An Example: Segmenting and Despeckling a Large Image

Figure 6.11 shows an original intensity DLR ESAR image after it has been averaged and resampled 3x3 to remove correlations as discussed above.

Figure 6.11: An Example DLR ESAR Image

We shall first segment this image and then despeckle it. In each case we show the residual ratio to indicate how effective the image-interpretation process is at removing speckle. The quality of reconstruction will be indicated by the absence of structure in the residual image and also the derived ENL. The results motivate our overall advice: despeckling on its own provides smoothed images which retain detail and are easier to interpret by eye than the original data; but for most purposes segmentation provides a better starting point for a processing chain.

Segmentation

Initially we segment the scene using the default segment parameter set, except that the shape parameter is set at 0.02. The segmented result is illustrated in Figure 6.12. Most of the structure is clearly visible in the reconstruction. However, some of the fine structure to the right of the top of the runway has not been reproduced. In addition, there are a large number of small regions visible within the scene. These may be partly caused by sloping field areas in the scene, which cannot be presented properly by the uniform region model imposed by segmentation other than by introducing small segments. Alternatively, they might be the result of small statistical fluctuations caused by speckle.

Figure 6.12: Segmentation of the scene in figure 6.11

The most revealing test for the quality of the reconstruction is to take the ratio of the original intensity image to its segmentation. If the segmentation corresponded precisely to the underlying RCS, then this ratio would have the properties of pure speckle. The residual ratio would therefore show no structure, related to the underlying scene, and the average statistical properties could be used to derive an Effective Number of Looks (ENL) that should be the same as the known value (4.0) imposed by the sensor. This residual ratio image is shown in Figure 6.13. Some minor evidence of the underlying scene structure is visible, indicating that the reconstruction is not perfect. On the other hand, the derived ENL is 4.03, which is close to the expected value. The fact that the ENL is approximately correct indicates that the average properties are well represented. However, the presence of structure effects in the residual image indicates those regions where detail has been lost in the reconstruction. This is a consequence of adopting a single shape parameter. If the segmentation algorithm used in segment were extended so that this parameter was allowed to adapt to the scene content the effects of structure would probably be reduced (but we have not tried this).

Figure 6.13: Residual ratio derived from figures 6.11 and 6.12

A more sensitive test as to whether the residual ratio corresponds to the predicted speckle model for a system with ENL = 4.0 is to compare the PDF of the residual ratio, at full resolution, with theory. This is illustrated in Figure 6.14. While the agreement is not perfect, it is clear that the PDF has approximately the correct form. The estimated mean for the residual ratio is almost exactly 1.0, as predicted. The observed discrepancy is not, however, entirely due to the fact that the estimated ENL = 4.03, rather than 4.0; there is actually a slight departure from the form of a gamma PDF.

Figure 6.14: Comparison of observed residual ratio (dotted curve) for segmented data, shown in Figure 6.13, with theoretical PDF for ENL = 4.0 (full curve) having mean = 1.0 and order = 4.0.

One way to eliminate differences between neighbouring segments that are relatively insignificant is to apply the merge algorithm. Rather than providing a global solution to the cartoon model implying uniform regions (segments), this examines pairs of adjoining segments and tests the statistical significance of their separation. This can be expressed in terms of the false alarm probability, $P_{fa}$, which describes the probability that a single segment could be split into two separate segments by speckle noise. For example, $P_{fa} = 10^{-5}$ would indicate that there was a probability of $10^{-5}$ that a segment containing a uniform RCS could be split by speckle noise. If a split of this probability is not significant then such regions should be merged; and this is what merge does.

The result of applying this merge process to the data of Figure 6.11 and the segmentation of Figure 6.12 is shown in Figure 6.15. There is no appreciable difference between this and the original segmentation in Figure 6.12, indicating that the many small regions visible are very unlikely to be a consequence of speckle fluctuations, and hence are indeed significant within the cartoon segmentation model used.

Figure 6.15: Result of merging segments with $P_{fa} = 10^{-5}$

Despeckling

Another method for removing speckle is to use the despeckling algorithm implemented in despeckle. Rather than impose the cartoon model of uniform RCS within each segment, this implies a local similarity over a neighbourhood of 3x3 pixels. It identifies which possible arrangement of 3 correlated pixels, out of the 12 possible, is most consistent with the data and speckle. It too depends on simulated annealing to determine the overall optimum despeckled solution. The consequence of applying this algorithm to the data of Figure 6.11 is shown in Figure 6.16. Since despeckle does not impose uniform regions with consequent sharp discontinuities (edges), the result appears to yield a gently varying background. This is likely to be more consistent with the actual real data than the cartoon model. One might deduce that this would be a better algorithm to use for image interpretation. However, the main weakness of this method is that it merely generates a continuously varying intensity, largely free of speckle noise, which still requires further image processing to identify regions of similar properties, i.e. classification. Segmentation can lead directly into this stage. Furthermore, there is no concept of an edge in this approach, whereas most information data bases, such as maps, require regions of similar content to be identified and their edges delineated.

The final drawback of this approach is that it actually misrepresents the speckle model. If we construct the residual ratio, assuming that the despeckled output corresponds to the underlying RCS, we obtain the result shown in Figure 6.17.

Figure 6.16: Despeckled version of Figure 6.11.

Figure 6.17: Residual ratio for the despeckled reconstruction in Figure 6.16.

While the uniform regions of the original image (Figure 6.11) yield a realistic speckle appearance, all structure in the image affects the residual ratio strongly. This is a consequence of the $3\times3$ window over which correlations in the data are identifed and exploited in the reconstruction process. When this is compared with the corresponding result following segmentation, in Figure 6.13, it is clear that the process introduces considerable distortion into the reconstruction. This is made apparent when the ENL is estimated, yielding a value of 4.26, compared with 4.03 for segmentation. This indicates the extent to which this method fails to satisfy the speckle model.

The effect is made still more obvious if the PDF of the residual ratio in Figure 6.17 is compared with the predicted gamma PDF of mean 1.0 and order 4.0. This is illustrated in Figure 6.18. It shows that both the order of the distribution and its shape differ from the ideal theory.

Figure 6.18: Comparison of observed residual ratio for despeckled data, shown in Figure 6.16, with the theoretical PDF for ENL = 4.0 (full curve) having mean = 1.0 and order = 4.0.

Conclusions

• We have illustrated the effect of removing speckle by invoking two different models: the cartoon model for segmentation and the local similarity model for despeckling.
• Segmentation yields the result that is closest to the speckle model in that the residual ratio resembles speckle most closely.
• Segmentation shows evidence of many small segments. These are retained when the data is merged, indicating that they are statistically significant.
• Despeckling presents a more continuous fluctuation in the background, inherent in the local similarity model.
• Despeckling shows strong correlations around structures in the scene as a consequence of the 3x3 construction window.
• Despeckling yields a poorer fit to the speckle model.