Note: Descriptions are shown in the official language in which they were submitted.
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CARTESIAN HUMAN MORPHO-INFORMATIC SYSTEM
CROSS REFERENCE TO RELATED APPLICATIONS
This application is a continuation in part of co-pending U.S. Patent
Application 11/428,926,
filed July 6, 2006. This application is also a non-provisional application of
currently pending
U.S. Provisional Patent Application 60/949,395, filed July 12, 2007.
FIELD OF INVENTION
This invention relates to a 3D Cartesian coordinate system for use with human
spatial
morpho-informatics.
BACKGROUND OF THE INVENTION
Human anatomy has traditionally been a descriptive rather than an objective
science. Except
for measurement protocols for skeletal morphology developed by physical
anthropologists,
there has been very little data developed to define human morphology. For
descriptive
purposes classic anatomists have describe the human body as being placed in
the
"anatomical position". When in anatomical position the body is standing erect
with the arms at
the sides with the palms of the hands facing forward. The feet are flat on the
ground with the
toes pointing forward. Structure location is always described relative to
other anatomical
features. For example the feet are inferior to the head, the ribs are
superficial to the heart, the
elbows are lateral to the body and the fingers are distal to the elbow.
Without implementation of a fixed coordinate system linked to specific
anatomical landmarks,
the possibility to define specific quantitative data to be used to describe
the specific location
and orientation of any anatomy feature of any individual or population does
not exist. The
absence of a quantitative information on human anatomy also impacts clinical
medicine.
Radiologists are trained to recognize patterns of anatomy as displayed in
medical images.
Until late in the 20th century these images were primarily planar x-ray films.
With the advent of
CT, MR and PET scanning during the past 3 decades, the types of images that
radiologists
evaluate have varied along with the methods for how they are obtained, but the
images
remained primarily planar in format. Identification and extraction of
quantitative anatomical
data from three dimensional medical images consumes a vast amount of workflow
in
medicinal diagnostics. The inefficiency is partially due to difficulties in
generalizing the steps
needed for successful image segmentation of medical imaging data.
The interface between the medical image scanning technology and the patient in
today's
imaging facilities is the radiology technician, who undergoes one to two years
of training on
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basic human anatomy and imaging technology. Medical imaging technology has
advanced to
the point that the imaging devices can capture and format the image data in a
very short
period of time. At the same time medical instrumentation has become so
sophisticated that
more and more expertise and time is required in the pre-scanning steps to
program the
device to collect the correct image data.
Only recently has volumetric medical image data been possible to obtain, and
few if any
processes are in place to effectively clinical evaluate this volumetric data.
Most often even
though the image data is obtained as digital volumetric data sets, a series of
2D images are
provided to the radiologist with which to make his clinical diagnosis.
Computer technology
currently plays very little role in the analysis of any medical images in
regards to assisting the
physician in making a differential diagnosis. Furthermore, radiologists today
treat each
patient as a new unique set of images for which he diagnoses pathology evident
in the
images based on his experience and expertise in recognizing specific patterns
in medical
image patterns representing the patient's morphology. This approach is
extremely inefficient,
expensive and time consuming. This approach also fails to utilize any
technology resources
to assist the physician with medical image analysis.
Much of the information contained in the volumetric image data is not taken
into consideration
because physicians currently do not have a recognized approach for utilizing
the information
and do not have reference normative data on which to base any level of
diagnostic decision.
The rows and column array format of digital voxel data that is typical of most
all volumetric
medical images lends itself perfectly for the application of computer
technology, but lack of a
standard format and orientation for human anatomical image data has hindered
the use of
computer technology in any type of analysis of medical images. In many
instances, the
analysis of the structure occurs in isolation, without a comparison to a
"normative" dataset of
similar anatomical structures. Computer technology will never play a
significant role in
medical image analysis until a standardized coordinate system and a supporting
set of
validated statistical data regarding the morphological organization of the
human body are
available.
Even current computerized, semi-automated techniques employed to analyze
medical images
require heavy user intervention, resulting in high variability in
quantification. US Pat. Appl.
10/271,916 provides a semi-automated system that attempts to reduce the labor,
while
increasing the accuracy using seeded region and snake segmentation methods.
Even in the
more simplified semi-automated techniques, experienced radiologists are needed
to provide
initial input, generally by outlining a structure of interest. The accuracy of
this initial input
affects all further processing. Differences in the examining radiologist and
the fatigue of the
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radiologist affect the segmentation input and impact the reliability of the
data obtained.
Moreover, many of these processes use 2D images to extract information.
The enumerated issues with traditional anatomical diagnosis affects the
quality of the medical
diagnosis and treatment provided to patients. The field therefore needs a
means by which to
establish the normative human morphology data necessary to implement at the
very least,
first pass, computer-based analysis of all volumetric medical image data.
Ultimately this will
result in faster, more accurate diagnosis of all medical conditions that rely
in some part on
medical image information in making a differential diagnosis.
SUMMARY OF INVENTION
The inventive method allows for the extraction of quantitative information for
human
morphology from volumetric medical image data. As such the invention uses any
imaging
technology providing volumetric data, or technology where the data may be
converted to
volumetric data. Non-limiting examples of medical imaging technologies include
computed
tomography (CT), magnetic resonance (MR) imaging, positron emission tomography
(PET),
X-ray imaging, computed axial tomography (CAT), ultrasound imaging, and
photoacoustic
imaging.
Use of a defined three dimensional coordinate system to align and register
volumetric medical
imaging data of the human body within three dimensional space makes possible
the objective
analysis of the morphometric organization of any individual human as well as
the ability to
compare and statistically define the morphological characteristics of
populations of humans.
This permits description of quantitative data of the morphometric features of
the body of any
individual human, relative to any set of three dimensional coordinates.
Further, changes in
any morphological feature over time that occur as a result of normal
development, growth,
aging, acute insult or progressive changes related to disease processes may be
described
using the three dimensional coordinate system. Moreover, patterns related to
normal
development, growth, aging, acute insult or disease processes may be
documented,
described, analyzed, and diagnosed using the present invention. Statistically-
derived data
sets of morphometric changes, patterns or changes in patterns of digital image
data
characteristics are also useful in the present invention.
Due to conventional standard imaging protocols, the proposed "anatomical
position" for this
system in accordance with the present invention is a supine orientation with
arms at the side
of the body and hands pronated and resting on either side of the midsagittal
plane, inferior to
transverse cardinal plane. However, the position of the patient's body may be
in any
contemplated position. The patient may be positioned on a gantry in a head-
first orientation
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relative to the scanning device. The gantry is oriented level with the ground
and the patient is
transported on the gantry through the scanning device with images being
collected in a
transverse plane through the patient. To permit the mining of objective data
from these
volumetric images for human morpho-informatics, the patient is positioned on
the gantry
relative to a defined morphometric coordinate system prior to initiation of
the scanning. A
plurality of imaginary planes are superimposed to the images, allowing
establishment of a
three dimensional coordinate system. Laser alignment lights, found on many
imaging
devices, may be used to align the patient on the gantry for proper positioning
of the patient.
The plane of the gantry is used to define an initial common plane of reference
for both the
scanner and the patient.
The patient's body is segmented into a plurality of regions by at least one
imaginary plane. In
some embodiments, the patient's body is segmented by two planes or three
planes. In
alternative embodiments, the imaginary planes establish a coordinate system
using the three
cardinal planes (X, Y and Z), in the universally recognized orientations and
segment the body
into regions of anterior/posterior, superior/inferior, and right/left. The
imaginary planes are
disposed along designated, relative positions of the patient's body. In some
embodiments,
the imaginary planes run through pre-designated anatomical features. The
cardinal planes
may include a Sagittal (midsagittal; symphysis pubis, the midpoint of the
upper border of the
manubrium of the sternum, and the nasion of the face/skull) plane, a
Transverse (superior-
most edges of the iliac crests) plane, and Coronal (anterior-most aspect of
the vertebral
canal) plane. However, other combinations of imaginary planes are
comtemplated, such as
running the Coronal Plane through the superior-most point on the iliac crests
and external
acoustic meatus or through the dorsal-most point on the spinous process. The
point at which
these planes intersect defines the 0, 0, 0 location in the human body. The
disposition of the
imaginary planes is, in some instances, standardized to allow comparison of
the images with
previous images of the same patient or images of other patients. Proper
alignment of the
patient within the coordinate system can be confirmed by any method known or
contemplated
by those in the art, like using the laser light guides built into most imaging
systems.
Structures in or on the human body may be quantitatively described, based on
the location
from the intersection point. Positional information may be described in terms
of arbitrarily
units, or English or metric distance measurements. Arbitrary units may be
utilized as linear or
exponentially increasing units.
There are situations where alignment of the patient within the scanner was not
accomplished
prior to image capture, such as utilizing previous medical images in the
present invention. In
such situations, volumetric image data can be post-processed to orient the
anatomical data.
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In some embodiments, post-processing involves re-slicing the original
volumetric data to
provide voxel array data oriented parallel with the coordinate system.
Alternatively, the image
data may be processed by reconstructing the image data, registering the image
data in
relation to the coordinate system, or rotating the image data to align with
the coordinate
system. The volumetric data may then be grafted onto the coordinate system and
analyzed
as though the data was originally aligned.
One set of resulting data will be the average location and orientation of the
bounding box for
each structure within the body along with statistical descriptors of possible
deviations from
these averages. Using statistically determined bounding boxes, the patterns of
digital image
arrays of any population of bounding boxes for each structure in reference to
the three
dimensional coordinate system me be mathematically defined. Digital image
array patterns
ranging from normal to the extremes of all described abnormal morphological
conditions can
be identified and statistically defined. This information is the used to
statistically define
specific patterns of the digital image arrays for each of the diagnosed
conditions contained
with image data base. This information would provide the first step in
teaching the computer
to do "first pass," providing a differential diagnosis based on a patient's
image data.
Volumetric medical images are composed of arrays of rows and columns of
voxels.
Regardless of how that voxels are obtained (CT, MR, PET, etc) the final
representation is
organized in a 3D array. One of the features provided by the bounding box data
approach is
that the 3D grey scale voxel array patterns can be defined for normal
conditions as well as for
any and all variants of pathological conditions. With sufficient validated
data sets of voxel
grey scale array patterns, the scanning device computer may track the
anatomical structures
it is actively scanning and compare the active-scan structures to a validated
database of voxel
grey scan array patterns. Comparing the patient's array patterns with known
patterns allows
the computer to perform a real-time, first pass differential diagnosis of the
image while the
patient is still on the scan table. The results of the scan may be analyzed
and, if the computer
requires more information to make a decision, it has the opportunity to rescan
the patient with
an appropriate protocol the patient is still in the scanner.
After the image data is oriented relative to the three dimensional coordinate
system, and with
the computer aware of the voxel dimensions of the image data, any of a wide
range of
quantitative, morphometric measures can be made of relevant morphological
features. These
measurements can be made on any set of features, in any orientation within the
volumetric
image data. Bounding boxes are used by the invention to define the position
and relative
volume of a structural component. The edges of the box lay "in-plane" with
those of the
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coordinate system. This permits the volume of the structural component
relative to that of the
whole body and position, within the bounding box of the whole body, to be
determined.
Medical imaging technology has advanced to the point that the imaging devices
can capture
and format image data in a very short period of time. The invention
contemplates that preset
conditions can be optionally programmed into the scanning computer. After the
patient is
properly oriented in the scanner, the scanner begins a series of programmed
preset image
protocols based on physician request of radiological diagnosis and
morphological data
contained within the human morphometric data based on the coordinate system,
and include
the regions of the patient that were imaged and which imaging protocols
utilized.
A normative human morphology database may be developed for all relevant
structures for a
large population of normal healthy individuals to describe complete array of
statistical
descriptors of the morphological features. Medical imaging of millions of
patients is
performed each year. For each of these scans a radiologist provides a medical
opinion as to
whether the morphology is normal or abnormal. When abnormal, the pathology is
described.
Using normal and validated abnormal morphology, a database or series of
databases may be
developed to define the array patterns of normal anatomical structures and
disease conditions
for which medical imaging is utilized as a diagnostic tool. This database then
can be used to
provide a measure of limits between normal (healthy) and abnormal
(diseased/pathological)
morphological structure. The information is used to develop software for a
first pass
differential diagnosis and more efficient and accurate scanning protocols.
This will ultimately
reduce the number of scans a person may require, reduce unnecessary radiation
exposure,
and will result in faster, cheaper and more accurate imaging processes.
Data may be stored in any format known in the art, including Picker SPECT, GE
MR SIGNA-
including SIGNA 3, 5, and Horizon LX- Siemans Magnatom Vision, CTI, CTI ECAT
7, SMIS
MRI, and ASI/Concorde MicroPET. The standard format for volumetric medical
image data to
be captured and stored is in the DICOM format. Images in DICOM format can be
viewed,
modeled and measured on a wide range of public domain and commercial software
available
today. Any and all volumetric medical image data oriented as described above
to a defined
human morphometric coordinate system can be data mined to provide precise and
comparable measurements for any and all relationships of anatomical features.
Software
plug-ins for several software packages have been developed to permit efficient
mining of data
from the DICOM image sets oriented within the coordinate system. The plug-ins
permit the
point and click identification and storage of the 3D coordinate of specific
anatomical features.
Line distant length between two anatomical features can be determined. Any 2D
area or 3D
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volume can be user defined by a point and click approach and the volume and 3D
coordinate
location recorded.
If and when volumetric image data of human morphology is placed in
registration within a
three dimensional coordinate system, a wide range of quantitative measurements
can be
made to better document the structural features of the body. When fully
implemented
computer based technology will be able to determine if all internal structures
are normal, and
if not what are the likely medical problems. Use of the coordinate system
permits quantitative
description and analysis of structural features includes but are not limited
to: location, volume,
orientation, length and diameter of all individual structure as well as the
spatial relationships
of any combination of morphological feature of the human body relative to a
any three
dimensional coordinate system. If a similar process is applied to a population
of humans with
image data all registered with the same three dimensional space relative to a
consistent
coordinate system, then detailed statistical analysis can be conducted to
establish
mathematical descriptors for all levels of normal human anatomy as well as
each and every
known pathological condition that has, as one of its features, an alteration
in the patient's
anatomical structure. The resulting human morphometric data sets can be used
in the
development of computer software for the automated analysis of medical images.
The ability
to quantitatively describe the structure of the human body will significantly
increase the value
of medical imaging in 215t century clinical medicine. This approach will
ultimately provide
faster, cheaper and more accurate initial stages of differential diagnosis of
a wide range of
medical conditions.
BRIEF DESCRIPTION OF THE DRAWINGS
For a fuller understanding of the invention, reference should be made to the
following detailed
description, taken in connection with the accompanying drawings, in which:
FIG. 1 is a view of the three cardinal planes relative to a human body.
FIG. 2 is a view of the three cardinal planes showing the intersection point
of all three planes.
FIG. 3 is a view of the three cardinal planes relative to a human body showing
circumscription
of the body and an anatomical structure using a bounding box.
FIG. 4 is a view of the three cardinal planes relative to a human body showing
the location of
a structure of interest, determined using a bounding box.
FIG. 5 is a view of the three cardinal planes relative to a human body showing
the
determination of distances and relationships between a structure of interest.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
In the following detailed description of the preferred embodiments, reference
is made to the
accompanying drawings, which form a part hereof, and within which are shown by
way of
illustration specific embodiments by which the invention may be practiced. It
is to be
understood that other embodiments may be utilized and structural changes may
be made
without departing from the scope of the invention.
The invention provides an establishment of a protocol to extract quantitative
information for
human morphology from volumetric medical image data. The approach incorporates
the
implementation of a defined three dimensional morphometric coordinate system
for
registration of the volumetric image data of the human body in three
dimensional space.
In most medical imaging technologies, including computed tomography (CT),
magnetic
resonance (MR) imaging and positron emission tomography ((PET), the patient is
positioned
lying supine on a gantry in a head-first orientation relative to the scanning
device. The gantry
is oriented level with the ground and the patient is transported on the gantry
through the
scanning device with images being collected in a transverse plane through the
patient. To
permit the mining of objective data from these volumetric images for human
morpho-
informatics, the patient is positioned on the gantry and oriented to
correspond to the
morphometric coordinate system prior to initiation of the scanning. Laser
light or other
orientation methods are used to orient the patient's body. Most imaging
technology utilizes,
or is capable of utilizing, alignment lasers. The lasers project lines onto
the patient's body,
one along the midsagittal axis and one along the transverse axis,
perpendicular to the
midsagittal axis. The radiologist aligns the transverse laser light with the
superior-most edges
of the iliac crests, identified on the patient by palpation. The lateral laser
light is oriented to
the sagittal plane by aligning the light to the symphysis pubis, the midpoint
of the upper
border of the manubrium of the sternum, and the nasion of the face/skull.
Final confirmation
of proper patient orientation can be made using scout images of the patient.
As seen in Figure 1, the patient's body is segmented into eight regions by a
plurality of
planes. The Coronal Plane 10 (or Frontal Plane) passes through the side of
body 1, dividing
body 1, or any of its parts, into anterior and posterior portions. Sagittal
Plane 20 (or Lateral
Plane) passes through the midline of body 1 from front to back and divides
body 1, or any of
its parts into right and left sides. Transverse Plane 30 (or Axial Plane)
passes through the
superior-most edges of the iliac crests dividing body 1, or any of its parts,
into upper and
lower parts. Coronal Plane 10, Sagittal Plane 20 and Transverse Plane 30
intersect at
intersection point 40, seen in Figure 2 with the body remove to allow
visualization of the
intersection point. Intersection point 40 is thereby used to define the 0, 0,
0 point of the body.
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The three cardinal planes (X, Y and Z) are disposed in a three dimensional
orientation, with
the Coronal Plane 10 defining the X-axis of a three dimensional coordinate
system, the
Sagittal Plane 20 defining the Y-axis, and Transverse Plane 30 defining the Z-
axis.
There are occasions where medical images of a patient are not aligned with the
morphometric
coordinated system prior to imaging. In these situations, the volumetric image
data can be
post-processed to accomplish the proper orientation of the anatomical data
relative to the
coordinate system. In these cases it may be necessary to re-slice the original
volumetric data
to provide voxel array data oriented parallel with the coordinate system. The
volumetric data
may then be grafted onto the coordinate system and analyzed as though the data
was
originally aligned.
First pass differential diagnosis
Volumetric medical images are composed of arrays of rows and columns of
voxels.
Regardless of how that voxels are obtained (CT, MR, PET, etc) their final
representation is as
digital voxel data organized in a 3D array. The present invention allows for a
user to select an
anatomical feature by circumscribing the feature in a bounding box.
One of the features provided by the bounding box data approach is that the 3D
grey scale
voxel array patterns can be defined for normal conditions as well as for any
and all variants of
pathological conditions. With sufficient validated data sets of voxel grey
scale array patterns,
the computer of the scanning device determines which anatomical structures it
is actively
scanning and utilizes a validated database of voxel grey scan array patterns
for comparison
at the time of scanning. By comparing the patient's array patterns with known
patterns, the
computer can perform a first pass differential diagnosis of the image as it is
acquired and
while the patient is still on the scan table. This permits the imaging system
to rescan the
patient with whatever protocol necessary if the computer determines it needs
more
information to make a decision. As this occurs in real-time, re-scanning of
the patient occurs
in the same imaging session as the original scan, while the patient is still
in the scanner.
A normative database of human morphology can be developed for all relevant
structures for a
large population of normal healthy individuals to describe complete array of
statistical
descriptors of the morphological features of each and every structure chosen
to be contained
with the database. Medical imaging of millions of patients is performed each
year. For each
of these scans a radiologist provides a medical opinion as to whether the
morphology is
normal or abnormal. When abnormal, the pathology is described. Using this
enormous data
base of both normal and validated abnormal morphology, array patterns are
clearly defined
for most of the disease conditions for which medical imaging is utilized as a
diagnostic tool.
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This data is used to develop the software for first pass differential
diagnosis and well as more
efficient and accurate scanning protocols. This data reduces the number of
scans a person
requires, thereby reducing any unnecessary radiation exposure. At the same
time the
imaging process can be made faster, cheaper and more accurate than currently
exists.
The volumetric medical image data is captured and stored in DICOM format
permitting the
images to be viewed, modeled and measured on a wide range of public domain and
commercial software available. DICOM formatted, volumetric medical image data
is oriented
to the defined human morphometric coordinate system and the data mined to
provide precise
and comparable measurements for any and all relationships of anatomical
features. Software
plug-ins for several software packages have been developed to permit efficient
mining of data
from the DICOM image sets oriented within the coordinate system. These plug-
ins permit the
point and click identification and storage of the 3D coordinate of specific
anatomical features.
Line distant length between two anatomical features can be determined. Any 2D
area or 3D
volume can be user defined by a point and click approach and the volume and 3D
coordinate
location recorded.
Example
The present invention's ability to quantitatively describe the location of a
structure in or on the
human body is illustrated in the following example. Arbitrarily-chosen
coordinates are utilized
to define the location from intersection point 40 (0, 0, 0). As seen in Figure
3, Sagittal plane
20 (X-axis) is defined from 50 (uppermost limit) to -50 (the lowermost limit);
Transverse plane
30 (Y-axis) defined as 20 (right-most lateral limit) and -20 (the left-lateral-
most limit); and
Coronal plane 10 (Z-axis) defined as 10 (anterior-most limit) and -10 (the
posterior-most limit).
Body 1 is defined by body bounding box 3. Anatomical structure 2 is defined by
structure
bounding box 4. The points of the bounding box are determined on the
corrdinate system. In
this example, the location of structure 2 would have a coordinate of
(approximately) 10, 10, 10
(X, Y, Z). In this example, structure 2 is located approximately 1/5 of the
distance upward on
the coronal plane (X-axis) from the transverse plane (Y-axis), approximately
1/2 of the
distance to the right on the transverse plane (Y-axis) from the sagital plane
(Z-axis); and the
full anterior distance on the sagittal plane (Z-axis) from the coronal plane
(X-axis).
By using the concept of "smallest bounding box" (sbb), data related to the
position and
relative volume a structural component of the body can be obtained. The sbb
represents the
smallest box into which the structure of interest will fit. The edges of the
box lay "in-plane"
with those of the coordinate system. Using this approach sbb 3 for body 1 as a
whole can be
identified and its volume calculated, as seen in Figure 4. The sbb 4 for
anatomical structure
2, for example the right kidney, can be determined and its volume calculated.
Using these
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two pieces of data, the volume of the right kidney relative to that of the
whole body, as well as
the specific location of the right kidney bounding box within the bounding box
of the whole
body, can be determined.
By using the sbb for a plurality of anatomical structures in body 1,
relationships between
different anatomical structures may be determined. For example, the distance
and relative
orientation between two anatomical structures may be determined by calculating
the
difference between points on the two anatomical structures' bounding boxes, as
seen in
Figure 5. A user selects a first anatomical structure 2a and circumscribes the
structure in
structure bounding box 3a, followed by selecting a second anatomical structure
2b and
circumscribing the structure in structure bounding box 3b. The present example
shows a
patient's right kidney and heart selected, however any anatomical structure
obtained by the
imaging system may be selected. The direct, linear distance 5 between the
points is
automatically calculated. Additionally, because the bounding boxes are aligned
with the
coordinate system of body 1, the position of the anatomical structures may be
determined in
relation to the patient's body and in relation to other anatomical structures.
Once these procedures are completed for all relevant structures for a large
population of
normal healthy individuals, a normative data base of human morphology is
developed to
describe statistical descriptors of the morphological features of each and
every structure
chosen to be contained with the data base. This data base then can be used to
provide a
measure of limits between normal (healthy) and abnormal
(diseased/pathological)
morphological structure.
One of the resulting data will be the average location and orientation of the
sbb for each
structure within the body along with statistical descriptors of possible
deviations from these
averages. Using these statistically determined sbbs, the patterns of digital
image arrays may
be mathematically defined for any population of sbb for each structure in
reference to the
three dimensional coordinate system. Digital image array patterns ranging from
normal to the
extremes of all described abnormal morphological conditions can be identified
and statistically
defined. With a large enough population of sbb for an anatomical structure and
assuming that
this population of sbb contains all defined diagnostic conditions then, it
should be possible to
statistically define specific patterns of the digital image arrays for each of
the diagnosed
conditions contained with image data base. This information is then useful in
teaching the
imaging computer to do "first pass", differential diagnosis based on a
patient's image data.
It will be seen that the advantages set forth above, and those made apparent
from the
foregoing description, are efficiently attained and since certain changes may
be made in the
above construction without departing from the scope of the invention, it is
intended that all
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matters contained in the foregoing description or shown in the accompanying
drawings shall
be interpreted as illustrative and not in a limiting sense.
It is also to be understood that the following claims are intended to cover
all of the generic
and specific features of the invention herein described, and all statements of
the scope of the
invention which, as a matter of language, might be said to fall there between.
Now that the
invention has been described,
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