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| As an example, consider MR (Magnetic
Resonance) images. In normal clinical practice, MR images are generally
used for qualitative examination. The aim of our study has been
the quantitative spatial analysis of MR data using the three fundamental
weighted images: PD (proton density), T1 (longitudinal relaxation
time, spin-reticulum) and T2 (transverse relaxation time, spin-spin).
Starting from three 2D MR images, of 256x256 pixels (each pixel
represented by 12 bits), at the same slice location in a given patient,
a new single image representation of all three parameters has been
generated by using the false-color technique on a HP
9000/730 workstation in a standard UNIX and X11 environment. A transformation
linking together the MR parameters and the RGB (Red, Green, Blue)
color components has been used. In particular, in our study, PD
corresponds to Green, T1 to Blue, and T2 to Red, respectively.
The operator has several interactive controls for modifying the
false-color compositing process. He/she interacts with the display
shown in Figure 1. |
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Figure 1: Layout of working environment
(in b/w) for multimodal MR image processing. On the left (top
to bottom) are T2, PD, T1(Gadolinium-enhanced), MR original
images. Center bottom is the color composite image. On the
bottom right is a view into the three-dimensional histogram
(PD, T1, T2). |
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| The image in the center, is the composite
result of the mapping of the three parameters by means of false-colors.
It is displayed using a resolution of 24 bits per pixel via an HP
CRX24 graphics board. This results in an image with high color definition
which is desirable in order to better identify regions of interest
for diagnostic purposes in radiology.
The operator may independently vary the mix of each of the three
components in the false-color composite via three (R,G,B) mixing
sliders. Each slider specifies a percentage of its associated component
to be included in the composite. The operator can also do proportional
"black-clipping" of the low intensity parts of the 3 components
via the horizontal "Black Clip Percent" slider above the
composite image. Furthermore, by using the pixel data in the PD,
T1, T2 component images, a three-dimensional space containing the
density distribution of these three parameters has been constructed.
This 3D histogram space is shown in Figure 1 (lower right side).
It is constructed as follows: On the three 2D images (see Figure
1, left part), each coordinate pair (x,y) identifies a specific
data triplet: PD, T1, T2. These data values, are the coordinate
indices of a 3D histogram. The values of the histogram identify
the number of pixels with the same PD, T1, T2. Memory requirements
are critical in the realization of such a data structure. In fact,
since each pixel is represented by 12 bits, in theory each coordinate
of the histogram may range between 0 and .
In a 3D space, the maximum dimension of the scatter-diagram will
be
pixels. Since each pixel has been defined as a "short int"
(2 bytes), the image would occupy up to
bytes. In order to reduce memory requirements, only six bits of
each R, G, B channel have been considered. These are generated in
3-steps for each component: (a) the 12-bit data is (1D) histogrammed
and mapped into an 8-bit range after clipping 1%off the high intensity
(white) tail of the distribution, and (b) This 8-bit scaled component
data may then be interactively attenuated by the mixing sliders
and/or black-clipped as described above, and (c) the high order
6-bits of each processed component are extracted to yield an 18-bit
address into a histogram array of 4-byte 'unsigned int' values.
In this case, the scatter-diagram requires a memory space equal
to .
The histogram (scatter-diagram) has been displayed in stereo: the
stereo monitor allows the three-dimensional rendering of visual
data through LCD (Liquid Crystal Display) shuttered glasses (Crystal
Eyes by StereoGraphics, Inc.). Each eye shutter alternately opens
and closes for half of a 72 Hz stereo cycle, while the graphics
board synchronously displays a 144Hz sequence of left and right
eye views. Using the mouse in this 3D space in a interactive way,
it is possible to define regions of interest (ROI) in the tissue
space by highlighting the anatomical zones corresponding to a given
data cluster (i.e. color range). Also, a sort of inverse operation
can be performed - i.e. to define some point of interest in one
of the component parameter images, and see the data cluster containing
its PD,T1,T2 values highlighted. This latter operation is more easily
understandable to a clinician. That is, it can be explained as equivalent
to asking the question: "Show me all pixels having similar
tissue parameters as the one I am pointing at," the criterion
for similarity being membership in a given data cluster.
We have what we think is a novel technique (patent applied for)
for defining a data cluster. Namely we treat the histogram function
as a data density function and apply a threshold T to it to define
a set of histogram locations where H(PD,T1,T2) >= T. This set,
in general will consist of several distinct connected components.
These components are our operational definition of data clusters
- i.e. all points in a given component are considered "similar".
Moreover, the user of the system can interactively vary the threshold
T, and view it's effect on the histogram clusters. Raising T will
cause the clusters to shrink in a manner similar to peeling layers
off an onion. Conversely, lowering T will cause the clusters to
expand.
This kind of approach offers an easier interpretation of MR data
and a clearer distinction between normal and pathologic tissues,
allowing an immediate visual evaluation of the parameters of MR
acquisition systems. The user can display in the same application
the scatter-diagram, the component parameter images, and the false-colored
composite tissue image. In such a way, it is possible to interact
with all the available images, simultaneously reasoning about both
qualitative and quantitative aspects.
Figure 2 shows a stereo pair which is an extension of this technique
for a stack of brain slices making up a complete 3D tissue volume.
It is from a 28 year old white male with three inoperable dural
based tumors. 9 months prior to the MR scan a ventricular meningioma
had been resected. The site of the resection can be seen as a dilation
of the left lateral ventricle. Radiation therapy was completed three
months before the MR scan, and was followed by chemotherapy. The
growth of the frontal lesion suggests this is a meningeal sarcoma.
The slice thickness of the MR scans is 5mm. The original data was
3 volumes of 27 slices 256x256x12 bits each. These were processed
as follows:
- Each 12-bit component volume was histogrammed and scaled into
12-bits by
- white_clip set by clipping .1% of the picture area off white
histogram tail
- black_clip set by clipping .1% of the picture area off black
histogram tail
- the reduced range [black-clip, white-clip] was linearly
mapped into 12-bits.
- The resulting volume at 36-bits per voxel was reduced to a 12-bit
per voxel volume and specific color palette by:
- using the high-order 6-bits of each component value to form
an 18-bit histogram bucket address in a 64x64x64 bucket color
space.
- choosing an initial palette consisting of the 4096 most
popular buckets in the histogram.
- the mean value of voxels in each bucket was used to represent
each bucket.
- voxels not lying in one of the chosen buckets were assigned
to the nearest one (in color space) and the resulting bucket
mean was updated accordingly.
- The resulting 12-bit paletted volume was then fed to the new
ISG/IAP paletted color volume renderer. No z-interpolation was
done. z-pixel dimension was set to be 3 times the x,y dimension.
- Palette colors were ordered on a HSV_12bit_order_code = vvvhhhssssss
For reordered color index i, color[i] is composited using an opacity
table interactively defined to be:
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[ 0 |
0
<= i < |
512 ] |
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transparent |
| Opacity(i) = |
[ramp |
512
<= i < |
2560 ] |
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[ 1 |
2560
<= i < |
4095 ] |
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opaque |
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| The result of this is that darker
tissues have been made transparent, creating cavities in the stereo
image which the user can peer into. |
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| Figure 2: stereo pair made using
3D direct volume rendering of a false-colored brain volume starting
from a sequence of 27 2D MR slices, 3 parameters per slice,
composited into false-color. Certain tissues have been made
transparent allowing a stereo view into cavities created. Dataset
courtesy of Dr L.P. Clarke and Robert Velthuizen of University
of South Florida and the H. Lee Moffitt Cancer Center and Research
Institute. |
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The intent is to add the 3D stereo
histogram display to this application. A 24-bit (non-paletted) colored
stereo pair view of the corresponding histogram for Figure 2 is
shown in Figure 3. |
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Figure 3: 3D Color Histogram
of dataset shown in Figure 2. Color is assigned by position
in the RGB color cube (origin is black corner of cube at top).
Opacity is proportional to histogram bucket occupancy. The
edges of the cube and the main 'neutral-axis' diagonal are
drawn in at full opacity for orientation purposes. This was
rendered by one of the authors (Sobel) using the Stanford
University "Volpack" fast volume renderer with some
extensions by Milon Mackey of HP
Labs.
» view
a QuickTime movie of the cube rotating (805KB)
If you have a StereoGraphics "CrystalEyes" stereo
display, to get a high quality, directly viewable, stereo
image:
- put the following line in your .mailcap file
image/*; xv -visual TrueColor %s
(you may have to restart your Browser after this for it
to take effect)
- click here
(2.62MB)
- then turn on stereo mode on your display
*if the depth appears inverted click here
(2.82MB) and try again
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This would allow simultaneous 3D visualization
of false-colored tissue space and histogram space. Moreover, in
contrast to Figure 2, the histogram cluster-selection technique
can be used to rationally set the opacity of a cluster of interest
to opaque (and everything else transparent), or alternatively transparent
(with everything else opaque). This allows us to create a very powerful
interactive virtual dissection tool.
Figure 4 shows a single stereo pair from a volume rendered cine-stereo
sequence for flow enhanced heart imaging. This is a monochrome dataset
acquired by a group at Picker, Inc. consisting of 10 volumes spaced
in time over a complete heart cycle. Each volume consists of a sequence
of 49 2D MR slices of a normal human thorax. For each given user
azimuth angle (i.e. about the vertical axis) all 10 volumes were
rendered into a cine loop of 10 stereo pairs. The resulting cine-stereo
display was quite compelling and informative - several radiologists
including at least one cardiac angiographer seemed interested enough
to examine at it quite closely for about 10 minutes. |
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| Figure 4: 3D rendering of a reconstructed
thorax starting from a sequence of 2D MR slices. Data courtesy
of Dr. Paul Margosian (formerly Picker Inc.) Marconi Medical
Systems, Inc., Cleveland, OH. |
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