Invert/Logical NOT

Common Names: Logical NOT, invert, photographic negative

Brief Description

Logical NOT or invert is an operator which takes a binary or graylevel image as input and produces its photographic negative, i.e. dark areas in the input image become light and light areas become dark.

How It Works

To produce the photographic negative of a binary image we can employ the logical NOT operator. Its truth-table is shown in Figure 1.

Figure 1 Truth-table for logical NOT.

Each pixel in the input image having a logical 1 (often referred to as foreground) has a logical 0 (associated with the background in the output image and vice versa. Hence, applying logical NOT to a binary image changes its polarity.

The logical NOT can also be used for a graylevel image being stored in byte pixel format by applying it in a bitwise fashion. The resulting value for each pixel is the input value subtracted from 255:

Some applications of invert also support integer or float pixel format. In this case, we can't use the logical NOT operator, therefore the pixel values of the inverted image are simply given by

If this output image is normalized for an 8-bit display, we again obtain the photographic negative of the original input image.

Guidelines for Use

When processing a binary image with a logical or morphological operator, its polarity is often important. Hence, the logical NOT operator is often used to change the polarity of a binary image as a part of some larger process. For example, if we OR

and

the resulting image,

shows the union of the background, because it is represented with a logical 1. However, if we OR

and

which are the inverted versions of the above image we obtain

Now, the result contains the union of the two circles.

We illustrate another example of the importance of the polarity of a binary image using the dilation operator. Dilation expands all white areas in a binary image. Hence, if we dilate

the object, being represented with a logical 1, grows and the holes in the object shrink. We obtain

If we dilate

which was obtained by applying logical NOT to the original image, we get

Here, the background is expanded and the object became smaller.

Invert can be used for the same purpose on grayscale images, if they are processed with a morphological or logical operator.

Invert is also used to print the photographic negative of an image or to make the features in an image appear clearer to a human observer. This can, for example, be useful for medical images, where the objects often appear in black on a white background. Inverting the image makes the objects appear in white on a dark background, which is often more suitable for the human eye. From the original image

of a tissue slice, we obtain the photographic negative

Interactive Experimentation

You can interactively experiment with this operator by clicking here.

Exercises

Apply the erode operator to

and

Which polarity of the image allows you to suppress the circles?
Compare the results of ORing

and

and ORing their photographic negatives.
Take the photographic negative of

Does it improve the visibility of the features in the image?

References

A. Jain Fundamentals of Digital Image Processing, Prentice Hall, 1989, p 238.

R. Gonzales and R. Woods Digital Image Processing, Addison Wesley, 1992, pp 47 - 51.

E. Davies Machine Vision: Theory, Algorithms and Practicalities, Academic Press, 1990, Chap. 2.

Local Information

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.