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02/16/2010

Older documentation and explanation.

Scatter Plots from Images  (using the 2 & 3 Variable Tool)

 

Images of the same dimensions can be displayed as scatter plots, sometimes called Concentration Histogram Images (a term applicable to quantitated x-ray maps).   You can make scatter plots for one, two or three images.  The scatter plot for one image is just the histogram for the image.  The scatter plot for two images is itself an image with each blob representing a group of matched pixel pairs (one from each image) with similar intensities.  The scatter plot for three images may be a cube, shown as a projection with orientation that you can change, or as a ternary plot.  Which type of plot you make, depents on which images are selected, and the value of the size parameter. See the table below.

The quick traceback feature allows you to select an area of the scatter diagram, and then show immediately which pixels in the original images correspond to that area.  You may display the mask to save it for use later with the traceback feature.  All of the masks that you make using the quick traceback (except by drawing) denote one simply connected area such as a rectangle or a circle.

The traceback feature, which is more flexible but more cumbersome to use, uses a mask to select which pixels will be "traced back".  Since you make the mask ahead of time, the shapes in it can be arbitrary, such as any number of rectangles and circles, or a mask made by thresholding.

Scatter Diagram Options

Number of Images Selected
Size Parameter
Resulting Scatter Diagram
Quick Traceback
Traceback
1
n/a
histogram
n/a
n/a
2
nil
 ok
 ok
2
ok
3
nil
 ok
ok
3
number
 ok
 ok
1 RGB image
n/a
3-D perspective
 ok
 ok

(The links in this table go to illustrations below, on this same page..)


Synthetic Image Example

Documentation

Images


 

Raney Nickel X-Ray Map Example

Opening the sample images:

The images are distributed with Lispix in this folder:   lx-Images\CHI-samples-1.  One way to open to these images quickly is to:

  1. Expand the Lispix Menu Bar.
  2. Select the demo images folder using  R / Demo images.  This sets the Lispix read directory to be lx-images, the demo images folder.
  3. File / Open, and double-click on the CHI-samples-1 folder
  4. Holding down the <control> key, which allows selection of more than one image, click on the three images AlK-kr.tif, FeK-kr.tif, NiK-kr.tif..  Each image will open in its own window. 
  5. The images will open one on top of another.  To see them all, use the Tile button (which is in the Lispix Menu Bar, second line of buttons), or use Window / CASCADE.
  6.  

    Dale Newbury of NIST supplied these images.  They come from elemental x-ray maps:  AlK-kr signifies: Al - an Aluminum image, K- x-ray line, kr - a k-ratio image rather than an image with original or scaled x-ray counts.
    The images are k-ratio images, made from x-ray maps (using the PPP Tool, FINI button) that is the pixel value corresponds to the atom fraction of the element.  Pixel values range from 0 to 1.0 (plus outliers due to noise that are either negative, or greater than one.)  Therefore, these are real valued pixels - single floats, or 4-byte IEEE floating point numbers.  ImageJ will also open these images files, Photoshop will not.  To move images such as these to Photoshop, first scale them:  Image / scale to byte, and save them:  File / save as TIFF.

 

 

 

 

 

 

 

 

 

Open the 2 & 3 Variable Tool

Tools / 2 & 3 Variable.  The tool appears like this:


Two-dimensional plot from two images.


Three Dimensional scatter diagram from three images.

Select the Nickel (NiK-kr) image as the blue or z image, so that the Tool now has these settings:

scatter plots / scatter plot (chi) now results in a projection of a three dimensional scatter diagram:

The traceback feature works for this type of diagram, keeping in mind that the region you select is interpreted as a cyllinder along the line of sight.  You may view this cubical scatter diagram, and thus select regions from it from different points of view by changing the rotation and tilt parameters, and then making a new scatter diagram.  Also, you can project the diagram onto any or all of the six faces of the cube using the faces! button.  The designation of the faces applies to the default orientation, shown here. Keep this in mind after you rotate the cube.  Also, please note that Lispix assumes when doing a traceback that the rotation, tilt and faces parameters are correct for the scatter diagram in front, i.e. the one which is being used to select regions of the diagram for a traceback.  If you change the parameters, then make an old diagram the front one, the traceback gives bogus results.


Ternary Diagram from Three Images

If the Size! parameter is a number rather than nil, the diagram will be a ternary diagram instead of the projection of a 3D diagram.  The size of the diagram is roughly equal to the size parameter. (The height is the size parameter plus 20 pixels, the width is larger, to allow the triangle to be equilateral.)

In the button window above, the only change from the previous example is that the Size! parameter has changed from nil to 400.  To get the diagram that follows, use scatter plots / scatter plot (chi) / scaled image values.

Note that the ternary plot of the original data looks very different.  In the first place, the difference is because the scaled image values (in this case) range from 0 - 255 for each image - the absolute relation of magnitudes between the images has been lost.  Scaling does tend to fill out the triangle, however, which makes things look pretty for this illustration.

Further, much of the data is outside the triangle.  This is because the data in the images include many negative pixel values values - an artifact of the k-ratio calculation due to stochastic noise in the original x-ray maps where each pixel in an image is an x-ray count.  Using Info / list size & limits (in the Lispix Menu Bar) shows the data ranges of the three images: