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Example of processing the ceramic composite image with macLispix.

The image will look like this:

 
 Image courtesy of Barbara Armbruster, Gatan Corp., 1977

The color in the dark green/gray areas looks blotchy, because the RGB version of the image has been converted to 256 color gif for this web page.

As is, not much can be done with the image -- Split out the three components with the Duplicate button. That results in these three images:

"Ceramic composite - red" (UNSIGNED-BYTE 8) (472 472) 217.6
"Ceramic composite - green" (UNSIGNED-BYTE 8) (472 472) 217.6
"Ceramic composite - blue" (UNSIGNED-BYTE 8) (472 472) 217.6

which are gray level images that MacLispix is meant to work with. (Usually RGB overlays are generated from the separate components, but in this case, the RGB overlay has been read in as a TIFF color image.)

The sample appears to consist of four phases: green, red, blue and black. A scatter diagram is often useful in checking on this. Make the scatter diagram:

  1. Get the Multivariate buttons window with the 'More Buttons' button.
  2. Select the three gray level images above as the X/Red image, Y/Green image and Z/blue image. The colors of the image don't have to correspond to the color labels in the image names. If they are different and an RGB overlay is reconstructed, the colors of the various phases in the image will change.
  3. Make a 3-D scatterplot with the 3D-XYZ button.
    1. A rotation diagram will appear first. Rotate the cube with the mouse if desired.
    2. When finished rotating, close the rotation window.
    3. After a few seconds, the scatter diagram window appears:


 

What is going here on?

The slider has been manipulated to highlight the centers of the clusters. The scatter in the data makes the clusters (which correspond to the phases in the material) blur together.

(Note - the median filtering of these images took about 3 1/2 minutes each on a 150 MHz Power Mac.)

There are a number of ways in macLispix to reduce the scatter in the data, all more or less using pixel averaging. First, I tried median filtering of each component (RGB) separately, giving this result in the color overlay:

The above image is a .jpeg RGB image. In case your web browsser doen't read JPEG image format, i've included the 256 color .gif version below, although it looks very 'contoured', whereas the RGB image looks very smooth.

This is an instructive example of the disadvantage of using 8 bit color for RGB color overlays. The color selection was done using Adobe Photoshop, 'adaptave' option, which performs as well as any.

The scatter diagram of these images has some structure that is most likely an artifact of the median smoothing algorithm:

This is a caution against smoothing images in this way, if subsequent analysis of pixel values is required.






(Note - mean filtering of all three images (kernel radius = 5) takes about 10 seconds.)

The RGB overlay of the mean filtered image looks like this:

and the Scatter diagram looks like this:

 

This seems to have similar artifacts to the median filtered image.

Here is a comparison of the artifacts:

 Median Mean
   

The artifacts introducted into the scatter diagrams are unacceptable. The images might look acceptable at half resolution - this is done with the Pixel Ops -> Shrink _Sum operation.

The color overlay:

The scatter diagram:

Note that this looks much like the original scatter diagram, except that the clusters are a little more separated.

Shrinking by a factor of four separates the clusters further:

And the image looks like this:

or, to compare resolution with the origional, like this:

where each pixel in this image is sum of 16 pixels (4x4 square) in the original. This can be seen by the range of values in this list of the images:

Ceramic composite - green Min 0 Max 232
Ceramic composite - blue Min 0 Max 255
Ceramic composite - red Min 0 Max 255
Ceramic composite - green S2 Min 0 Max 840
Ceramic composite - blue S2 Min 0 Max 1004
Ceramic composite - red S2 Min 0 Max 989
Ceramic composite - green S4 Min 7 Max 3091
Ceramic composite - blue S4 Min 7 Max 3889
Ceramic composite - red S4 Min 0 Max 3823

Which was obtained using the Limits button in the Images collumn.


Various clusters and regions in the scatter plot correspond to phases, phase boundaries and other features of the image.

 Seven regions are selected in the scatter diagram. Since the diagram is three dimensional, the regions are paralleloidal prisims extending into the screen (along the line of sight).  This table shows the colors corresponding to the regions.

The regions in the maps are color coded acording to the table at the upper left. 

This shows the maps to the same scale - to compare with the regions (left). 


Statistics on the regions are available with the Traceback -> Stats and Traceback -> Map Stats button.

Statistics for Maps

               MEAN       MIN       MAX     SIGMA     COUNT     IMAGE

Phase  1:     438.95      6.00   3680.00    881.61    834.00  Ceramic composite - red S4
Phase  1:     110.39     15.00   2031.00    117.26    834.00  Ceramic composite - green S4
Phase  1:     106.20      7.00    451.00     92.27    834.00  Ceramic composite - blue S4

Phase  2:     468.14      0.00   2513.00    270.15   4303.00  Ceramic composite - red S4
Phase  2:    1840.64   1302.00   2434.00    245.70   4303.00  Ceramic composite - green S4
Phase  2:     708.76    392.00   1019.00    116.01   4303.00  Ceramic composite - blue S4

Phase  3:     922.00     10.00   2531.00    457.86   1695.00  Ceramic composite - red S4
Phase  3:    1080.57    675.00   2031.00    170.56   1695.00  Ceramic composite - green S4
Phase  3:     716.24    283.00   1041.00    148.66   1695.00  Ceramic composite - blue S4

Phase  4:    2278.18     52.00   3793.00    707.52   1813.00  Ceramic composite - red S4
Phase  4:     263.00      7.00   2031.00    125.55   1813.00  Ceramic composite - green S4
Phase  4:     676.74    178.00   1309.00    233.56   1813.00  Ceramic composite - blue S4

Phase  5:     762.67      9.00   2144.00    404.45   2090.00  Ceramic composite - red S4
Phase  5:     757.98     13.00   2031.00    409.76   2090.00  Ceramic composite - green S4
Phase  5:    1721.31    415.00   2591.00    333.10   2090.00  Ceramic composite - blue S4

Phase  6:     179.62      0.00    980.00    133.45    448.00  Ceramic composite - red S4
Phase  6:    2602.16   2031.00   3066.00    161.04    448.00  Ceramic composite - green S4
Phase  6:     681.93    311.00   1101.00    140.15    448.00  Ceramic composite - blue S4

Phase  7:     304.86      0.00   1296.00    223.42    147.00  Ceramic composite - red S4
Phase  7:     426.47    122.00   2031.00    169.28    147.00  Ceramic composite - green S4
Phase  7:    3218.05    415.00   3889.00    396.62    147.00  Ceramic composite - blue S4


The table above shows the statistics for the various regions in the images. Note that the original maps were the R,G,B color planes from an RGB file. As such the pixel range from 0 - 255, so this table should be identical to the one below, if it were for the original data. The data that is used here, though, is for the images shrunk down by a factor of four, so that each pixel is really a sum of 16 original pixels.

 

Statistics for Scatter diagram

         MEAN       MIN       MAX     SIGMA     COUNT   REL_SIG

X 0:      28.72      0.00    245.00     58.77    834.00      2.05
Y 0:       8.06      0.00     47.00      9.71    834.00      1.20
z 0:       6.03      0.00     29.00      6.06    834.00      1.01

X 1:      30.68      0.00    167.00     18.00   4303.00      0.59
Y 1:     151.26    107.00    200.00     20.33   4303.00      0.13
z 1:      45.59     25.00     66.00      7.62   4303.00      0.17

X 2:      60.94      0.00    168.00     30.53   1695.00      0.50
Y 2:      88.35     55.00    122.00     14.10   1695.00      0.16
z 2:      46.07     18.00     67.00      9.76   1695.00      0.21

X 3:     151.35     14.00    252.00     47.17   1813.00      0.31
Y 3:      20.68      0.00     50.00     10.38   1813.00      0.50
z 3:      43.49     11.00     85.00     15.34   1813.00      0.35

X 4:      50.31      0.00    142.00     26.97   2090.00      0.54
Y 4:      61.66      0.00    150.00     33.91   2090.00      0.55
z 4:     112.08     65.00    169.00     21.87   2090.00      0.20

X 5:      11.48      0.00     65.00      8.86    448.00      0.77
Y 5:     214.29    194.00    253.00     13.36    448.00      0.06
z 5:      43.79     19.00     71.00      9.19    448.00      0.21

X 6:      19.77      0.00     86.00     14.89    147.00      0.75
Y 6:      34.24      9.00     75.00     14.00    147.00      0.41
z 6:     210.41    170.00    255.00     26.05    147.00      0.12
 This table shows the relative positions and extent of the clusters of dots inside the parallelograms in the scatter diagram above. The pixel values in the maps are scaled 0 - 255.