2L3L4 SimIL1L2L3L4

SYNTH1= Warping

SimIL1L2L3L4SimL0L1L2L3L4SimB0L1L2L3L4SimB0B1L2L3L4SimB0B1B2L3L4SimB0B1B2B3L4

SimIL1L2L3L4SimB0L1L2L3L4


690 ~

pyramids and it means that for registration of multitemporal images by SA-ML, band-pass output SimB3 is more proper than the low-pass output SimL3 to be used as the first level of pyramid. However, it is reasonable because radiometric differences between multitemporal images correspond to the low-frequency differences and are filtered in band-pass output SimB3. Occurrence of heavy errors for image pair's b, e, h and k of dataset Quchan is due to presence of heavy differences in the content of these images. Except for these image pairs, SA-ML based on the SimIB1B2B3 pyramid yields mean registration consistency of 0.2439 and 0.1403 pixels for datasets Quchan and Tehran, respectively.

TABLE II2-DATE REGISTRATION CONSISTENCY FOR SA-ML METHOD (PIXELS) WITH

DIFFERENT HYBRID PYRAMIDS

V. CONCLUSIONS

Herein, we have implemented the second order Marquardt-Levenberg algorithm proposed for registration of medical images in [7], combined with the Simoncelli steerable pyramid suggested in [5], in order to optimize mutual information preferred in [6], over the three parameters of translation in the x- and y-directions and rotation for

registration of synthetic satellite imagery. Then, we have introduced the Simulated Annealing based Marquardt-Levenberg (SA-ML) technique for extending the convergence region of ML. It has been tested on several sets of synthetic and multitemporal satellite imagery and several hybrid Simoncelli pyramids. SA-ML method has improved the convergence region beside desirable accuracy magnificently, with 5-level pyramid SimIL1L2L3L4 for low-noise synthetic images, with 5-level pyramid SimB0B1B2B3L4 (with no 100% convergence to sub-pixel) for high-noise images of dataset SYNTH3, with 5-level pyramid SimL0L1L2L3L4 (low-pass) for high-noise images of dataset SYNTH4, and with 4-level pyramid SimIB1B2B3 for multitemporal images. Since the most time consuming part of the algorithm is due to the finest level of the pyramid, the quest for reducing the computation time in this level will be pursued in our future works.

ACKNOWLEDGMENTS

This research was supported by Iran Telecommunication Research center. The authors would like to acknowledge National Geographical Organization (NGO) of Iran for providing remotely sensed images.

REFERENCES

[1] L. Brown, “A survey of image registration techniques,” ACM Comput. Surv., Vol. 24, No. 4, Dec. 1992.

[2] X. Dai and S. Khorram, “The effects of image misregistration on the accuracy of remotely sensed change detection,” IEEE Trans. Geosci. Remote Sensing, Vol. 36, PP. 1566–1577, Sept. 1998. H. M. Chen, P. K. Varshney, and M. K. Arora, “Performance of Mutual Information Similarity Measure for Registration of Multitemporal Remote Sensing Images,” IEEE Transactions On Geoscience And Remote Sensing,Vol. 41, No. 11, November 2003.

[3] H. M. Chen, P. K. Varshney, and M. K. Arora, “Performance of Mutual Information Similarity Measure for Registration of Multitemporal Remote Sensing Images,” IEEE Transactions On Geoscience And Remote Sensing, Vol. 41, No. 11, November 2003.

[4] J. Le Moigne,W. J. Campbell, and R. F. Cromp, “An Automated Parallel Image Registration Technique Based on the Correlation of Wavelet Features,” IEEE Transactions On Geoscience And Remote Sensing, Vol. 40, No. 8, August 2002.

[5] I. Zavorin and J. Le Moigne, “Use of Multiresolution Wavelet Feature Pyramids for Automatic Registration of Multisensor Imagery,” IEEETransactions On Image Processing, Vol. 14, No. 6, June 2005.

[6] A. A. Cole-Rhodes, K. L. Johnson, J. LeMoigne, and I. Zavorin, “Multiresolution Registration of Remote Sensing Imagery by Optimization of Mutual Information Using a Stochastic Gradient,” IEEE Transactions On Image Processing, Vol. 12, No. 12, December 2003.

[7] Ph. Thévenaz, and M. Unser, “Optimization of Mutual Information for Multiresolution Image Registration,” IEEE Transactions On Image Processing, Vol. 9, No. 12, December 2000.

[8] Ph. Th´evenaz, U. E. Ruttimann, and M. Unser, “A Pyramid Approach to Subpixel Registration Based on Intensity,” IEEE Transactions On Image Processing, Vol. 7, No. 1, January 1998.

[9] E. Simoncelli,W. Freeman, E. Adelson, and D. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory, Vol. 38, No. 3, PP. 587–607, Jun. 1992.

[10] J. C. Spall, “Introduction to Stochastic Search and Optimization: Estimation, Simulation and Control,” Hoboken, NJ: Wiley, 2003.

4-level Pyramid

Imag

ePa

irs 5-level PyramidSimIL1L2L3L4

SimIL1L2L3 SimIB1B2B3 SimIB1B2L3

a 64.4467 61.3962 0.1630 77.8602 b 205.6569 10.0370 11.4817 170.0277 c 226.9208 0.1519 0.1656 201.8362 d 16.9160 0.4605 0.2273 0.4383 e 188.6504 21.3444 2.6075 40.8023 f 0.1378 0.0979 0.1687 0.0910 g 186.1087 189.5515 0.3905 189.9733 h 14.7934 23.3234 32.5001 91.4115 i 101.9357 7.0353 0.1792 4.2152 j 22.8440 0.2875 0.3147 0.4541 k 16.9290 77.7536 16.3763 85.9915 l 0.1081 0.1497 0.2211 0.1895

m 0.1946 0.2119 0.4469 0.3470 n 213.5820 0.4464 0.0601 0.1355

Quc

han1

& 2

o 0.1615 0.2581 0.3454 0.2229 MEAN 83.9590 26.1670 4.3765 57.5998

a 0.0612 0.1458 0.1569 0.1120 b 45.5296 36.4408 0.2135 36.5281 c 129.9210 0.0748 0.0457 0.1283 d 0.0747 0.1226 0.0841 0.1253 e 69.4227 30.2012 0.0844 35.8034 f 135.5457 0.2071 0.2048 0.0763 g 158.5948 0.0220 0.0603 0.0543 h 0.0869 0.3690 0.2271 0.0970 i 0.1241 0.1780 0.1270 0.1135 j 90.6241 0.0317 0.0392 0.0857 k 0.1018 0.1796 0.1137 0.0764 l 0.0985 0.0620 0.1534 0.0391

m 0.0413 0.1238 0.0355 0.0824 n 0.3670 0.0517 0.2276 0.1014

Tehr

an1&

2

o 53.5722 18.3879 0.3319 19.9797 MEAN 45.6110 5.7732 0.1403 6.2269

04658475

Documents