Finding thin objects in multidementional data is a difficult problem. It is also an important problem because maleable objects such as drugs or explostives can be concealed by making them thin. If we want to be able to detect concealed objects using non-invasive imaging methods, we must be able to find thin objects.
Thin objects are difficult to detect because of noise. Normally when there is noise in an image, we can compensate by sacrificing some resolution of the image to reduce the noise, i.e, smooth the data. However, when the object we are looking for is thin, we have no resolution to give up; we need it all.
Look at the figure below. The pulse in the one dimensional signal on the upper left is thick. That means we can sacrifice some resolution, smooth the signal, and the pulse and it is still clearly present in the signal (lower left). The pulse on the upper right is thin. When it is smoothed, it starts to disappear (lower right). If we want to detect it we cannot smooth it to reduce the noise.
First, we assume that the data are binary in nature. That is, a pixel or a voxel in the data should be either a one or a zero. This is not a safe assumption in general, but it is valid for many types of inspection methods.
We then figure out what patterns of ones and zeros are possible in any neighborhood of the image. Binary restoration restores the data by computing the best value for a pixel based on the measured values of the pixels and the probabilities of the possible pixel patterns.
The assumption of binary data allows us to restore images when there are very high levels of noise. We can find thin objects by adjusting the pattern probabilities to reflect the fact that we expect to find such objects.