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BACKGROUND OF THE INVENTION
The present invention is generally directed to a system and method for
displaying internal surface information. More particularly, the present
invention is directed to a system and method for displaying internal
surfaces existing at various depths within a three-dimensional body. The
images of the surfaces displayed are typically contained within the
interior regions of solid bodies which are examined by computer axial
tomographic (CAT) x-ray systems or by nuclear magnetic resonance (NMR)
imaging systems, either of which is capable of generating
three-dimensional arrays of data representative of one or more physical
properties at various locations within a three-dimensional object. The
images generated in the practice of the present invention are particularly
useful in that they provide three-dimensional data for examination by
physicians, radiologists and other medical practitioners. The present
invention is particularly useful in that it permits the simultaneous
display of select tissue types on a display device. Even more
particularly, the present invention is directed to a parallel, pipeline
architecture for simultaneously determining surface type and for the
generation of surface normal vectors for the display of shading
characteristics.
In conventional x-ray systems, a two-dimensional shadow image is created
based upon the different x-ray absorption characteristics of bone and soft
tissues. A great improvement on the conventional x-ray system as a
diagnostic tool is provided by computed axial tomographic systems, which
have been developed over the last ten years or so. These so-called CAT
systems are x-ray based and have been used to produce single
two-dimensional views depicting transverse slices of a body, object or
patient. Three-dimensional information was thereafter gleaned from CAT
scan data by generating data for a number of contiguous slices and using
the inferential abilities of the radiologist to suggest a
three-dimensional representation for the various internal organs. In the
present invention, shaded and contoured three-dimensional images are
generated from the three-dimensional array of data generated by a sequence
of such contiguous CAT scans or magnetic resonance imaging scans. The
images are typically displayed on a two-dimensional screen, but the
shading provided produces an illusion of a three-dimensional structure,
just as in a conventional motion picture.
The newer magnetic resonance imaging technology possesses the capability to
better discriminate between various tissue types, not just between bone
and soft tissue and therefore offers the capability for producing more
discriminating images in many situations. NMR imaging systems are also
capable of generating physiological data rather than just image data.
However, whether NMR or CAT systems are employed, data has generally been
available only as a sequence of slices, and systems have not generally
been available which provide shaded two-dimensional images which
accurately depict three-dimensional views.
Prior work by at least one of the inventors herein has significantly solved
some of the major problems associated with the production of high
resolution, three-dimensional medical images. In particular, a system
referred to as "dividing cubes" was disclosed in patent application Ser.
No. 770,164 filed on Aug. 28, 1985 now U.S. Pat. No. 4,719,585, issued
Jan. 12, 1988. At the time of the invention, all of the individuals in the
present case and other related prior cases assigned to the same assignee,
were under an obligation of assignment to the same assignee. The present
application is also assigned to the same assignee.
Attention is now directed to the specific problem solved by the system of
the present invention. In the display of three-dimensional images, and
more particularly in the display of medical images, one often encounters
three-dimensional objects having multiple interior surfaces which occur in
layers at various depths. For example, three-dimensional data associated
with physical measurements of the human head produce data associated with
skin, bone (the skull), the brain, nasal cavities and various internal
soft tissue structures. In a three-dimensional view of the head, for
example, there are circumstances in which it would be desirable to be able
to simultaneously display both brain and bone tissue structures. Likewise,
there are situations in which it would be desirable to be able to quickly
switch back and forth between views of skin and bone and/or brain tissue
to reveal underlying structures and relationships between the structures.
This ability is particularly useful prior to certain surgical procedures.
While the dividing cubes system is capable of displaying selected tissues
such as bone or skin or brain tissue, it is also nonetheless desirable to
be able to display selected structures and/or to simultaneously display
these structures on the screen simultaneously so as to more clearly
indicate their relationship. This is particularly advantageous as a
surgical planning method since it is capable of showing the relationship
between various bodily structures. It is noted, however, that while the
present invention is particularly directed to the medical imaging arts,
there is nothing contained herein which would limit its use thereto. Any
three-dimensional measurement process performed on an object having an
internal structure is amenable to processing in accordance with the system
of the present invention. All that is required is that measurements of
physical properties be made so as to associate the physical property
measurements within regularly spaced locations with the body being
studied.
An image of the anatomy typically consists of the visible surfaces of
tissues computed by scanning the data and projecting the surface patches
onto a view plane. In a three-dimensional array of data, the volume
element is called a "voxel", in analogy with that of the area element
which is referred to as a "pixel" in two-dimensional situations. In
certain systems, voxel size limits the resolution of three-dimensional
reconstructions thereby resulting in images that appear block-like or
stepped as compared to having the smooth surfaces of real tissues.
Attempts to produce smoother images by averaging over neighboring voxels,
however, actually tends to reduce the resolution of the images. Other
methods for three-dimensional display generation of images have been based
upon measurement of the distance from an imaginary observation point to a
patch on the surface of the object and on the estimated surface normal of
the patch.
To shade the surface of a three-dimensional image projected onto a plane,
an intensity is calculated from the component of the unit normal vector
which component is parallel to the view direction. Surfaces with normal
vectors parallel to the view plane are fully illuminated, while those with
normal vectors at oblique angles to the view plane are gray and surfaces
with normal vectors perpendicular to the view plane are dark or black. The
dividing cubes system estimates the surface normal direction from a
gradient vector of the three-dimensional density function. This is a
useful estimate since the gradient is perpendicular to surfaces of
constant density. Consequently, the gradient vector is substantially
parallel to the unit surface normal vector. The unit normal vector is
calculated by normalizing the gradient vector at the surface of interest.
In the dividing cubes system, the gradient vector defined at each lattice
point is linearly or nonlinearly interpolated over the voxel to give a
local value of the gradient vector at desired intermediate voxel
locations. A unit surface normal is computed by dividing the gradient
vector by its magnitude. The surface that results from the use of these
interpolated normalized vectors appears smooth because the interpolated
gradient vector continuously varies with distance across a voxel boundary.
This form of gradient shading is preferably employed in the dividing cubes
system in general and in the variation of the dividing cubes system.
SUMMARY OF THE INVENTION
In accordance with a preferred embodiment of the present invention, a
system for the display of internal surfaces of three-dimensional objects
employs comparison means for comparing signal pattern values associated
with the grid locations of a parallelopiped volume element with at least
two threshold values so as to generate an indicia of the relationship
between each volume element and internal surface features of a body being
investigated, the features being defined by said threshold values. The
system also includes means for storing the three-dimensional signal
patterns which are representative of the value of at least one physical
property associated with a three-dimensional body at regularly spaced
parallelopiped grid locations which define volume elements, or voxels,
within the body. Means are provided for retrieving the signal pattern
values associated with individual volume elements. For purposes of
supplying appropriate information to a display processor, signal values
are associated with an appropriate three-dimensional location, as
determined by each grid location. In a preferred embodiment of the present
invention, simultaneously operative means are provided for generating the
normal vector to one side of a select surface. Each normal vector is
associated with either a given original grid location or with interpolated
grid locations lying within a voxel element or on surfaces defining a
voxel element. Thus, the operation of normal vector generation is carried
out simultaneously with the determination of surface referencing indicia.
Means are also provided for associating each volume element with
appropriate surface indicia references. Accordingly, the system of the
present invention supplies surface indexed normal vector information to a
display processor means for receiving location values, normal vectors and
surface indicia references so as to provide a shaded image, the image
representing at least on select surface.
Also, in accordance with a preferred embodiment of the present invention,
the normal vectors are also normalized prior to supplying them to a
display processor means. As used herein and in the appended claims, the
terms "normal" and "normalize" possesses two distinct meanings which are
well known to those skilled in the engineering arts. The use of the terms
"normal" and "normalize" is nonetheless appropriate because it is used in
the art and because context clearly distinguishes its two meanings. In
particular, in one context, a normal vector is one which is perpendicular
to another geometric object, such as a surface. In the other context, a
normalized vector, is a vector which possesses unit magnitude. A
normalized vector is therefore one which is produced by dividing each of
its vector components by the magnitude of the vector. In generally, the
magnitude of a vector is determined by the square root of the sum of the
squares of its components. Thus, one can speak of a normalized normal
vector which is a vector of unit magnitude perpendicular to some geometric
object.
Likewise, in the present specification and the claims which depend
therefrom, the term "cubically adjacent" is used to refer to that set of
eight grid locations which define a parallelopiped volume element.
Although some of the figures herein and the discussions associated
therewith are directed to a situation in which the parallelopiped forms a
cube or rectangular prism, it should nonetheless be understood that the
present invention is not limited to such grid location patterns. Rather,
in the present invention, any regularly spaced, parallelopiped grid
location pattern may be employed for measurement of the physical
parameters.
It is also noted herein that the present invention employs means for
providing the three-dimensional location associated with each grid
location. In this regard, it is noted that this particular aspect of the
present invention may be provided simply by establishing a predefined data
scanning sequence so that the pipelined, parallel processing system of the
present invention and the display processor operate upon the data provided
in a standard order.
Accordingly, it is seen that it is an object of the present invention to
provide a system and method for the simultaneous display of two or more
shaded three-dimensional images on a display device.
It is a further object of the present invention to provide a display system
which is capable of rapidly selecting one or more of several surface
structures for display.
Another object of the present invention is to provide a system and method
for use in junction with CAT scanners, ultrasound devices, MR imaging
systems and any and all other systems capable of generating
three-dimensional data representative of one or more physical properties
within a body to be studied.
It is yet another object of the present invention to provide a graphical
system for medical image display which is capable of interactive use and
yet at the same time produces high quality images providing textural
shading and other visual clues to the user.
It is yet another object of the present invention to provide a
three-dimensional graphics display system which is compatible with various
CAD/CAM systems.
Another object of the present invention is the generation and display of
three-dimensional raster format based information.
Still another object of the present invention is the generation of images
specified by a three-dimensional data array for the purpose of surface
representation.
It is also an object of the present invention to provide a system and
method which is readily fabricatable in conventional electronic hardware.
It is a particular object of the present invention to provide a parallel
pipelined architecture for the rapid generation of image information.
It is a still further object of the present invention to be able to assign
surface indicia information to individual vector and voxel elements.
It is yet another object of the present invention to provide medical
practitioners with the ability to more easily prepare for surgical
procedures prior to undertaking invasive measures.
Additionally, it is an object of the present invention to provide a
plurality of three-dimensional surface views from a single set of
collected data.
It is a still further object of the present invention to provide a system
and method for the display of selected internal surface structures of a
three-dimensional objects.
Lastly, but not limited hereto, it is an object of the present invention to
provide a system and method for the display of three-dimensional images of
internal surface structures in such a way that the specific viewing angle
and cross-sectional viewing plane may be selected by the user in an
interactive manner.
DESCRIPTION OF THE FIGURES
The subject matter which is regarded as the invention is particularly
pointed out and distinctly claimed in the concluding portion of the
specification. The invention, however, both as to organization and method
of practice, together with further objects and advantages thereof, may
best be understood by reference to the following description taken in
connection with the accompanying drawings in which:
FIG. 1 is a perspective view illustrating a single voxel element defined by
eight grid locations and surrounded by 24 "additional" data points (grid
locations);
FIG. 2 is a schematic diagram illustrating a system in accordance with the
present invention, and more particularly illustrating the presence of a
vector pipeline and a surface indicia generation pipeline;
FIG. 3 is a schematic diagram illustrating, in two dimensions, the various
cases that arise with respect to voxel intersection and various nested
surface structures;
FIG. 4 is a schematic diagram more particularly illustrating surface
indicia generation means, particularly for the case in which up to two
surface indicia are generated;
FIG. 5 is similar to FIG. 3 but more particularly illustrates the situation
in which three nested surfaces are present;
FIG. 6 is a schematic diagram illustrating a surface indicia generator for
the case structure illustrated in FIG. 5.
DETAILED DESCRIPTION OF THE INVENTION
In the method and apparatus of the present invention, a sequence of voxel
elements is examined. In a preferred embodiment of the present invention,
data from four consecutive NMR or CAT scan slices is analyzed at one time.
The reason for the desirability of employing four slices of data is seen
in FIG. 1 which illustrates a single voxel element with vertices V1
through V8. Each voxel element naturally spans two slices of image
information. Associated with each vertex point is a signal pattern value
which represents a measurement of at least one physical property which is
associated with a three-dimensional body at regularly spaced grid
locations within the body. The grid locations define volume elements or
voxels. Additionally, for the practice of the present invention, each
voxel vertex V1 through V8 is also associated with three adjacent grid
locations. These adjacent grid locations are the ones which lie along grid
coordinate lines and which are not specifically included in the voxel
itself. There are 24 such "additional data" points. For example, it is
seen that vertex V1 is associated with additional grid locations W1, W5
and W12. In a similar fashion, vertex location V7 is associated with grid
locations W16, W17 and W23. These other additional grid locations are
shown as open circles in FIG. 1. The voxel grid locations themselves are
shown as filled in circles. It is therefore seen that each voxel vertex
grid location is associated with three adjacent grid locations. In FIG. 1,
these additional grid locations are labeled as W1 through W24 as shown. It
is therefore seen that these additional grid locations are 24 in number
and occupy four data slices. In the system and method of the present
invention, the data values at these additional grid locations are
employed, along with the data values at the voxel vertex locations (if
desired), to generate data value triplets which represent normal vectors
associated with each vertex point. The various normal vector components
are computed using finite difference methods. For example, a central
difference may in particular be employed. More particularly, to compute
the x component of the normal vector at vertex V1, data values at V4 and
grid location W5 are differenced. In a like manner, the z component of the
normal vector associated with vertex V1 may similarly be computed using
data values at grid locations V5 and W1. Lastly, the y component of the
normal vector associated with vertex V1 may be generated using a
difference based on the data values associated with grid locations V2 and
W12. The differences may also be scaled to reflect coordinate distance
differences in the three coordinate directions. The order in which the
difference is taken is naturally selected to be consistent with the
orientation of some coordinate system (see axes shown) and the method is
employed uniformly throughout for the other voxels. In this manner, it is
seen how data from four slices is employed to generate normal vectors
associated with each voxel vertex location. The resulting vector formed
from differences is then scaled to unit magnitude, as is more particularly
described below.
FIG. 2 illustrates, in schematic form, both a flow chart and hardware
description of a system in accordance with the present invention. In one
embodiment of the present invention, three-dimensional signal data is
provided from an MR or CT scan system 10. This data is typically stored in
an appropriate storage system 15. Typically this storage system comprises
some form of magnetic storage medium such as a floppy disk, hard disk
drive, or tape. The data is organized in a format which permits
associating each physical measurement representation with a corresponding
grid location associated with that measurement.
In a preferred embodiment of the present invention, four-slice buffer 20 is
employed. This buffer includes layer No. 1, No. 2, No. 3 and No. 4, with
each memory layer containing representations for the signal pattern values
at the various grid locations. Each layer preferably contains the data for
an entire two-dimensional slice of the body being imaged. A slice scanner
is employed so as to scan the data from storage means 15 into 4slice
buffer 20 along one of the axis directions. In a preferred embodiment of
the present invention, there is a direct correlation between buffer
address value and grid location within the body. It should be borne in
mind that as one scans through the data in one axis direction by using
buffer 20, it is only necessary to retrieve a single additional slice of
information at a time. In short, the scanner can be made to operate in a
fashion so that only data from a single image plane need be retrieved at
one time.
In general, four signal values from one voxel face are provided from layer
No. 2, and at the same time, four signal values from layer No. 3 are
similarly provided to voxel vertex data register 30 and to gradient
generator 60. Gradient generator 60 also receives data from the 24
"additional" data grid locations as described above and as shown in FIG.
1. Each cell in register 30 contains the corresponding physical
measurement in an appropriate and consistent representational format. In
this way, for each voxel element, the values associated with vertices V1
through V8 are supplied to register 30. In a like fashion, the physical
measurement values associated with additional grid locations W1 through
W24 are supplied to gradient generator 60 along with the physical
measurement values associated with vertices V1 through V8, since all 32
pieces of information are generally required for the generation of
gradient vector data. At this point, an especially useful feature of the
present invention should be pointed out. In particular, it is seen that
physical measurement data is simultaneously supplied to register 30 and to
gradient vector generator 60. Thus, the generation of gradient vectors is
performed simultaneously with the determination of surface indicia
information which is later associated with resultant gradient vectors.
These operations are carried out in parallel. Surface indicia generation
is carried out in the "cubes pipeline" comprising register 30 and surface
indicia generator 40. At the same time in the "normal vector pipeline",
gradient vectors are produced by generator 60 and interpolated in
functional block 70 and subsequently normalized (that is, unit vectors are
generated) by functional block 80. Ultimately, surface indicia information
together with normalized vector information is provided to gate/labeler
90. Functional block 90 operates to associate surface indicia information
with the voxel grid locations associated with the vertex data
simultaneously supplied to blocks 30 and 60. In the case that it is
determined that the voxel in question does not intersect a desired
surface, block 90 also preferably operates as a gate to disable supplying
vectors to graphics processor 100. Graphics processor 100 comprises
standard equipment of this type which receives normal vector information
associated with each grid location and, depending upon the view selected,
produces a shaded image on display 110, which typically comprises a
cathode ray tube (CRT) type device. Functional blocks 60, 70 and 80
essentially perform the dividing cubes operations as disclosed in the
aforementioned patent application.
Gradient generator 60 preferably includes 24 subtractor circuits for
forming the differences described above for generating normal vector
components. In general, each subtractor processes n bits of data. Each n
bit signal represents a signal which is proportional to the aforementioned
physical measurement. In one embodiment of the present invention, such
measurements are represented by 12bit signal values. The result of these
24 subtractions is supplied to gradient vector interpolator 70 which
preferably performs the dividing cubes function described in the
aforementioned patent application. In particular, the 24 subtractions
carried out in block 60 produce the components of 8 gradient vectors, each
of which is associated with a particular voxel vertex. The grid axes are
partitioned into a number of subvoxel elements and, using various
interpolation methods, intermediate vector gradient approximations are
produced. For example, in one form of interpolation, a simple averaging
along grid axes is employed. Likewise, for interpolation points which lie
on voxel faces, the average of the four face vertex gradient vectors may
be generated. For interior points generated by interpolation, a weighted
average of a larger number of vectors may be generated. It is also
possible to generate interpolated gradient vectors which are weighted by
the magnitudes of the voxel vertex data values.
Functional block 80 operates to normalize each of the interpolated vectors
from interpolator 70. In particular, normalizer 80 generates the squares
of the vector components, sums them and also generates the square root of
the sum for each of the vectors. Each component is then divided by this
magnitude to produce a unit vector. Thus normalizer 80 supplies to
gate/labeler 90 a set of unit gradient vectors associated with a given
voxel element. Whether or not these vectors are passed on to graphics
processor 100 and if so, their surface label is determined by a signal
supplied from surface indicia generator 40.
In accordance with the present invention, surface indicia generator 40
preferably operates simultaneously with normal vector generation to
determine two things. First, it is determined whether or not a given voxel
element intersects surfaces defined by threshold values. Secondly, if
voxel intersection is indicated, an indicia is generated to indicate which
surface is intersected.
One of the functions performed by surface indicia generator 40 is the
classification of voxel intersection with internal surface structures. In
particular, FIG. 3 illustrates, for an analogous two-dimensional
situation, the various ways that a voxel element may intersect two
surfaces. In case I, the voxel element does not intersect the outer
surface at all. In case II, surface No. 1 passes through the voxel
element. In case III, the voxel element lies between surface No. 1 and
surface No. 2. In many cases, the region between surface No. 1 and surface
No. 2 is actually the region of a solid object, such as bone. As used
herein, the term "solid" in FIGS. 3-6 does not mean to suggest that any
particular tissue type is present and in fact, a "solid" region might
represent the interior of a sinus cavity, for example. Similarly, case IV
illustrates a situation in which a voxel element intersects a second
interior surface. Similarly, case V represents the situation in which a
voxel element lies inside of surface No. 1 and also inside surface No. 2
so as to be present in a second interior solid. This situation is
generalized in FIG. 5, discussed below.
A system for determining whether or not a given voxel element represents
cases I through V is shown in FIG. 4. In particular, vertex data values
from a given voxel element, having been stored in registers 30 are
supplied to comparators 41 and 42. Comparator 41 preferably comprises
eight n-bit comparators which compare each of the voxel vertex signal
pattern values with a threshold value which is generally selected by the
operator to pick out particular tissues. For example, a different
threshold value is selected for bone tissue as opposed to cerebral tissue.
Each of the eight vertex values is compared with the threshold value and
in each case, a single bit is generated to indicate whether or not the
threshold value is exceeded. The result of this operation, carried out by
comparators 41 and 42, is an eight-bit index. Comparator 41 produces an
eight-bit index based upon threshold value No. 1; comparator 42 produces
an eight-bit index based upon threshold value No. 2. With specific
attention being directed to the output of comparator 41, it is seen that
the eight-bit index is applied to "ALL ZERO" test circuit 44 and
simultaneously to "ALL ONES" test circuit 47. If the eight-bit index is
all zeroes, then the output of circuit 44 is a one which indicates that
the voxel element is outside of surface No. 1. In order to carry out this
objective, zero values may be supplied to zero test circuit 44 from zero
register 50 or its equivalent. In the same manner, ones test circuit 47
produces an output which is a binary one if the eight-bit index from
comparator 41 comprises all ones. This is indicative of the voxel element
being inside surface No. 1. If the voxel element is neither inside surface
No. 1 nor outside surface No. 1, then it must therefore lie on surface No.
1 so that NOR gate 52 produces a "1" output in the event that the voxel
element straddles surface No. 1.
In an almost identical fashion, comparator 42 produces an eight bit index
comparison based on threshold value No. 2. This eight bit index is applied
to zero test circuit 45 and to ones test circuit 48. Zero test circuits 44
and 45 are supplied with a constant zero value from zero register 50 or
its equivalent. Likewise, ones test circuits 47 and 48 may be similarly
supplied by a ones constant value from ones register 51. Zero test circuit
45 produces a binary "1" output whenever the voxel element is outside of
surface No. 2. Similarly, if the voxel element lies inside surface No. 2,
the output of ones test circuit 48 is a one. If the voxel is neither
outside surface 2 nor inside surface 2, then it must straddle surface 2.
Accordingly, NOR gate 53 produces a binary "1" output in the event that
the voxel element is positioned as shown in case IV. Additionally, it is
seen that if the voxel element is inside surface No. 1 and outside surface
No. 2, then the voxel element is actually within solid No. 2 and case III
holds. In this fashion, surface indicia are generated indicating, for each
voxel element, a surface upon which the voxel lies, if any. The surface
indicia generator 40 also preferably supplies a "disable gate" signal from
zero test circuit 44 to gate/labeler 90 in the event that the voxel
element being processed is not associated with any of the surfaces being
selected for viewing.
The concepts presented in the discussions above, may be readily extended to
the case in which an additional surface, surface No. 3, is present. In
this situation, cases VI and VII, as shown in FIG. 5, are also present. It
is seen that surface No. 3 is selected by means of a third threshold value
which may be supplied to a third comparator 43, as shown in FIG. 6. FIG. 6
is readily seen as a logical extension of FIG. 4 to the situation in which
one additional surface is present. The extension of FIG. 6 to even more
surfaces for selection is readily accomplished simply by adding additional
sets of eight n bit comparators. Each such comparator is associated with a
zero test circuit and a one test circuit, such as shown in blocks 46 and
49 of FIG. 6. NOR gates are employed in each such extension to generate
indicia which are indicative of the fact that the voxel being processed
lies on a certain surface. Likewise, AND gates may be employed, as shown
in FIG. 6, to indicate that a selected voxel element lies strictly between
two internal surfaces. These surface indicia are associated with
appropriate voxel elements in gate/labeler 90. This enables graphic
processor 100 to selectively display one or more of the surfaces, as
selected by the user. Naturally, as with many graphics processors, the
user is also permitted to select a particular view direction. It is
understood that problems similar to hidden line removal and/or the problem
of determining visible surfaces are in fact problems solved by
conventional graphics processing systems. In this respect then the system
of the present invention may be thought of as a graphic preprocessor.
From the above, it should be appreciated that the display system of the
present invention provides several significant advantages. In particular,
the system of the present invention offers significant speed advantages as
a result of the parallel computations associated with surface indicia
generation which are carried out at the same time as unit normal vector
generation for each voxel element. It should also be appreciated that the
system of the present invention also provides a means for associating
surface indicia with various data generated for each voxel element. This
enables the rapid and simultaneous display of selected tissue structures.
It also permits rapid switching of the view between various structural
overlays so as to provide the user with a more detailed pictorial
representation of internal bodily structures and their relationships.
It is noted that while the description of the present invention provided
above is expressed in terms of "positive" logic quantities, that it is
also possible to express the logical relationships involved in the present
invention using alternative logical variables. In particular, "negative"
logic variables may be employed in various parts of the present invention
with only minor modifications. It is also pointed out that logically
equivalent functional blocks may also be employed particularly in the case
of the NOR gates and the AND gates, again particularly if "negative"
logical variables are employed. It is also noted that the system described
herein has expressed tissue selection in terms of whether or not a given
measured physical quantity exceeds a specified threshold value. Still in
keeping with the present invention, it is also possible to select tissue
types based upon other criteria particularly based upon whether or not a
given measured physical parameter lies between two expressed values,
rather than merely just exceeds one of them. Accordingly, the description
above and the appended claims are intended to include this situation
through the use of the thresholding descriptions. Additionally, it is
noted that the description herein has been directed to a hardware specific
implementation of the present invention. Nonetheless, the various means
recited in the present invention may in fact be implemented and carried
out upon one or more digital computer processing elements which have been
programmed in accordance with the instructions provided in the present
description. Accordingly, such means for carrying out the practice of the
present invention are specifically contemplated herein.
While the invention has been described in detail herein in accord with
certain preferred embodiments thereof, many modifications and changes
therein may be effected by those skilled in the art. Accordingly, it is
intended by the appended claims to cover all such modifications and
changes as fall within the true spirit and scope of the invention.
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