## Whole Image Analysis

There are three basic reasons for looking at the statistical properties of a digital image: (1) to determine whether the image is technically sound; (2) to establish the range of values in the image, in order to determine the best way to display it; and (3) to determine the optimum brightness scaling to use in processing and displaying a final image.

### 7.2.1 Image Statistics

Image statistics are usually computed by pixel-by-pixel analysis of the entire image. The procedures pays no attention to the subject of, or features in, the imageall they "see" are pixel values. However, the inventory of pixel values resulting from performing the statistical procedures can ferret out a great deal of information that is invisible in a simple inspection of the image.

• Tip: AIP4Win's Statistics Tool computes and displays the statistical properties of the whole image. This provides information that you can use to evaluate the quality and integrity of your images.

### 7.2.1.1 Minimum Pixel Value

This value defines the bottom of the range of pixel values found in an image. In a raw image, the minimum should be the pixel value of the bias plus dark current plus the pixel value of the background sky—a positive number. In a calibrated image, bias and dark have been removed, so the minimum value should be the pixel value of the background sky—a positive number. A minimum pixel value of zero probably means one of three things:

2. pixel values in the sky are very low, and a few are zero, or

3. calibration was performed incorrectly, truncating negative values.

Masked lines and columns are common on many CCDs, so a zero value after calibration is normal. If the sky background is low, the normal variation due to noise occasionally produces a zero or negative value, which is normal. Incorrect calibration might involve a dark frame taken at a different integration or temperature than the image, generating negative values in dark subtraction. In this case, you should find the cause.

### 7.2.1.2 Maximum Pixel Value

The maximum is the top of the range of pixel values found in an image. This can serve as a useful diagnostic, especially if it is close to either the minimum or maximum possible pixel value.

If the range (i.e., the maximum minus the minimum pixel value) is small compared to the maximum possible pixel value (255 for 8-bit integers, 4095 for 12-bit integers, and 65,535 for 16-bit integers), then the image has either received very little exposure; or it shows a very bland subject, such as a flat-field image.

If the maximum is close to the maximum possible value, then some of the pixels represent non-linear or fully saturated photosites on the CCD. A high maximum pixel value warrants investigation, especially if the image will be measured for astrometric or photometric information.

7.2.1.3 Mean Pixel Value

An image that is M pixels wide by TV pixels deep contains a total of MN pixels. The mean pixel value is the sum of the pixel values divided by MN: