Análisis PEST

The MAP-GMRF and MAP-ABM methods need the estimation window to perform the despeckling and to estimate texture parameters. The size of the estimation window

should be determined by the complexity of the scene or texture, for example, we can guess that a larger estimation window could better estimate larger structures, being a consequence of using more data for the computations. However, the use of larger esti- mation window increases the computation time.

The model order is also determined according to the structural complexity of the scene since a higher model orders uses larger neighborhoods, which can capture high structural complexity in the images. To use a higher model order implies to use a larger analyzing window. Then, we need to find a good compromise between the estimation

window size, model order and computation time.

In the next experiments, the impact of the estimation window and the model order on despeckling performance is evaluated using model order from two to four and an estimation window from (2× 2) to (32 × 32) pixel size. We start by presenting the results of Figure 5.11, where the 1) visual inspection is used to evaluate the despeckling and gives an idea about how the estimation window size and the model order affect the despeckling quality. Later, 2) the quantitative measurements versus the computation time are detailed in Table 5.7 and the results are commented. Finally, 3) the level of preserving the details is shown in Figure 5.12.

1. Visual inspection

One of the textures (T1) from TerraSAR-X mosaic (See Figure 5.5) was despeckled using both methods.

The despeckled images are shown in Figures 5.11(a)-(b) in the case of MAP-GMRF method with model order 2 and 4, and Figures 5.11(c)-(d) show despeckled images using model order 2 and 4 with MAP-ABM method. The window size for each model was changed from 2× 2 to 32 × 32.

• MAP-GMRF results

The model order 2 of the GMRF gives good quality of despeckled images from win- dow size of 8× 8 pixels. The model order 4 of the GMRF, shown in Figure 5.11(b) requires larger window sizes to allow the convergence of the evidence maximiza- tion algorithm to the right texture parameters of the scene. It is clear to see that some distortions were introduced with estimation windows 2× 2 and 8 × 8. The vi- sual impressions are acceptable when using estimation windows larger than 16× 16 pixels size.

• MAP-ABM results

The speckle remains in the reconstructed images, when the model order 2 of the MAP-ABM method is used. The evidence maximization algorithm models the speckle instead of the scene. By increasing the model order larger structures are modelled and speckle is removed from the image.

The model order 4 with window size of 32× 32 pixels is a good compromise between the quality of despeckling and the complexity of the methods. MAP-ABM properly works with model order three or higher.

5.3. QUANTITATIVE EVALUATION OF DESPECKLING 87

(a) Despeckled images using MAP-GMRF with Model Order 2.

(b) Despeckled images using MAP-GMRF with Model Order 4.

(c) Despeckled images using MAP-ABM with Model Order 2.

(d) Despeckled images using MAP-ABM with Model Order 4.

Figure 5.11: Despeckling results obtaining using (a-b) MAP-GMRF and (c-d) MAP-ABM method with estimation window of (from left to right) 2× 2, 8 × 8, 16 × 16 and 32 × 32 pixels.

2. Quantitative measurements versus computation time

Table 5.7 shows the objective results for the despeckling, where the estimation window and the model order of MAP-GMRF and MAP-ABM models were changed. The exper- imental results were performed using two synthetic textures from Brodatz mosaic (B7 and B4 in Figure 5.4(b)) and two real SAR images from TerraSAR-X mosaic (T1 and T7 in Figure 5.5).

• MAP-GMRF results

The experimental results obtained with the MAP-GMRF method reported in Table 5.7(a) show that by increasing window size the fidelity decreased and the best results on average are obtained with a window size of 32× 32 pixels. The fidelity is also

88 5. DATA-DRIVEN EVALUATION OF SARINFORMATION EXTRACTION METHODS

decreasing by increasing the model order. The best results were obtained with a model order 4. The reconstructed images are becoming smoother by the increasing the window size and model order, which indicates that the speckle is well removed. Speckle noise is well estimated, because reconstructed images have almost no bias and the mean of ratio is very close to 1. The SSIM value is very close to 0.9, which indicates that the reconstructed images are similar to the original images.

• MAP-ABM results

The MAP-ABM method behaves similarly to the MAP-GMRF method, when the model order and the window sizes are changed. The experimental results in Table 5.7(b) show, that the fidelity is decreasing by increasing the window size and in- creasing the model order of the ABM. The speckle was well estimated, the images were not biased, and the mean of estimated speckle was close to 1. The SSIM in- creased when the model order gets higher and images were not over smoothed by changing the window size, which means that some textures are well preserved. The

MAP-ABM method gives better objective results, but it is 3−5 times more compu- tationally demanding than the MAP-GMRF method. The reason is the estimation of the textures and the numerical computation of the MAP.

3. Level of preserving details

In order to complete the evaluation, in Figure 5.12, we display the despeckled image from small parts of the Hamburg sub-scene. Here, we can notice that the level of despeck- ling and detail preservation. Despeckled images with higher model order and larger window sizes produce more detailed despeckled images, meanwhile model order 2 and small window size produce blurred images, as shown in Figures 5.12(a) and 5.12(b), us- ing MAP-GMRF method.

The despeckling results obtained with the MAP-ABM, presented in Figures 5.12(c) and 5.12(d) show that the quality of despeckling is improving when using larger window sizes. Details and strong scatterers are well preserved using model 4 and window size of 32× 32 pixels.

5.3.3 Conclusions

The goal of this section is to conclude which method (MAP-ABM or MAP-GMRF) gives the best despeckling results. The MAP-GMRF and MAP-ABM methods were compared using synthetically generated data, speckled Brodatz textures and real SAR data. The ef- ficiency of MAP methods using texture models depends on how well the texture model adapts to the original scene. The texture estimation algorithm for MAP-GMRF and MAP- ABM methods is based on second level Bayesian inference. The despeckling performance of MAP-GMRF and MAP-ABM methods depends on the image textures, selected win- dow size, and the model order of the Markov Random Field. In general, we should esti- mate the complexity of the scene to select the most convenient model order and window size.

• In this thesis we used fixed model order and window size, which were defined ex- perimentally using trade-off between the complexity and efficiency of the methods. • The MAP-GMRF method well estimates textures, the mean value of which does not change dynamically, meanwhile the MAP-ABM method better performs on the

5.3. QUANTITATIVE EVALUATION OF DESPECKLING 89

Table 5.7: Quantitative despeckling criteria versus run-time processing, estimation win- dow and model order in the case of MAP-GMRF and MAP-ABM despeckling methods.

(a) MAP-GMRF

Fig. 5.4(b)-B7

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32 × 32 Time(s) 11.1 13.7 23.2 49.9 140.2 2 Bias 0.6 0.6 0.59 0.59 0.58 Ratio 1.00 1.01 1.01 1.01 1.00 Smoothness 4.82 5.51 5.08 4.57 4.44 Fidelity 3993.75 3973.52 3960.65 3912.97 3894.14 SSIM 0.44 0.45 0.46 0.46 0.46 Time(s) 12.9 15.5 27.6 64.7 185.3 3 Bias 0.64 0.51 0.46 0.59 0.51 Ratio 1.68 1.69 1.71 1.75 1.77 Smoothness 2.17 2.24 2.04 2.04 1.92 Fidelity 3974.10 3917.56 3905.76 3985.11 3901.07 SSIM 0.44 0.44 0.45 0.45 0.45 Time(s) 24.2 31.5 58.0 131.4 340.4 4 Bias 0.53 0.53 0.46 0.59 0.51 Ratio 1.67 1.68 1.70 1.75 1.77 Smoothness 2.16 2.21 2.03 2.03 1.91 Fidelity 3876.67 3868.50 3825.87 3813.75 3794.31 SSIM 0.44 0.44 0.44 0.44 0.44 Fig. 5.4(b)-B4

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32 × 32 Time(s) 10.8 13.4 23.5 53.2 142.7 2 Bias 0.2 0.2 0.21 0.21 0.21 Ratio 1.01 1.01 1.01 1.01 1.01 Smoothness 4.91 5.58 5.17 4.66 4.88 Fidelity 1483.61 1413.26 1352.29 1267.20 1174.42 SSIM 0.92 0.92 0.91 0.89 0.88 Time(s) 12.7 16.3 31.0 71.5 192.4 3 Bias 0.19 0.18 0.17 0.14 0.13 Ratio 1.01 1.01 1.01 1.01 1.01 Smoothness 4.84 5.53 5.06 4.57 4.59 Fidelity 1346.12 1248.28 1176.93 1092.10 1003.08 SSIM 0.91 0.91 0.91 0.89 0.88 Time(s) 20.4 27.9 56.4 133.5 354.7 4 Bias 0.02 0.02 0.00 0.14 0.21 Ratio 1.00 1.01 1.01 1.01 1.00 Smoothness 4.82 5.51 5.08 4.57 4.44 Fidelity 1233.75 1190.52 1173.65 1012.97 994.14 SSIM 0.90 0.91 0.91 0.89 0.88 Fig. 5.5-T1

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32 × 32 Time(s) 6.0 6.6 10.9 25.5 74.3 2 Bias 0.19 0.20 0.25 0.22 0.15 Ratio 0.99 0.99 0.99 0.99 0.99 Smoothness 316.34 412.51 601.24 341.39 337.79 Time(s) 6.4 7.7 13.9 33.2 97.8 3 Bias 0.17 0.19 0.24 0.26 0.18 Ratio 0.99 0.99 0.99 0.99 0.99 Smoothness 234.44 268.78 814.61 426.36 445.15 Time(s) 8.4 12.6 23.6 65.7 171.9 4 Bias 0.24 0.26 0.24 0.29 0.19 Ratio 1.00 0.99 0.99 0.99 0.99 Smoothness 122.40 175.35 1012.00 494.19 496.07 Fig. 5.5-T7

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32 × 32 Time(s) 6.8 8.9 14.7 33.0 87.5 2 Bias 0.57 0.24 0.07 0.91 0.44 Ratio 1.00 1.01 1.01 1.01 1.02 Smoothness 8.13 6.07 5.69 5.27 5.91 Time(s) 9.0 10.4 17.5 38.6 107.7 3 Bias 0.29 1.19 0.03 0.20 0.65 Ratio 1.00 1.00 1.00 1.00 1.00 Smoothness 5.88 4.12 4.06 3.21 3.53 Time(s) 10.8 17.5 31.0 68.8 171.7 4 Bias 0.94 0.50 0.56 0.75 0.23 Ratio 1.00 1.00 0.99 1.00 1.00 Smoothness 6.47 6.80 6.79 6.03 6.17 (b) MAP-ABM Fig. 5.4(b)-B7

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32× 32 Time(s) 112.32 219.76 555.12 1892.38 5072.89 2 Bias 0.34 0.31 0.46 0.59 0.51 Ratio 1.11 1.11 1.10 1.09 1.09 Smoothness 12.86 9.60 6.91 5.05 4.90 Fidelity 3214.98 3163.44 3096.65 3027.77 2994.98 SSIM 0.41 0.42 0.44 0.46 0.49 Time(s) 163.12 307.52 800.33 2790.64 7583.60 3 Bias 0.34 0.31 0.46 0.59 0.51 Ratio 1.09 1.09 1.08 1.07 1.07 Smoothness 12.99 10.27 7.06 4.90 4.74 Fidelity 2963.64 2958.28 2946.84 2942.56 2822.17 SSIM 0.41 0.43 0.45 0.48 0.50 Time(s) 253.99 474.58 1281.53 4318.00 11886.13 4 Bias 0.60 0.59 0.56 0.59 0.57 Ratio 1.07 1.07 1.06 1.05 1.05 Smoothness 15.32 11.31 7.23 4.96 4.66 Fidelity 2933.74 2909.37 2915.09 2861.90 2794.35 SSIM 0.41 0.43 0.45 0.60 0.63 Fig. 5.4(b)-B4

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32× 32 Time(s) 80.69 157.31 395.79 1199.30 3539.06 2 Bias 0.52 0.52 0.52 0.52 0.52 Ratio 1.14 1.15 1.17 1.18 1.18 Smoothness 243.41 677.73 149.11 149.03 85.18 Fidelity 700.42 719.20 766.86 835.41 854.01 SSIM 0.67 0.66 0.66 0.65 0.66 Time(s) 112.98 221.58 579.71 1881.03 6194.95 3 Bias 0.52 0.52 0.51 0.51 0.52 Ratio 1.14 1.15 1.17 1.19 1.19 Smoothness 271.04 754.26 142.16 91.08 40.67 Fidelity 699.73 718.04 770.50 850.84 886.94 SSIM 0.67 0.66 0.66 0.66 0.67 Time(s) 186.317 367.54 966.08 3143.31 10913.78 4 Bias 0.56 0.52 0.51 0.51 0.51 Ratio 1.14 1.15 1.17 1.19 1.19 Smoothness 11.80 11.99 11.50 11.40 11.61 Fidelity 930.16 915.61 866.27 845.92 595.63 SSIM 0.59 0.60 0.67 0.66 0.66 Fig. 5.5-T1

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32× 32 Time(s) 26.03 47.07 111.06 295.76 875.61 2 Bias 8.27 7.70 7.11 6.67 5.87 Ratio 0.93 0.93 0.94 0.94 0.94 Smoothness 271.88 305.74 431.18 316.59 317.83 Time(s) 39.92 73.21 177.61 478.98 1551.342 3 Bias 8.77 8.04 7.38 6.82 6.01 Ratio 0.92 0.93 0.93 0.94 0.94 Smoothness 338.24 386.75 553.78 374.74 401.87 Time(s) 70.36 120.72 314.37 842.02 2785.59 4 Bias 9.57 8.67 7.76 7.08 6.17 Ratio 0.92 0.93 0.93 0.94 0.94 Smoothness 402.80 485.10 697.62 456.27 488.99 Fig. 5.5-T7

Model Criterion Estimation window

Order 2× 2 4× 4 8× 8 16 × 16 32× 32 Time(s) 73.78 153.49 399.44 1160.64 3410.69 2 Bias 27.82 28.93 30.97 32.46 34.59 Ratio 1.12 1.12 1.14 1.15 1.17 Smoothness 20.42 17.18 14.68 12.85 12.16 Time(s) 106.40 212.15 536.42 1395.08 3996.9 3 Bias 28.61 30.01 32.34 33.42 35.27 Ratio 1.12 1.13 1.15 1.16 1.17 Smoothness 18.27 15.39 12.29 11.70 11.85 Time(s) 168.12 343.83 962.23 2437.73 6831.13 4 Bias 28.21 29.61 32.09 33.43 35.29 Ratio 1.12 1.13 1.15 1.16 1.17 Smoothness 20.37 16.95 13.40 11.98 12.42

90 5. DATA-DRIVEN EVALUATION OF SARINFORMATION EXTRACTION METHODS

(a) Despeckled images using MAP-GMRF with Model Order 2.

(b) Despeckled images using MAP-GMRF with Model Order 4.

(c) Despeckled images using MAP-ABM with Model Order 2.

(d) Despeckled images using MAP-ABM with Model Order 4.

Figure 5.12: Despeckled images provided by (a-b) MAP-GMRF and (c-d) MAP-ABM method with model order 2 and 4, and estimation window of (from left to right) 4× 4, 16× 16, and 32 × 32 pixels, respectively. A good quality of the despeckled images is ob- tained with estimation windows bigger than 4× 4 pixels. A good compromise is model order 4 and estimation window 32× 32.

5.4. QUANTITATIVE EVALUATION OFSARINFORMATION EXTRACTION 91

blob-like textures, which appear often in real SAR images. The synthetic case shows that the MAP-GMRF can introduce bias, if the analyzing window does not corre- spond to the structures in the scene.

• The MAP-ABM method is able to model local statistics and better preserves point- like characteristics of the original image. The MAP-ABM model better adapts to the local changes, because it can model larger variety of textures. The MAP-ABM better preserves textures in the urban scenes and is more suitable for real SAR scenes such as the cities, scenes with real structures, etc.

• The impact of the window size was addressed to the synthetic and real SAR images. The images are better modelled by increasing the model order and the window size.

A good compromise is model order 4 and estimation window 32× 32 pixel size.