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Chapter 3 ■ Digital Morphology 115

placed outside of the bounds of the image. The complement operator produces
an image of the same size as the image being complemented, although when
using sets this would not be so. This problem can be avoided by copying the
input image to a bigger image before doing the complement.

(a) (b) (c)

(g)

(d) (e) (f)
Figure 3.18: Illustration of the hit-and-miss transform. (a) The image to be examined. (b)
Foreground-structuring element for the location of upper-right corners. (c) The erosion of
(a) by (b) — the ‘‘hit’’ portion of the computation. (d) The complement of (a). (e) The
background-structuring element, showing that the three pixels to the upper right of the
corner must be background pixels. (f) The erosion of (d) by (e), or the ‘‘miss’’ portion of
the computation. (g) The intersection of (c) and (f) — the result, showing the location of
each of the two upper-right corners in the original image.

The MAX program that performs a hit-and-miss transform is:

// Hit-and-miss transform
image a, se1, se2;
begin
do a << “$1“;
se1 := {[5,5], [2,1], “0000000000110000100000000“};
se2 := {[5,5], [2,1], “0000001100001000000000000“};
a := (a--se1)*(~a -- se2);
message a;
end;