FeatureJ: Statistics

General Description

This plugin enables you to compute gray-value statistics of an image. If a region of interest (ROI) was selected prior to running the plugin, the computations are limited to that region. All ROI types are accepted, except line selections. If no ROI exists, the statistics are computed over the entire image.

Description of Dialog Components

Minimum. The smallest gray-value in the image.

Maximum. The largest gray-value in the image.

Mean. The average gray-value of the image.

Median. The median gray-value of the image.

Elements. The number of image elements (pixels/voxels).

Mass. The gray-value mass, or sum, of the gray-values in the image.

Variance. The variance, or second-order moment about the mean, of the gray-values in the image.

Mode. The most frequently occuring gray-value in the image.

S-deviation. The standard deviation from the mean of the gray-values in the image.

A-deviation. The average absolute deviation from the mean of the gray-values in the image.

L1-norm. The absolute gray-value mass, or sum of the magnitudes, of the gray-values in the image.

L2-norm. The zero-mean standard deviation, or root of the sum of the squares, of the gray-values in the image.

Skewness. The Fisher skewness, or third-order moment about the mean, of the gray-values in the image.

Kurtosis. The Fisher kurtosis, or fourth-order moment about the mean, of the gray-values in the image.

More details on these statistics can be found in the references below.

Clear previous results. The results of the statistics measurements are numbered and displayed sequentially in the results window of ImageJ, always keeping the results of previous measurements, except in the cases mentioned below. Select this option if you want the plugin to first clear the window and reset the numbering before displaying the results of every new measurement.

Image name displaying. Select this option if you want the plugin to display also the name of the image data set. Since this requires an additional column in the results window, the window is cleared (and the numbering reset) in the next run.

Channel/Time frame/Slice numbering. By default, the statistics are computed over the entire image. Select these options to see the results per channel, per time frame, or even per slice. Since this may require additional columns (the channel, time frame, or slice number) in the results window, the window is cleared (and the numbering reset) in the next run.

Decimal places. Most of the statistics measurements result in non-integer numbers, even in the case of 8- or 16-bit images. Here you can specify the maximum number of decimals beyond the period with which these numbers should be displayed. That is, numbers that would require more decimal places for exact representation, are rounded to the specified number of decimal places.

Algorithmic Details

The median and mode are extracted from the histogram of the gray-values in the image. In the case of 8-bit (byte) and 16-bit (short) images the results are exact. In the case of 32-bit (floating-point) images, however, the results are merely estimates of the true median and mode with an inaccuracy of at most +/- 0.0005 percent of the dynamic range of the image. This is caused by the fact that building a histogram of floating-point gray-values requires binning.

References

[1]	S. Kotz, N. L. Johnson (eds.). Encyclopedia of Statistical Sciences. John Wiley & Sons, New York, NY, 1982-1989.
[2]	W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. 2nd ed., Cambridge University Press, 1992.