Edge-preserving smoothing for segmentation of seismic images

A hybrid approach

From the examples in Figure 3, it appears that traditional smoothing does perform very well in areas devoid of sharp boundaries or edges. Therefore, we can develop an approach that combines the characteristics of box smoothing in areas without edges, and takes advantage of the edge-preserving features of MH filtering when edges are present. For the MH algorithm, we already calculate variances for each of the bar masks passing through a given pixel. Comparing the largest and smallest of these calculated variances indicates the likelihood that an edge is present. If the ratio between the smallest and largest variances is large (close to 1), the pixel is in a relatively ``isotropic'' area, and an edge is unlikely to be present. Conversely, a smaller ratio implies that an edge is present in at least one of the bar mask orientations. If $\alpha$ is a user-determined threshold value, then if $\frac{\min(\sigma)}{\max(\sigma)}>\alpha$ , traditional smoothing can safely be used in lieu of MH filtering for that particular location.

Figure 5 demonstrates this strategy on the synthetic example shown earlier. As the threshold value $\alpha$ decreases, the algorithm is more biased toward traditional smoothing; consequently, the amount of ``speckle'' noise decreases. However, near the two reflectors, MH filtering still holds sway. The final result is an image with the speckle noise removed as well as in the traditional smoothing result in Figure 3(a), but with the reflector edges preserved as well as the standard MH result in Figure 3(b).

syn-hyb-50,syn-hyb-25,syn-hyb-10
Figure 5. The results of applying the hybrid-MH filter with $\alpha$ set at (a) 0.5, (b) 0.25, and (c) 0.1 to the original noisy synthetic image in Figure 2. As $\alpha$ decreases, more speckle-noise is removed from the image, while the sharpness of the reflectors is preserved.

Edge-preserving smoothing for segmentation of seismic images