Teem: nrrd: Visible Female Color Data Processing: Joint Histograms


teem	/	nrrd	/	Visible Female	Joint Histograms

The images of the gray scale strips don't look very different, but the changes in brightness became more obvious, and easier to characterize, with the help of joint histograms of pairs of grayscale strips. Also called a co-occurance matrix, the joint histogram of two gray-scale images records the number of pairs of spatially corresponding pixels with a given combination of brightness values; this is useful for automatic image registration by mutual information. For instance, the joint histogram between the red channels of gray235.ppm and gray236.ppm can be generated with:

unu slice -i gray235.ppm -a 0 -p 0 -o 0.pgm
unu slice -i gray236.ppm -a 0 -p 0 -o 1.pgm
unu jhisto -i {0,1}.pgm -b 256 256 -t uchar | topng doc/2356R.png

unu jhisto ... This creates a nrrd with as many dimensions as there were input nrrds, in this case two. Axis i of the joint histogram corresponds to the range of values in the ith input nrrd.

Nearly all the hits are along the diagonal because the brightnesses of these two images are very similar. We can also joint histogram all the color components at the same time, because unu jhisto treats all the input nrrds as basically 1-dimensional lists of values.

unu jhisto -i gray235.ppm gray236.ppm -b 256 256 -t uchar | topng doc/2356.png

Now for the fun part. We can visualize the inter-slice brightness changes between four slices by putting the joint histograms of the gray scales from successive pairs of slices into the red, green, and blue channels of a color image.

unu jhisto -i gray235.ppm gray236.ppm -b 256 256 -t uchar -o 0.pgm
unu jhisto -i gray236.ppm gray237.ppm -b 256 256 -t uchar -o 1.pgm
unu jhisto -i gray237.ppm gray238.ppm -b 256 256 -t uchar -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o grjh23.ppm
unu jhisto -i gray324.ppm gray325.ppm -b 256 256 -t uchar -o 0.pgm
unu jhisto -i gray325.ppm gray326.ppm -b 256 256 -t uchar -o 1.pgm
unu jhisto -i gray326.ppm gray327.ppm -b 256 256 -t uchar -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o grjh32.ppm
unu jhisto -i gray417.ppm gray418.ppm -b 256 256 -t uchar -o 0.pgm
unu jhisto -i gray418.ppm gray419.ppm -b 256 256 -t uchar -o 1.pgm
unu jhisto -i gray419.ppm gray420.ppm -b 256 256 -t uchar -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o grjh41.ppm
unu jhisto -i gray292.ppm gray293.ppm -b 256 256 -t uchar -o 0.pgm
unu jhisto -i gray293.ppm gray294.ppm -b 256 256 -t uchar -o 1.pgm
unu jhisto -i gray294.ppm gray295.ppm -b 256 256 -t uchar -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o grjh29.ppm

convert grjh23.ppm doc/grjh23.png
convert grjh32.ppm doc/grjh32.png
convert grjh41.ppm doc/grjh41.png
convert grjh29.ppm doc/grjh29.png


`grjh23.png`	`grjh32.png`	`grjh41.png`	`grjh29.png`

We can use ilk to stretch the joint histograms away from the diagonal, to get a clearer picture of what changed:

ilk -i grjh23.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/grjh23st.png
ilk -i grjh32.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/grjh32st.png
ilk -i grjh41.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/grjh41st.png
ilk -i grjh29.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/grjh29st.png


`grjh23st.png`	`grjh32st.png`	`grjh41st.png`	`grjh29st.png`

Well, this is troubling. The manner in which the brightness changed in the first case is diferent than the second case (the second is quite non-linear), meaning that the method of brightness correction would ideally vary according to Z location. Worse yet, in the third case, where there is an isolated darker slice, the gray strip joint histograms indicate that there is not any obvious brightness change among the four slices, at least not significantly more than in the fourth case, where we know that there is no brightness variation in the head. For comparison, we can form joint histograms of the head images themselves, and again stretch them with ilk:

unu jhisto -i avf1079{b,c}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 0.pgm
unu jhisto -i avf10{79c,80a}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 1.pgm
unu jhisto -i avf1080{a,b}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o hdjh23.ppm

unu jhisto -i avf1109{a,b}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 0.pgm
unu jhisto -i avf1109{b,c}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 1.pgm
unu jhisto -i avf11{09c,10a}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o hdjh32.ppm

unu jhisto -i avf1140{a,b}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 0.pgm
unu jhisto -i avf1140{b,c}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 1.pgm
unu jhisto -i avf114{0c,1a}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o hdjh41.ppm

unu jhisto -i avf1098{b,c}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 0.pgm
unu jhisto -i avf109{8c,9a}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 1.pgm
unu jhisto -i avf1099{a,b}.raw.Z.head.ppm -b 256 256 -t int \
  | unu quantize -b 8 -max 700 -o 2.pgm
unu join -i {0,1,2}.pgm -a 0 -incr -o hdjh29.ppm

convert hdjh23.ppm doc/hdjh23.png
convert hdjh32.ppm doc/hdjh32.png
convert hdjh41.ppm doc/hdjh41.png
convert hdjh29.ppm doc/hdjh29.png

ilk -i hdjh23.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/hdjh23st.png
ilk -i hdjh32.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/hdjh32st.png
ilk -i hdjh41.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/hdjh41st.png
ilk -i hdjh29.ppm -t rotate:-45 scale:1,4 rotate:45 | topng doc/hdjh29st.png


`hdjh23.png`	`hdjh32.png`	`hdjh41.png`	`hdjh29.png`

`hdjh23st.png`	`hdjh32st.png`	`hdjh41st.png`	`hdjh29st.png`

The joint histograms of the head images in the first two cases look very similar to those of the gray scale strips. In these cases, the strips seemed to work well to record the brightness variations that affected the central region of the images. The third and fourth cases are more troubling. The joint histograms of the gray scale strips in neither of these cases indicated obvious brightness variations, but the joint histograms for the head images show otherwise. There is a significant variation recorded in the third histogram, while in the fourth case, the histogram confirms that these slices had no variation.

It seems, then, that the gray scale strips unfortunately did not fully do the job of recording brightness variations that affect the data inside the body. Even if the gray scale strips were extracted for every single slice, they don't contain the necessary information to automatically correct the brightness.