Attribute combinations for image segmentation

Attribute combinations in 3D

An ideal goal for an image segmentation algorithm is to be able to extend information gathered from a 2D seismic section by using it to guide the segmentation for a 3D volume. For instance, if an interpreter picks an interface on the 2D section, an automated inversion scheme could determine which combination of attribute information would have led the segmentation algorithm to produce the same boundary. This information would then be used to segment the entire 3D cube. Here, we have an opportunity to test a primitive version of this process.

Figure 5 displays a depth slice, inline section and crossline section of the 3D cube containing a portion of the seismic section (Figure 1) used to demonstrate the 2D boundary combinations above; the inline section shown is not the same as the one used for Figure 1. Single-attribute 3D segmentations with amplitude and dip variability attributes produce the eigenvectors seen in Figure 6. As we saw in the 2D case, the amplitude segmentation shows greater certainty in most locations; however, the dip variability eigenvector is noticeably superior in the two indicated areas. We seek to combine the two eigenvector volumes such that the most accurate information from each attribute is contained in a single eigenvector volume.

unocal4
Figure 5. Depth slice and inline and crossline sections of a seismic data cube used for 3D image segmentation. [ER]

3deigs
Figure 6. Slices of the 3D eigenvectors calculated from amplitude (top) and dip variability (bottom) attributes corresponding to the image in Figure 5. The circles indicate areas where the dip eigenvector is noticeably superior to the amplitude eigenvector. [CR]

Previously, we used an uncertainty-weighted eigenvector combination scheme to produce the boundary in panel (d) of Figure 4. From this process, we can retain the individual weight values used for each attribute's eigenvector at each $x$-direction sample. By making the assumption that these weights will remain constant in the crossline direction, we can combine the 3D eigenvector volumes by using these same weight values for every crossline section. Figure 7 shows the results of this process for the same slices displayed in Figure 5. The new eigenvector improves on the ambiguities indicated on the amplitude eigenvector in Figure 6, yet retains the amplitude eigenvector's superior results in other locations. The corresponding zero-contour boundaries for these slices are seen in Figure 8; the boundary accurately tracks the salt interface on all three sections.

comboeig
Figure 7. Combined eigenvector, using a linear combination of the eigenvectors in Figure 6 with weights determined during the 2D example. [CR]

3dbnd
Figure 8. Zero-contour boundary corresponding to the combined eigenvector in Figure 7. The salt interface is accurately tracked on all three sections. [CR]

Attribute combinations for image segmentation