The hit-and-miss transform is a binary morphological operation that can detect particular patterns in an image. It uses a structuring element containing foreground and background pixels to search an image. If the structuring element pattern matches the image pixels underneath, the output pixel is set to foreground, otherwise it is set to background. The hit-and-miss transform can find features like corners, endpoints, and junctions and is used to implement other morphological operations like thinning and thickening. It is performed by matching the structuring element at all points in the image.

1. BY:
KRISHNA PRASAD BACHU

2. Brief Description
 The hit-and-miss transform is a general binary morphological operation
that can be used to look for particular patterns of foreground and
background pixels in an image. It is actually the basic operation of binary
morphology since almost all the other binary morphological operators can
be derived from it. As with other binary morphological operators it takes as
input a binary image and a structuring element, and produces another
binary image as output.
Common Names: Hit-and-miss Transform,
Hit-or-miss Transform

3. How It Works
 The structuring element used in the hit-and-miss is a slight
extension to the type that has been introduced
for erosion and dilation, in that it can contain both foreground
and background pixels, rather than just foreground
pixels, i.e. both ones and zeros. Note that the simpler type of
structuring element used with erosion and dilation is
often depicted containing both ones and zeros as well, but in that
case the zeros really stand for `don't care's', and are just used to
fill out the structuring element to a convenient shaped kernel,
usually a square. In all our illustrations, these `don't care's' are
shown as blanks in the kernel in order to avoid confusion. An
example of the extended kind of structuring element is shown in
Figure 1. As usual we denote foreground pixels using ones, and
background pixels using zeros.

4. Figure 1 Example of the extended type of structuring element used in hit-and-miss
operations. This particular element can be used to find corner points, as explained
below.
 The hit-and-miss operation is performed in much the same way as
other morphological operators, by translating the origin of the
structuring element to all points in the image, and then comparing the
structuring element with the underlying image pixels. If the
foreground and background pixels in the structuring element exactly
match foreground and background pixels in the image, then the pixel
underneath the origin of the structuring element is set to the
foreground color. If it doesn't match, then that pixel is set to the
background color.

5.  Figure 2 Four structuring elements used for corner finding in binary images
using the hit-and-miss transform. Note that they are really all the same
element, but rotated by different amounts.
• For instance, the structuring element shown in Figure 1 can be used to find
right angle convex corner points in images. Notice that the pixels in the
element form the shape of a bottom-left convex corner. We assume that the
origin of the element is at the center of the 3×3 element. In order to find all the
corners in a binary image we need to run the hit-and-miss transform four
times with four different elements representing the four kinds of right angle
corners found in binary images. Figure 2 shows the four different elements
used in this operation.

6. After obtaining the locations of corners in each orientation, We can then
simply OR all these images together to get the final result showing the
locations of all right angle convex corners in any orientation. Figure 3 shows
the effect of this corner detection on a simple binary image.
 Figure 3 Effect of the hit-and-miss based right angle convex corner detector on
a simple binary image. Note that the `detector' is rather sensitive.

7.  Implementations vary as to how they handle the hit-
and-miss transform at the edges of images where the
structuring element overlaps the edge of the image. A
simple solution is to simply assume that any
structuring element that overlaps the image does not
match underlying pixels, and hence the corresponding
pixel in the output should be set to zero.
 The hit-and-miss transform has many applications in
more complex morphological operations. It is being
used to construct
the thinning and thickening operators, and hence for
all applications explained in these worksheets.

8. Guidelines for Use
 The hit-and-miss transform is used to look for occurrences
of particular binary patterns in fixed orientations. It can be
used to look for several patterns (or alternatively, for the
same pattern in several orientations as above) simply by
running successive transforms using different structuring
elements, and then ORing the results together.
 The operations
of erosion, dilation, opening, closing, thinning and thicken
ing can all be derived from the hit-and-miss transform in
conjunction with simple set operations.
 Figure 4 illustrates some structuring elements that can be
used for locating various binary features.

9. Figure 4 Some applications of the hit-and-miss transform. 1 is used to locate isolated
points in a binary image. 2 is used to locate the end points on a binary skeleton Note
that this structuring element must be used in all its rotations so four hit-and-miss passes
are required. 3a, 3b, and 3c are the kernels used to locate the triple points (junctions)
on a skeleton. All three structuring elements must be run in all orientations so twelve
hit-and-miss passes are required.

10. We illustrate two of these applications on an image skeleton.
We start with
 which is the skeleton of

11.  shows the triple points (i.e. points where three lines meet) of the skeleton.
Note that the hit-and-miss transform itself merely outputs single foreground
pixels at each triple point (the rest of the output image being black). To
produce our example here, this image was then dilated once using a cross-
shaped structuring element in order to mark these isolated points clearly, and
this was then ORed with the original skeleton in order to produce the overlay.
 The image
• The image