# Point Operations An Overview

The four basic types of point operation are distinguished primarily by the method used to identify the numerical range of interest. They are:

• direct function specification,

• direct endpoint specification,

• histogram endpoint specification, and

• histogram specification.

The most basic method of changing pixel values is direct function specification. In this method, you specify how the software should change the pixel values in the image, using a mathematical rule such as: "subtract 100 and extract the square root of the remainder" without explicitly stating the range of pixel values. In this example, if, after subtracting 100, the pixel value is negative, it will not be possible to extract the square root and therefore impossible to apply the function.

Figure 13.1 This image of the galaxy M101, a 40-minute track-and-stack exposure made by Rob West, shows the object much as it would look to you if you had eyes as sensitive as a CCD chip. On paper, however, the image looks dark. What it needs is a point operation to transform it into a brighter image.

Figure 13.1 This image of the galaxy M101, a 40-minute track-and-stack exposure made by Rob West, shows the object much as it would look to you if you had eyes as sensitive as a CCD chip. On paper, however, the image looks dark. What it needs is a point operation to transform it into a brighter image.

The rule used to convert old to new values is called a transfer function. You can transfer pixel values using a linear function; or you can reverse the range, raise , pixel values to a power, take their logarithm, raise their logarithm to a power, divide the range of pixel values into steps—anything to make the features that you want to see stand out clearly and distinctly.

Direct endpoint specification explicitly separates the point operation into two parts: isolating the range of important pixel values, and converting the values inside the range using a transfer function. With direct endpoint specification, you inspect the images and decide the pixel values that will display as black and white; for example, "Set black to 26; set white to 2100," and you also select a function that is capable of handling the pixel values between those limits.

Histogram endpoint specification automates the process of finding the black and white endpoints. Instead of selecting specific pixel values, you specify what percentage of pixels is allowed to saturate to black or white; for example, "Let 0.1% of the image be black; keep 99.9% from saturating white." The software figures out the black and white pixel values and then applies the transfer function that you have selected to generate the new image.

However, a sophisticated point operation called histogram specification or histogram shaping automates the choice of transfer function. In histogram shap-

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