If checked, the background value in the vicinity of the area being measured is calculated automatically. This obviates the need to adjust the background manually in images having uneven backgrounds. The algorithm performs a fuzzy k-means analysis on the area being measured to calculate the background density (see below). This gives sub-pixel-value accuracy, which is much greater than could be achieved by manually specifying (or allowing the computer to estimate) a single integer background value. It is therefore recommended to keep this option checked. When using this option, the area selected should contain a portion of the background as well as the spot of interest for most accurate results.
If ``auto calculate background'' is checked, the foreground and background pixel densities are computed from the selected region by the fuzzy k-means algorithm [2,3,4,5]. As shown in the above figure, this algorithm estimates the contribution to each pixel from the foreground and background clusters. The centroid (modal value) of the resulting population of partition coefficients is the most probable density of the pixels in each cluster. If the algorithm converges, a table containing statistical information about the analysis is also displayed. The most useful parameters are:
The densitometry results are shown in a list, which can be saved into a file by clicking the ``save'' button. The list displays:
bkg.: Integrated signal in the entire spot minus background
in the spot. (i.e., net density 
no. of pixels in spot).
This is the number to use when analyzing images of SDS or agarose gels,
in which the entire spot represents a quantity of some substance.
Because the background density is calculated from all the pixels, background values can have sub-pixel accuracy. For this reason, results obtained with this method are significantly more accurate than those obtained from programs that use a median value or some other integer as the estimate of background density. For example, I was once asked to analyze an 8-bit image of a Western blot that had bands with pixel values averaging about 211 (on a scale of 0...255), while the background was in the range of 206-209. The person did not want to repeat the experiment, since these were autopsy samples, and had first tried to analyze the image with another well-known image analysis program, which selected integer values for the background. When the other program happened to use 209 instead of 208, it resulted in an error of 50% because of the inaccuracy in the background estimate. Even after taking multiple measurements and discarding those which gave negative numbers, it was impossible to get an accurate measurement from the other program. Increasing the image contrast merely increased the error by the same factor. Using the fuzzy k-means method here, the background could be determined to several decimal points, and clear-cut results were easily obtained.
Maximum signal
Selects whether pixel value corresponding to `black' or `white' (0 or 255 in 8 bpp mode) is to be considered the strongest signal. If you have an image of a protein gel, for instance, the bands appear black and maximum signal should be set to ``black''. For DNA gels, the bands appear white and maximum signal should be set to ``white''.
Note: Selecting ``Black'' as the maximum signal will cause the reported values to be calculated as 1 - (measured value). Thus, if the average uncorrected pixel intensity of a spot is 0.25, the density (with ``pixel compensation'' off) will be 0.75.
Background
Select the fractional pixel value (between 0 and 1) which is to be considered the `background level'. The background level is important in automatic area selection as described above. The background value will be automatically subtracted from the results.
Pixel density calibration
Making density measurements on an image requires some way of relating pixel values to the real quantity being measured. Ordinary scanners do not produce a linear relationship between pixel value and the quantity being measured. Even expensive densitometry imaging equipment and analysis systems, such as MolecularDynamics' PhosphorImager, may not yield linear relationships between band ``density'' and concentrations. This is particularly true for 8-bit images, in which a wide signal has been compressed into only 256 different values. Some software packages use a gamma correction function, which assumes an exponential relationship between signal and pixel value. However, general-purpose software should not attempt such corrections, because many people scan images from nonlinear sources such as film autoradiograms or HRP-stained Westerns, all of which have different inherent response characteristics. When the physical nonlinearities are combined with the nonlinearities in the image acquisition process, the relationship is too complex for accurate results to be obtained using a simple exponential relationship.
For example, exposing a grain on X-ray film or emulsion requires two photons striking a grain within a short period of time, which means that at low light levels, the signal on the film is related to some power of the photon flux. However, at high levels, the unexposed grains become depleted, making the signal independent of light intensity. These factors are highly dependent on numerous factors including temperature, film speed, etc. For Western blots, the production of a colored signal by the immobilized enzyme follows time, temperature, and concentration-dependent hyperbolic saturation kinetics. Clearly, the only accurate way to estimate the true signal under such conditions is by using standards.
Options:
OD value If checked, this will cause tnimage to use the value in the optical density table in its calculations instead of the raw pixel value. This information is sometimes provided by digital scanners in the form of a `gray response curve' or `gamma curve' that is embedded in the TIFF file. For most images, this option will have no effect since no gray response curve is present. However, you can easily create a curve by clicking ``Config..Show OD table'' and modifying the graph to create a curve of any desired shape. Since this curve has only 256 elements, it is only applicable for 8-bit grayscale images.
z units If checked, this causes tnimage to use the calibrated pixel value in its calculations instead of the raw pixel value. Pixel value calibration is performed before starting densitometry, by clicking ``Process..Calibration'', checking the desired equation to which the `z value' is to be fitted, and then clicking on each calibration standard in the image (See Sec. 7.7) and entering the known value in the spreadsheet. Tnimage performs a linear regression on the data and uses these coefficients to calibrate pixels in the image.
No. of terms Sets the number of polynomial terms used in the linear regression for fitting coordinates to calibrated values. If `1' does not give a satisfactory fit, up to 3 terms can be used. Using higher terms will result in lower accuracy in areas extrapolated beyond your calibration points.
NOTE: For this option, the ``Maximum Signal Black/White'' setting is ignored, because the user calibration automatically defines what pixel value is the maximum signal.
None In this option, the signal and density are given as raw densities
(expressed as a number between 0 and 1). (signal = density
number of pixels.)
Calibration factor If a value is entered here, the result is multiplied by that number. This is useful in converting to micrograms of protein, for example, on an image of an SDS gel.
After each measurement, a list box appears with the results. This contains: (1) The area (total number of pixels) analyzed; (2) The total signal measured (either in total pixel values or total O.D. units, depending on whether pixel compensation is active); (3) The average signal, i.e., the quotient of (2)/(1); (4) The corrected total signal minus background. For most purposes, including gel analysis, the number of interest is (2) or (4), because it is desired to measure the total amount of absorbing (or fluorescing) material in the entire band. For other purposes, the signal density or concentration per unit area on the image may be desired. The total area is of interest in morphometry.
NOTE: See the warning under Contrast.
NOTE: Densitometry may not work correctly on zoomed images. Use ``Change size'' first.
WARNING: Pixels beyond the edges of the screen are not included in the area or density calculations.
WARNING: If a monochrome or 8-bit image is converted to color, the original correspondence of pixel values to optical density (if one existed), may be lost. This will result in inaccurate densitometry results.