From Numerical Intervals to Set Intervals (Interval-Related Results Presented at the First International Workshop on Applications and Theory of Random Sets)

image set or not, these pixels form the desired set (image) S 0 . In real life, however, measurements are never absolutely accurate; as a result, we still get a set of pixels S, but the location of each point from the observed set S may 1 be slightly different from its location in the (unknown) actual set S 0 . 1.2 How to describe the relationship between the observed set and the actual set: Hausdorff distance If we know the upper bound " ? 0 on the distance between the actual and mapped locations, then we can formulate the relationship between the known approximate set S and the actual (unknown) set S 0 as follows: ffl each "mapped" point s (i.e., a point from the "mapped" set S) is "\Gammaclose to some "actual" point (i.e., to some point from S&lt