Problem Definition ::


In order to discuss the shape from probing problem, one has to define the particular type of probe used. Informally a probe can be defined as a geometric object displaced in the region of interest. The movement of the probe and its collisions with the shape under investigation give information about the shape. There are many possible types of probes. One possibility is an infinite line that moves in the direction perpendicular to its length. We will use a different definition.

In this tutorial, a probe is defined as a directed line. Imagine that an arrow is shot from a point at infinity toward the shape. The arrow either hits or misses the shape. If it misses the shape, it traces a clear path from which information can be gathered. If it hits the shape, information is obtained both from the point of contact and from the clear path traced by the arrow. Probes can be directed such that the knowledge about the shape is maximized.

The following figure illustrates the probing mechanism. The probe on the left hits the shape while the one on the right misses it. As we will see in the next section, a lot of information can be deduced from the outcome of these probes.


Information Gained by Probing