Calibrate

Calibrates the image x and y coordinates and pixel values.

'x units' and 'y units' both calibrate x and y coordinates to user-specified calibration values. The coordinates are fitted to a straight line or a polynomial curve depending on the setting of ``No. of terms'':

No. of terms	Type of curve
1	Straight line
2	Quadratic curve
3	Cubic curve

The coordinates are also fitted to the calibration values that you enter using the same type of curve.

The calibration units are labeled 'x' and 'y' for convenience, but in fact they are independent of each other and can be in any direction, including any diagonal direction, or can even be parallel to each other. The 'x' and 'y' calibration is useful if the position of a point on the image corresponds to some parameter, such as molecular weight, longitude, etc.

'z units' calibrates pixel values only, and is independent of the pixel's location. This is useful when pixel value represents some position-independent parameter such as altitude, height, temperature, etc. Densitometry results can also be calculated in terms of calibrated z values.

If you change a calibration point by clicking ``Edit data'', or if you change one of the fitted parameters in the boxes (such as `y intercept'), a new calibration curve will be calculated when you click ``Recalculate''. The new calibration values take effect immediately.

Each image can have a different x, y, and z calibration curve.

Procedure for calibrating an image:

1. Click on the image to select it.
2. Select ``Calibration'' from the menu.
3. Set Non-directional or Directional calibration type.
4. For each dimension to calibrate, select the equation which will be used to fit the data (linear, logarithmic, polynomial, or distance from 0).
5. Click on ``Obtain data'' to select calibration points from the image, or enter the desired parameters if already known.
6. When calibrating from calibration points, click at the points on the image where the x, y, or z value is known. A small box will appear indicating the control point. This box can be dragged to a different location.
7. Continue clicking until all the desired control points have been acquired, then press any key or space bar to finish.
8. A small spreadsheet will appear allowing you to edit the x and y coordinates and to enter the calibration value for each point. When calibrating the z dimension, the spreadsheet has two columns instead of 3. In this case, enter the calibration value that corresponds to the indicated pixel value and edit the pixel value if necessary.
9. Click OK. The image is automatically calibrated. The f value and correlation coefficient for the curve fitting are shown.
10. Repeat with other dimensions if desired.
11. The calibration points can be modified by clicking on ``Edit data''.
12. The calibration parameters can also manually altered. Any changes in these boxes take place immediately. Clicking on ``Recalc from data'' will recalculate the calibration parameters from the data points.
13. The data points and calibration parameters can also be read from and saved to a disk file by clicking on the corresponding button.

Each image, as well as the background, can be calibrated separately and can have a different title. The calibrated value is shown in the left information panel below the Relative Coordinates display.

Several types of calibration are possible:

1. Non-directional linear calibration: The distance between the starting and ending points is multiplied by a conversion factor to give the calibrated value. This calibration is useful for morphometric measurements on images, where the units are independent of the angle.
2. Directional linear calibration: Measures the distance from a line perpendicular to the best-fit line passing through your calibration points. This calibration is useful for images of isoelectric focusing gels, or other situations where the distance in one direction is the parameter of interest.
3. Logarithmic calibration: Same as (2) except distances are logarithmic (For example, if 10 pixels corresponds to 1 unit of distance, 20 pixels would be 10 units, and 30 pixels would be 100 units). This calibration is suitable for acrylamide and agarose gel electrophoresis images.
4. 2nd-order polynomial calibration: Same as (1) except distances are fitted to a quadratic equation. Could be useful.
5. Distance from 0: Distances are calculated as the distance from a (0,0) point somewhere in the image. This calibration type is suitable for calibrating to objects of known size on the image, for example if a ruler was included in the image.
6. Exponential: pixel values raised to some exponent. This equation is often used as `gamma correction'.

For example, to calibrate a 2D SDS acrylamide gel, set the calibration type to ``Directional'', calibrate the first dimension from the molecular weight standards (using a logarithmic function), and then calibrate the isoelectric point from the IEF standards using a linear function. Set the Units to ``MW'' and ``pI'' respectively.

Example 1: Calibrate an SDS-PAGE gel for molecular weight standards.

1. Select ``Calibration''.
2. Select ``logarithmic'' and ``Directional'' calibration from the dialog box.
3. Check to ensure the correct image number is shown.
4. Change units to ``Molecular weight'' (optional).
5. Click on ``Obtain data'' to start calibration.
6. Click on each size standard in the image. Each point will be shown by a small box. In case of a mistake, you can go back and drag any of the boxes to a new location. A best-fit line is automatically drawn connecting the boxes. Make sure that this line is in the same orientation as the lanes in your gel (i.e., vertical or near vertical if your lanes are straight).
7. When finished, press a key. The Data Entry dialog will appear. Enter the corresponding molecular weights in each box.
8. When finished, press Enter or click on OK. The dialog box will disappear.
9. The molecular weight is now displayed continuously.

Image calibration dialog

Example 2: Calibrate coordinates on the image to centimeters using a ruler in the image.

1. Select ``Calibration''.
2. Select ``Distance from 0'' and ``Non-directional'' calibration from the dialog box.
3. Check to ensure the correct image number is shown.
4. Click on ``Obtain data'' to start calibration.
5. Click on the ruler markings on the strip in the image. A small box indicates the calibration point. Move the box by clicking-and-dragging if necessary.
6. Press a key when finished, then enter the centimeter value.
7. When finished, press Enter .
8. The image is now calibrated. Each image, as well as the background, can have a different calibration. The distance is measured as the distance from 0,0 in any direction as defined by the calibration points. Calibrated distance measurements can now be performed.

Notes:

1. If the image is calibrated from data, at least 3 points are required. Values less than or equal to 0 are not permitted for logarithmic calibration.
2. If the parameters are already known, they can be entered directly (see below). It is not necessary to acquire calibration points in this case. The `statistics' fields will remain blank.
3. The control points do not need to be obtained in any particular order.
4. The x, y, and z calibrations are calculated independently, using separate parameters. This means the calibration axes do not need to be orthogonal with respect to each other or to the screen axes. They also do not need to be oriented in any particular direction. This means, for example, that you could calibrate both the 1st and 2nd dimensions to different scalings in the same direction to indicate inches and centimeters in the same direction.
5. The z calibration is different from the x and y calibrations in that only the pixel values are considered, and is independent of the x and y coordinates.
6. The calibrated distances are also used for distance and angle measurements and strip densitometry area calculations. Z calibration can also be used to calibrate densitometry density measurements.

Entering calibration coefficients directly

If the calibration coefficients are already known, they may be entered directly into the dialog box. For calibrating pixel values, imal interprets these parameters as follows:

Calibration type	Equation
Exponential	answer = $q_0$ + pixel$^{q_1}$
Logarithmic	answer = $q_0$ + 10$^{pixel}$
Linear	answer = $q_0$ + pixel $\times q_1$
Polynomial	answer = $q_0$ + pixel $\times q_1$ + pixel$^2$ $\times q_2$

where q$_0$ to q$_2$ are the 0, 1st, and 2nd order polynomial coefficients of the best fit line and `pixel' is the pixel value. For calibrating x and y coordinates, imal interprets the parameters as follows:

Calibration type	Equation
Exponential	answer = $q_0$ + x$^{q_1}$
Logarithmic	answer = $q_0$ + 10$^{x}$
Linear	answer = $q_0$ + x $\times q_1$
Polynomial	answer = $q_0$ + x $\times q_1$ + x$^2$ $\times q_2$

where x is the distance from the origin point in pixel units. The x and y origin points are calculated from

$$x_o = first\_x\_data\_ point$$

$$y_o = q_0 + first\_x\_data\_point \times q_1$$

The slope and intercept of a line perpendicular to the best-fit line are also shown but have no effect on the calibration if they are changed.

For example, if the 1st order coefficient in z is set to 1.3 and the z calibration is set to `exponential', the program will use (pixel value)$^{1.3}$ instead of the pixel value in density calculations.

Calibrating images based on a reference image

Often it is necessary to calibrate a series of images to a known standard, such as a scanned image of a ruler. This can be done as follows:

1. Calibrate the standard image as described above. In this example, the calibration type (i.e., ``Calibration for x'' ) would be ``1-D Non-Directional''.
2. Select ``Image Properties...Copy tables'' and select ``Copy calibration''. Set the ``Image to change'' to the image number of the new image, and ``Copy from'' to the image number of the standard image.
3. Click OK. The new image now has the same calibration as the standard.