Global background value determination

 

The application HISTPEAK examines the pixel values within an image and determines a number of statistical quantities.

The application can be used with the following syntax:

% histpeak in=p2 use=w sfact=4 device=x2w

This leads to the NDF p2 being examined, using the whole image, smoothing the histogram with a filter of radius 4 counts and displaying the histogram on device x2windows. Full details of the parameters may be found in Appendix B.1.

The alternative to using the whole image is to use an ARD file to define the parts of the image to be ignored. In that case the syntax is:

% histpeak in=p2 use=a ardfil=^areas.dat sfact=4 device=x2w

In this example the source image p2 is used together with the ARD file definition areas.dat (note the use of the `^ ' character). The histogram generated to calculate the modal value is smoothed using a Gaussian filter of radius 4 counts. The histogram generated is displayed on device x2w. Other examples are shown in Appendix B.1.

Full details of ARD files may be found in Appendix C.

The program output generated is in the the following format:

Filename:   p2
Title:      Raw Plate Image
Shape:      201 x 201  pixels
Bounds:     x = 1700:1900  y = 600:800
Image size: 40401 pixels

HISTPEAK Results: p2

Pixels (used):              40401     Pixels (bad):                0
Lowest count:            4768.000     Highest count:        9388.000
Skewness:                   0.516     Kurtosis:                1.795

Mean:                    6226.607     Median:               6210.462

Histogram modal values:
Unsmoothed:              6179.000     Smoothed:             6176.000
Projected:               6175.306     Interpolated:         6193.840

Absolute dev.:            333.494     Variance:              183890.
Standard. dev.:           428.824     Back. st. dev.:        365.752

Smoothing filter radius:
Radius request:                 4     Radius actual:               4

Contents of the most occupied histogram bin:
Unsmoothed:                60.000     Smoothed:               46.204
Interpolated:              39.609

The first section gives the name of the file used, the shape of the image, its title and the co-ordinate range involved. This is output as soon as the file name has been input, thereby allowing you to exit the application at an early stage if the wrong file has been requested.

The later sections are data derived either directly from the pixel values in the file or are determined following the construction of a histogram containing the pixel values. Each of the histogram bins has a default width of 1 count (or larger if the count range present in the image is large). The peak in the histogram is used to determine the modal value by a number of routes. The methods are as follows:

Unsmoothed:

The histogram bins are examined to identify the most occupied bin.

Smoothed:

The histogram is smoothed using a Gaussian filter of radius SFACT and then searched to identify the most occupied bin.

Projected:

A number of chords through the histogram peak at different heights are taken. The length and midpoint of each of these is calculated and an extrapolation used to determine the location of the midpoint of a zero length chord.

Interpolated:

The part of the smoothed histogram near to its peak is identified and data from that region `fitted' with a Gaussian curve. The location of the fitted peak is calculated. Under normal conditions this should be the most accurate estimate of the modal pixel value.

The standard deviation of the pixel values in the image is calculated using the standard equations for a Normal distribution. A value (SIGMA) is also derived, evaluating the standard deviation of the pixel value distribution in the region of the histogram immediately surrounding the modal value. For a pure noise image these two values would be expected to be the same, but the presence of any objects or image flaws acts to skew the distribution, generating `outliers' which quickly causes the standard deviation of the image as a whole to become large compared to the value obtained for parts of the image where no objects are imaged.

A crude estimate of the influence of the outliers may be obtained by considering the ratio of the normal standard deviation to the absolute deviation of the image. Alternatively, the skewness and kurtosis (third and fourth moments of deviation from a Gaussian distribution) may also be considered. It should be noted that the kurtosis value provided has had its base value of three subtracted to allow more digits to be displayed.

As a result of the default bin width used (1), images with a pixel count range less than 3 will not be examined by HISTPEAK. To overcome this, images may be manipulated using KAPPA's CMULT to increase their range by a suitable factor.