OR and NOR are examples of logical operators having the
truth-tables shown in Figure 1.
Figure 1 Truth-tables for OR and NOR.
As can be seen, the output values of NOR are simply the inverses of the corresponding output values of OR.
The OR (and similarly the NOR) operator typically takes two binary or graylevel images as input, and outputs a third image whose pixel values are just those of the first image, ORed with the corresponding pixels from the second. A variation of this operator takes just a single input image and ORs each pixel with a specified constant value in order to produce the output.
The operation is performed straightforwardly in a single pass. It is important that all the input pixel values being operated on have the same number of bits in them or unexpected things may happen. Where the pixel values in the input images are not simple 1-bit numbers, the OR operation is normally (but not always) carried out individually on each corresponding bit in the pixel values, in bitwise fashion.
We can illustrate the function of the OR operator using
and
The images show a scene
with two objects, one of which was moved between the exposures. We can
use OR to compute the union of the
images, i.e. highlighting all pixels which represent an object either
in the first or in the second image. First, we
threshold the images, since the process is simplified
by use binary input. If we OR the resulting images
and
we obtain
This image shows only the position of the object which was at the same location in both input images. The reason is that the objects are represented with logically 0 and the background is logically 1. Hence, we actually OR the background which is equivalent to NANDing the objects. To get the desired result, we first have to invert the input images before ORing them. Then, we obtain
Now, the output shows the position of the stationary object as well as that of the moved object.
As with other logical operators, OR and NOR are often used as sub-components of more complex image processing tasks. OR is often used to merge two images together. Suppose we want to overlay
with its histogram, shown in
First, an image editor is used to enlarge the histogram image until it is the same size as the grayscale image as shown in
Then, simply ORing the two gives
The performance in this example is quite good, because the images contain very distinct graylevels. If we proceed in the same way with
we obtain
Now, it is difficult to see the characters of the histogram (which have high pixel values) at places where the original image has high values, as well. Compare the result with that described under XOR.
Note that there is no problem of overflowing pixel values with the OR operator, as there is with the addition operator.
ORing is usually safest when at least one of the images is binary, i.e. the pixel values are 0000... and 1111... only. The problem with ORing other combinations of integers is that the output result can fluctuate wildly with a small change in input values. For instance 127 ORed with 128 gives 255, whereas 127 ORed with 126 gives 127.
You can interactively experiment with this operator by clicking here.
and
and AND their negatives. Compare the results.
and
? Use graylevel ORing to combine the two images. Can you detect all the locations of the objects in the two images? What changes if you invert the images before combining them.
R. Gonzalez and R. Woods Digital Image Processing, Addison-Wesley Publishing Company, 1992, pp 47 - 51, 171 - 172.
E. Davies Machine Vision: Theory, Algorithms and Practicalities, Academic Press, 1990, Chap. 2.
B. Horn Robot Vision, MIT Press, 1986, pp 47 - 48.
Specific information about this operator may be found here.
More general advice about the local HIPR installation is available in the Local Information introductory section.
©2003 R. Fisher, S. Perkins,
A. Walker and E. Wolfart.
