U.S. patent application number 12/885910 was filed with the patent office on 2011-04-21 for method and system for creating three-dimensional images using tomosynthetic computed tomography.
Invention is credited to Roger A. Horton, Richard L. Webber.
Application Number | 20110092812 12/885910 |
Document ID | / |
Family ID | 21879481 |
Filed Date | 2011-04-21 |
United States Patent
Application |
20110092812 |
Kind Code |
A1 |
Webber; Richard L. ; et
al. |
April 21, 2011 |
METHOD AND SYSTEM FOR CREATING THREE-DIMENSIONAL IMAGES USING
TOMOSYNTHETIC COMPUTED TOMOGRAPHY
Abstract
A system for constructing image slices through a selected
object, the system comprising an identifiable fiducial reference in
a fixed position relative to the selected object, wherein the
fiducial reference comprises at least two identifiable reference
markers. A source of radiation is provided for irradiating the
selected object and the fiducial reference to form a projected
image of the selected object and the fiducial reference which is
recorded by a recording medium.
Inventors: |
Webber; Richard L.;
(Winson-Salem, NC) ; Horton; Roger A.;
(Winston-Salem, NC) |
Family ID: |
21879481 |
Appl. No.: |
12/885910 |
Filed: |
September 20, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11505255 |
Aug 16, 2006 |
7801587 |
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12885910 |
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10972887 |
Oct 25, 2004 |
7110807 |
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11505255 |
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09862006 |
May 21, 2001 |
6810278 |
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10972887 |
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09034922 |
Mar 5, 1998 |
6289235 |
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09862006 |
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Current U.S.
Class: |
600/426 |
Current CPC
Class: |
G06T 11/008 20130101;
A61B 6/12 20130101; G06T 11/005 20130101; A61B 6/145 20130101; G06T
2211/436 20130101 |
Class at
Publication: |
600/426 |
International
Class: |
A61B 5/05 20060101
A61B005/05 |
Claims
1-23. (canceled)
24. A computer program product, comprising a computer usable medium
having a computer readable program code embodied therein, the
computer readable program code adapted to be executed to implement
a method for synthesizing an image slice through a selected object
at a selected slice position through the object from a plurality of
projected images of the object comprising the steps of: a.
receiving the plurality of projected images of a region of interest
of a selected object and a fiducial reference, the images recorded
at different arbitrary relative positions between (1) a source of
radiation, (2) the selected object and fiducial reference, and (3)
a recording means; and b. synthesizing an image slice of the
selected object at a selected slice position through the object
from the projected images.
25. The computer program product according to claim 24, the
computer readable program code adapted to be executed to implement
a method for synthesizing an image slice through a selected object
at a selected slice position through the object from a plurality of
projected images of the object comprising the step of computing the
effective magnification of each projected image by determining a
radiographic diameter of the projected image of a reference marker
of the fiducial reference, and scaling each projected image to the
same magnification.
26. The computer program product according to claim 25, wherein
computing the effective magnification of each projected image
comprises determining when the gradient along a minor diameter of
the image of the reference marker is a maximum.
27. The computer program product according to claim 26, wherein
computing the minor diameter comprises generating a series of
tomosynthetic slices through the center of the reference marker
using a range of values for the reference marker diameter
decreasing systematically from the actual value.
28. The computer program product according to claim 24, wherein the
step of synthesizing an image slice comprises aligning the
projected images based on parameters related to a first marker of
the fiducial reference displayed in the plurality of images and
projectively warping a projected image from an actual projection
plane to a virtual projection plane using parameters related to a
second reference marker of the fiducial reference displayed in the
plurality of images.
29. The computer program product according to claim 24, the
computer readable program code adapted to be executed to implement
a method for synthesizing an image slice through a selected object
at a selected slice position through the object from a plurality of
projected images of the object comprising the step of generating a
projected transformation matrix.
30. The computer program product according to claim 29, wherein the
step of generating the projected transformation matrix comprises
mapping the position of a reference marker of the fiducial
reference displayed in the projected image onto a corresponding
position of the reference marker in a virtual projection plane.
31. The computer program product according to claim 24, wherein the
step of synthesizing an image of the selected object at a selected
slice position through the object includes the steps of: a.
projectively warping each projected image onto a virtual projection
plane; b. generating an image slice through the object at a
selected slice position.
Description
RELATED APPLICATION
[0001] This application is a continuation of U.S. application Ser.
No. 09/034,922, filed on Mar. 5, 1998, still pending, the subject
matter of which is incorporated herein by reference.
FIELD OF THE INVENTION
[0002] The present invention relates to a method and system for
creating three-dimensional displays or images from a multiplicity
of two-dimensional projections and, more specifically, to a method
and system for use in computed tomography systems in which random
relative positional geometries between the source of radiation, the
object of interest, and the recording means may be used for
recording radiographic images for tomosynthesis.
BACKGROUND OF THE INVENTION
[0003] A wide range of tomosynthetic imaging techniques has
previously been demonstrated to be useful in examining
three-dimensional objects by means of radiation. These imaging
techniques differ in the size and configuration of the effective
imaging aperture. At one extreme, the imaging aperture approaches
zero (i.e., a pinhole) and the resulting display is characterized
by images produced from a single transmission radiograph. This
yields an infinitely wide depth of field and therefore no depth
information can be extracted from the image. At the other extreme,
the aperture approaches a surrounding ring delimiting an infinite
numerical aperture resulting in projection angles orthogonal to the
long axis of the irradiated object. This yields an infinitely
narrow depth of field and hence no information about adjacent
slices through the object can be ascertained. It therefore follows
that a "middle ground" approach, which provides the ability to
adapt a sampling aperture to a particular task, would be highly
advantageous.
[0004] The key to achieving the full potential of diagnostic
flexibility lies in the fact that perceptually meaningful
three-dimensional reconstructions can be produced from optical
systems having any number of different aperture functions. That
fact can be exploited since any aperture can be approximated by
summation of a finite number of appropriately distributed point
apertures. The key is to map all incrementally obtained projective
data into a single three-dimensional matrix. To accomplish this
goal, one needs to ascertain all positional degrees of freedom
existing between the object of interest, the source of radiation,
and the detector.
[0005] In the past, the relative positions of the object, the
source, and the detector have been determined by fixing the
position of the object relative to the detector while the source of
radiation is moved along a predetermined path, i.e. a path of known
or fixed geometry. Projective images of the object are then
recorded at known positions of the source of radiation. In this
way, the relative positions of the source of radiation, the object
of interest, and the detector can be determined for each recorded
image.
[0006] Previously, a method and system has been described which
enables the source of radiation to be decoupled from the object of
interest and the detector. This is accomplished by fixing the
position of the object of interest relative to the detector and
providing a fiducial reference which is in a fixed position
relative to the coupled detector and object. The position of the
image of the fiducial reference in the recorded image then can be
used to determine the position of the source of radiation.
[0007] However, none of the existing techniques can be used in the
most general application wherein the radiation source, the object
of interest, and the detector are independently positioned for each
projection. In such systems, there are nine possible degrees of
freedom: 2 translational and 1 displacement degrees of freedom for
the radiation source relative to the selected object and 2
translational, 1 displacement, 2 tilting, and 1 rotational degrees
of freedom for the recording medium relative to the selected
object. It is highly desirable to have a system and a method for
constructing a three-dimensional radiographic display from
two-dimensional projective data wherein the source of radiation,
the object of interest, and the detector are all allowed to
independently and arbitrarily vary in position relative to each
other.
SUMMARY OF THE INVENTION
[0008] The present invention relates to an extension of
tomosynthesis which facilitates three-dimensional reconstructions
of an object from any number of arbitrary plane projections of the
object produced from any number of arbitrary angles. The
information required to produce the three-dimensional
reconstructions is derived from fiducial analysis of the projection
themselves or from analyses of functional relationships established
through known fiducial constraints. In accordance with the present
invention, a system and methods are provided for creating
three-dimensional images using tomosynthetic computed tomography in
which the system and methods significantly simplify the
construction of image slices at selected slice positions through an
object. Following a one-time transformation of a series of
projected images, only simple offset and averaging operations are
required in selected embodiments of the invention for a variety of
subsequent reconstructions of a volumetric region within which
projective variations may be considered negligible.
[0009] The system comprises an identifiable fiducial reference
located in a fixed position relative to the object. The fiducial
reference comprises at least two reference markers which are in a
fixed geometry relative to each other. One of the reference markers
may be used as an alignment marker during construction of a
tomosynthetic slice through the object. The other reference marker
or markers may be used to projectively warp or transform a
projected image from an actual projection plane to a virtual
projection plane. Each reference marker may be small enough to be
considered point-size or, alternatively, may be finite in size.
However, there are advantages to using markers of a known geometry
such as spherical markers with a measurable diameter. In one
embodiment, the fiducial reference comprises five point-size or
finite reference markers that are arranged so that four of the
reference markers are co-planar and no three or more reference
markers are collinear.
[0010] A radiation source is provided for irradiating the object
with the fiducial reference in a fixed position relative to the
object. The preferred radiation source depends upon the particular
application. For example, the present invention may be practiced
using x-rays, electron microscopy, ultrasound, visible light,
infrared light, ultraviolet light, microwaves, or virtual radiation
simulated by manipulation of magnetic fields (magnetic resonance
imaging (MRI)).
[0011] A recording medium or detector is used to record a series of
projected images. Each projected image may include an object image
of the object and a reference marker image for each of the
reference markers. The recording medium may be in the form of a
photographic plate or a radiation-sensitive, solid-state image
detector such as a charge-coupled device (CCD), or any other system
capable of producing two-dimensional projections or images suitable
for digitization or other analysis.
[0012] In operation, the system of the present invention is used to
synthesize a three-dimensional reconstruction of the object to
obtain, for example, an image slice through the object, at a
selected slice position through the object, from a plurality of
projected-images detected at the recording medium. The
simplification of the construction method is achieved by warping,
i.e. transforming or mapping, a series of projected images onto a
virtual projection plane to yield modified images that would match
those that would have been generated had the detector been in a
fixed position relative to the object. By warping the projected
images onto the virtual projection plane, the computation required
for each image slice construction is greatly reduced. In addition,
the solution of the projective transformations can be performed via
a direct method that is both efficient and computationally robust.
Further, magnification differences can be compensated for by
appropriate scaling of the images.
[0013] A series of two-dimensional projected images of an object
with an associated fiducial reference is recorded. The fiducial
reference markers are coupled in fixed position relative to the
object. The projected images can be recorded with (i) the source,
(ii) the recording medium, and (iii) the fiducial reference markers
coupled to the object, in various or arbitrary projection
geometries. Further, the projection geometry preferably varies from
projected image to projected image. Some variation is required to
produce a finite depth of field.
[0014] The virtual projection plane may preferably correspond to
the position of a plane through at least one of the reference
markers in real space or to a plane defined by one of the existing
projected images. Imaging systems that use projective geometries,
which include optical and radiographic systems, can be
appropriately warped using a projective transformation matrix. The
projective transformation matrix is generated by solving each
projected image relative to the virtual projection plane.
[0015] The resulting transformations compensate for magnification
and/or projective differences between the various images. Such
differences are introduced when the source is sufficiently close to
the object and/or the source moves in a direction which is not
parallel to the projection plane.
[0016] Once the projected images are warped and scaled to
compensate for projective artifacts, construction of an image slice
of the object at a selected slice position is performed based on
techniques used in single reference marker applications. An example
of such a technique is described in U.S. Pat. No. 5,359,637, which
is incorporated herein by reference. Accordingly, the single
reference point projection required by this technique may be
abstracted from characteristics known to be associated with the
object being projected, or from one or more fiducial reference
markers either attached to or otherwise functionally related to the
irradiated object.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] The foregoing summary, as well as the following detailed
description of the preferred embodiments of the present invention,
will be better understood when read in conjunction with the
accompanying drawings, in which:
[0018] FIG. 1 is a schematic representation of a system for
creating three-dimensional radiographic displays using computed
tomography in accordance with the present invention;
[0019] FIG. 2 is a flow chart showing the steps involved in
creating three-dimensional radiographic displays using computed
tomography in accordance with the present invention;
[0020] FIG. 3 is a flow chart showing details of a method of
projectively warping or transforming a projected image from an
actual plane of projection onto a virtual projection plane;
[0021] FIG. 4 is a schematic representation of a system having nine
degrees of freedom in which a source is shifted and displaced
relative to an original projection plane and in which a projection
plane of a recording medium is shifted, rotated, displaced, and
tilted relative to the original projection plane;
[0022] FIG. 5 is a schematic representation showing an arrangement
of reference markers in accordance with the an embodiment of the
present invention, wherein five spherical reference markers are
positioned at five of the eight vertices of a cube;
[0023] FIG. 6 is a schematic representation of a system having
seven degrees of freedom in which an infinite point source is
shifted relative to an original projection plane and in which a
projection plane of a recording medium is shifted, displaced, and
tilted relative to the original projection plane;
[0024] FIG. 7 is a schematic representation of a system having four
degrees of freedom in which an infinite point source is shifted
relative to an original projection plane and in which a projection
plane of a recording medium is shifted relative to the original
projection plane;
[0025] FIG. 8 is an exploded, schematic representation of a
charge-coupled device (CCD) for use as a recording medium;
[0026] FIG. 9 is a schematic representation of an embodiment of the
present invention wherein the recording medium is smaller than the
projected image of the object;
[0027] FIG. 10 is a schematic representation of an embodiment of
the present invention wherein the source is a hand-held X-ray
source with a laser aiming device;
[0028] FIG. 11 is a schematic representation of an embodiment of
the present invention wherein the reference markers of the fiducial
reference are positioned at the vertices of a square pyramid;
[0029] FIG. 12 is a schematic representation of an embodiment of
the present invention wherein the source is a hand-held X-ray
source which is constrained relative to the recording medium by a
C-arm;
[0030] FIG. 13 is an enlarged schematic representation of the
object of interest and the recording medium depicted in FIG.
14;
[0031] FIG. 14 is a schematic representation of an embodiment of
the present invention wherein the reference markers of the fiducial
reference are positioned at the centers of the faces of a
parallelepiped;
[0032] FIG. 15 is a schematic representation of an embodiment of
the present invention wherein the corners of a frame define four
reference markers;
[0033] FIG. 16 is a schematic representation of a reference image
cast by a spherical reference marker showing the resulting
brightness profile;
[0034] FIG. 17 is a schematic representation of the parameters
associated with a system comprising three spherical, non-collinear
reference markers wherein the orthogonal distance between the
radiation source and the recording medium is fixed at a distance
short enough so that the images cast by the reference markers are
magnified relative to the size of the actual reference markers;
[0035] FIG. 18 is a schematic representation of the relevant
parameters associated with a reference image associated with a
spherical reference marker;
[0036] FIG. 19 is a schematic representation of an embodiment of
the present invention wherein the fiducial reference comprises a
radiopaque shield with a ring-like aperture;
[0037] FIG. 20 is a schematic, perspective view of an embodiment of
the present invention, wherein the detector comprises a
charge-coupled device (CCD) and the fiducial reference comprises a
frame, shown with the front and a section of the top removed;
[0038] FIG. 21 is a sectional view of the embodiment depicted in
FIG. 22 taken along the 23-23 line;
[0039] FIG. 22 is an alternate embodiment of a laser aiming device
in accordance with the present invention;
[0040] FIG. 23 is a graph of the projection angle, q, versus the
major diameter of the reference image, d.sub.p;
[0041] FIG. 24 is a graph of the distance from the center of a
reference marker to the source, a.sub.p, versus the major diameter
of the reference images, a;
[0042] FIG. 25 is a graph of the projection angle, .theta., versus
the major diameter of the reference images, a;
[0043] FIG. 26 is a graph of the offset correction distance, delta,
versus the projection angle, q;
[0044] FIG. 27 is a graph of an ellipse showing the variables x, y,
b/2, and a/2; and
[0045] FIG. 28 is a graph of a plot of y versus x for the equation
of the ellipse shown in FIG. 27.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0046] The present invention generally relates to a system 20, as
depicted schematically in FIG. 1, for synthesizing an image of an
object 21 at a selected slice position 35 through the object 21
from a plurality of radiographic projected images 38 of the
selected object 21. A fiducial reference 22 is held in a fixed
position relative to the selected object 21, for example, by
directly attaching the fiducial reference 22 to the object 21. The
fiducial reference comprises two finite sized, identifiable
reference markers, 23 and 123, which are maintained coupled
together in a fixed geometry relative to each other by a
radiolucent bar 24. However, the fiducial reference 22 may comprise
various numbers and arrangements of reference markers 23. A
radiation source 27 is provided to irradiate the object 21 along
with the fiducial reference 22. Irradiation of the object 21 casts
a projected image 38 onto a recording medium 31. The projected
image 38 comprises an object image 40 of the object 21 and
reference images, 39 and 139, of the reference markers, 23 and 123,
respectively.
[0047] In general, the pattern of source 27 positions does not need
to be in any fixed geometry or position. Indeed, the position of
the source 27 may be totally arbitrary in translation and
displacement relative to the object 21. Likewise, the recording
medium 31 may also be arbitrarily movable relative to the object 21
by translation, displacement, tilting, or rotation. The only
requirement is that for every degree of freedom in the system
resulting from movement of the source 27 or the recording medium 31
relative to the object 21, the fiducial reference 22 must include
sufficient measurable or defined characteristics, such as size,
shape, or numbers of reference markers 23, to account for each
degree of freedom.
[0048] The minimum number of reference markers required to
completely determine the system depends on the constraints, if any,
imposed on the relative positions of (1) the radiation source, (2)
the object and fiducial reference, and (3) the recording medium.
The system may have a total of nine possible relative motions (2
translations and 1 displacement for the radiation source relative
to a desired projection plane and 2 translations, 1 displacement, 2
tilts, and 1 rotation for the recording medium relative to the
desired projection plane). Each of these possible relative motions
must be capable of analysis either by constraining the system and
directly measuring the quantity, by providing a sufficient number
of reference markers to enable the quantity to be determined, or by
estimating the value of the quantity. Each unconstrained relative
motion represents a degree of freedom for the system. For a system
to be completely determined, the total number of degrees of freedom
in the system must be less than or equal to the total number of
degrees of freedom associated with the fiducial reference.
[0049] More than the minimum number of reference markers can be
used. In such cases, the system is overdetermined and least squares
fitting can be used to improve the accuracy of the resulting image
slices. If, however, less than the minimum number of reference
markers is used, then the system is underdetermined and the unknown
degrees of freedom must either be estimated or measured
directly.
[0050] Although the reference markers can be essentially any size
and shape, spherical reference markers of known diameter may be
used. When using spherical reference markers of a finite size, a
single reference marker can account for up to five degrees of
freedom. When a spherical reference marker is projected obliquely
onto the recording medium, the reference image cast by the
spherical reference marker is elliptical and is independent of any
rotation of the reference marker. Determining the position of the
reference image in the projection plane (X- and Y-coordinates) and
the magnitudes of the major and minor diameters of the elliptical
image accounts for four degrees of freedom. Further, when the
distance between the radiation source and the reference marker is
sufficiently short, the reference image will be magnified relative
to the actual size of the reference marker, thereby accounting for
an additional degree of freedom. In contrast, only two degrees of
freedom (the X- and Y-coordinates) are typically associated with
the reference image of a point-size reference marker.
[0051] The most complex, yet most generally applicable, arrangement
is depicted in FIG. 4, wherein the radiation source 27 and the
recording medium 31 are completely unconstrained and uncoupled from
the selected object 21. In this arrangement, there are nine degrees
of freedom: 2 translational (.DELTA.X and .DELTA.Y) and 1
displacement (AZ) degrees of freedom for the radiation source 27
relative to an original or desired projection plane 37 and 2
translational (.DELTA.X' and .DELTA.Y'), 1 displacement
(.DELTA.Z'), 2 tilting (.DELTA..gamma. and .DELTA..PHI.), and 1
rotational (.DELTA..PSI.) degree of freedom for the recording
medium 31 relative to the original or desired projection plane.
Accordingly, a fiducial reference system sufficient to solve a
projection system having nine degrees of freedom is needed to
completely determine the system.
[0052] One embodiment of the present invention that permits this
general arrangement to be realized conveniently involves
two-dimensional projected images from a system comprised of a
fiducial reference having five point-size or finite reference
markers. This approach conveniently facilitates three-dimensional
reconstructions when exactly four reference markers are coplanar
and no three or more reference markers are collinear. Under these
conditions, only the projection from the non-coplanar marker need
be distinguished from the other four because the projections from
the latter always bear a fixed sequential angular arrangement
relative to each other which simplifies identification of
homologous points in all projections. For example, the reference
markers can be placed at five contiguous vertices of a cube as
shown in FIG. 5. Fiducial reference 122 comprises five reference
markers, 23, 123, 223, 323, 423, positioned contiguously at five
vertices of a cube. The object 121 is preferably positioned within
the cube. The four co-planar reference markers, 23, 123, 223, and
323, then can be used for projectively warping or transforming the
projected images onto a desired projection plane while the
remaining reference marker 423 serves as the alignment marker
required to determine the normalized projection angle as described
in U.S. Pat. No. 5,359,637.
[0053] The most general reconstruction task requiring information
sufficient to determine all nine possible degrees of freedom
requires computation of separate projective transformations for
each projected image in each and every slice. However, by limiting
the region of interest to a subvolume constrained such that the
magnification across and between its slices may be considered
constant, it is possible to generate veridical three-dimensional
images within the volume much more efficiently. The increase in
efficiency under these conditions results from the fact that all
projections within this region can be mapped by a single fixed
transformation, and that associated slice generation can be
accomplished by simple tomosynthetic averaging of laterally shifted
projections as described in U.S. Pat. No. 5,359,637.
[0054] Another useful arrangement of the fiducial reference
comprising five reference markers is shown in FIG. 11, wherein a
fiducial reference 222 employing a pyramidal distribution of
reference markers 323 is used. The fiducial reference 222 comprises
five reference markers 23, 123, 223, 323, and 423, which are held
in a fixed relationship relative to each other and to the object
221. As was the case in FIG. 5, four of the reference markers, 23,
123, 223, and 323, lie in a plane that can be used to establish the
desired projection plane. Here, they define the four corners of the
base of a pyramid. The fifth reference marker 423 is positioned to
define the apex of the pyramid and serves as the means for
determining the projection angles relative to the desired
projection plane as described in U.S. Pat. No. 5,359,637. In use,
the fiducial reference 222 may be attached or fixed relative to the
object 221 such that the base of the pyramid is proximate to the
recording medium and the apex of the pyramid is proximate to the
source.
[0055] In FIG. 15, a fiducial reference 322 having an alternative
arrangement of reference markers in a pyramidal distribution is
shown. In this arrangement, the fiducial reference 322 comprises a
radiopaque frame 25 having a radiolucent central window. The four
inside corners of the radiopaque frame 25 define four reference
markers, 23, 123, 223, and 323, at the base of the pyramid. The
fifth reference marker 423 is positioned at the apex of the
pyramid. Preferably, the object 321 is positioned between the frame
25 and the reference marker 423.
[0056] In FIG. 14, a fiducial reference 422 which is also useful
for solving a system with nine degrees of freedom is shown.
Fiducial reference 422 comprises a rectangular parallelepiped 33
with radiopaque reference markers, 23, 123, 223, 323, 423, and 523,
centered on each of the six faces of the parallelepiped 33. The
reference markers, 23, 123, 223, 323, 423, and 523, are marked with
distinguishable indicia, such as X, Y, Z, {circle around (X)},
{circle around (Y)}, and {circle around (Z)} so that the reference
images cast by the markers, 23, 123, 223, 323, 423, and 523, can be
identified easily and distinguished from one another. Alternatively
or additionally, two or more of the edges of the parallelepiped 33
may be defined by radiopaque bars 26 such that the intersections of
the bars 26 provide additional reference markers, such as reference
marker 623 located at the intersection of the three bars labeled 26
in FIG. 14.[HRt] Reducing the uncertainty of the projection
geometry through the constraint of one or more degrees of freedom
reduces the complexity of the resulting reconstruction. An
arrangement of the system of the present invention which is
somewhat constrained is depicted in FIGS. 12 and 13, wherein a
hand-held X-ray source is provided such that the orthogonal
distance between the radiation source 127 and the recording medium
131 is fixed by a C-arm 129 at a distance short enough so that the
image cast by the fiducial reference 122 is magnified relative to
the size of the actual fiducial reference 122. Preferably, the
C-arm 129 is connected to the recording medium 131 by a concentric
swivel collar 149 to allow the C-arm 129 to be rotated relative to
the recording medium 131. A disposable and crushable radiolucent
foam cushion 130 may be attached to the surface of the recording
medium 131 to permit comfortable customized stable adaptation of
the detector 131 to the object 121. The other end of the C-arm 129
is attached to a potted X-ray source 145 so that radiation
emanating from the potted X-ray source 145 impinges upon the
recording medium 131. A trigger 146 is provided for operating the
source 127. The source 127 optionally comprises a circular beam
collimator 147 for collimating radiation emanating from the source
127. The collimator 147 may provide a relatively long focal-object
distance to provide nearly affine projection geometries.
Preferably, a handle 148 is also provided to enable the operator to
more easily maneuver the source 127. The hand-held X-ray source 127
is connected to a computer/high voltage source 128 for controlling
operation of the device. In addition, a disposable plastic bag 132
can be positioned around the detector 131 for microbial isolation.
The source 127 can optionally comprise a rotatable transparent
radiopaque plastic cylinder 119 and a transparent radiopaque shield
152 to protect the operator from scattered radiation. In this
arrangement, there are 3 degrees of freedom (two translational and
one displacement for the radiation source 127). Accordingly, a
fiducial reference compensating for at least three degrees of
freedom is necessary to completely describe or analyze the system.
One convenient embodiment for solving the system depicted in FIGS.
12 and 13 employs a fiducial reference 122 comprising a single
radiopaque sphere of finite diameter. Under those conditions, the
length of the minor axis of the resulting elliptical shadow plus
two translational measurements are sufficient to define the
projection geometry completely.
[0057] The computational steps involved in synthesizing a
three-dimensional image using three spherical, non-linear reference
markers in a system wherein the orthogonal distance between the
radiation source and the recording medium is fixed at a distance
short enough so that the images cast by the reference markers are
magnified relative to the size of the actual reference markers
(i.e., a system with eight degrees of freedom as depicted in FIGS.
12 and 13) can be derived with reference to FIGS. 17 and 19. In the
drawings, c is the fixed distance between the source and the
projection plane; P.sub.s is the orthogonal projection of the
source onto the projection plane; B, M, and T are the reference
markers; r is the radius of the reference markers; a.sub.p is the
distance from the center of a reference marker to the source; .phi.
is the angle subtended by the center of a reference marker relative
to a line orthogonal to the projection plane through the source;
.phi. is the angle at the apex of an isosceles triangle having a
base of length r and a height of length a.sub.p; B.sub.s, M.sub.s,
and T.sub.s are the reference images associated with the reference
markers; a (or, alternatively, d.sub.p) is the major diameter of
the reference images; b is the minor diameter of the reference
images; x is the length of a section of an arc associated with a
reference image measured from the projection of the center of the
corresponding reference marker onto the projection plane along the
major diameter, b, in a direction toward P.sub.s; y is the length
of an arc associated with a reference image through the projection
of the center of the corresponding reference marker onto the
projection plane and parallel to the minor diameter of the
reference image; and d.sub.s is the major diameter of a reference
image in a virtual projection plane. The derivation of the solution
to the system depicted in FIGS. 17 and 18 is attached hereto as
Chart A and accompanying FIGS. 23-28. FIG. 25 illustrates a graph
of the solution for the projection angle, theta, and FIG. 26
illustrates a graph of the solution for the offset correction
distance, delta.
Chart A
[0058] a = d p 2 y = d s ( c + t / cos .theta. ) / c t = c ( 1 -
cos .theta. ) ##EQU00001## d p = { tan [ .theta. + arctan ( d s / 2
c ) ] - tan [ .theta. - arctan ( d s / 2 c ) ] } c ##EQU00001.2## a
p = r sin .theta. 2 = r sin ( arctan d s 2 c ) ##EQU00001.3## d s =
{ 2 tan [ arctan ( x - c tan .theta. ) c ] + .theta. } c
##EQU00001.4## x = a sin .theta. cos .theta. + c + i a 2 cos
.theta. 4 - a 2 cos .theta. 2 - c 2 2 sin .theta. cos .theta.
##EQU00001.5## Therefore , a p is f ' cn of r , c , .theta. , and a
##EQU00001.6## tan ( .theta. + .phi. 2 ) = d p + w c sin .phi. 2 =
r a p ##EQU00001.7## tan ( .theta. - .phi. 2 ) = w c cos .phi. 2 =
r d .thrfore. tan ( .theta. + .phi. 2 ) = d p + tan ( .theta. -
.phi. 2 ) c c .thrfore. tan .phi. 2 = d a p ##EQU00001.8## d p = [
tan ( .theta. + .phi. 2 ) - tan ( .theta. - .phi. 2 ) ] c a p 2 d =
c d s .thrfore. d p = [ tan ( .theta. + arctan d s 2 c ) - tan (
.theta. - arctan d s 2 c ) ] c .thrfore. .phi. 2 = arctan d s 2 c
tan .theta. = x + w c .thrfore. x = c { tan .theta. - tan [ .theta.
- arctan ( d s 2 c ) ] } a = c [ tan ( .theta. + arcsin r a p ) -
tan ( .theta. - arcsin r a p ) ] ##EQU00001.9##
tan ( q + f 2 ) = dp + w c #1 tan ( q - f 2 ) = w c #2 ##EQU00002##
[0059] Solving #2 for w and substituting the result into #1
yields:
[0059] tan ( q + 1 2 f ) = ( dp - tan ( - q + 1 2 f ) c ) c #3
##EQU00003## [0060] Solving #3 for dp yields:
[0060] dp = ( tan ( q + 1 2 f ) + tan ( - q + 1 2 f ) ) c #4 sin (
f 2 ) = r ap #5 cos ( f 2 ) = r d Dividing #5 by #6 yields : #6 tan
( f 2 ) = d ap #7 ap 2 d = c ds #8 ##EQU00004## [0061] Solving #7
for d and substituting the result into #8 yields:
[0061] 1 ( 2 tan ( 1 2 f ) ) = c ds #9 ##EQU00005## [0062] Solving
#9 for f/2 yields:
[0062] f 2 = atan ( ds 2 c ) #10 ##EQU00006## [0063] Substituting
#10 into #4 yields:
[0063] dp = ( tan ( q + atan ( ds 2 c ) ) + tan ( - q + atan ( ds 2
c ) ) ) c #11 ##EQU00007## [0064] Solving #11 for q . . . . [0065]
Guess value: q:=1 [0066] Given
[0066] dp = ( tan ( q + atan ( ds 2 c ) ) + tan ( - q + atan ( ds 2
c ) ) ) c ##EQU00008## [0067] Angle(dp, ds, c):=Find(q) [0068]
Example: [0069] dp:=10, 11 . . . 100 [0070] ds:=10 [0071]
c:=100
[0072] The result is shown in the graph of FIG. 23.
TABLE-US-00001 dp Angle(dp, ds, c) 10 2.776 10.sup.-5 11 0.306 12
0.42 13 0.5 14 0.563 15 0.615 16 0.658 17 0.696 18 0.729 19 0.758
20 0.784 21 0.808 22 0.83 23 0.849 24 0.868 25 0.885 26 0.9 27
0.915 28 0.929 29 0.941 30 0.954 31 0.965 32 0.976 33 0.986 34
0.996 35 1.005 36 1.014 37 1.022 38 1.03 39 1.038 40 1.045 41 1.052
42 1.059 43 1.065 44 1.072 45 1.078 46 1.083 47 1.089 48 1.094 49
1.1 50 1.105 51 1.11 52 1.114 53 1.119 54 1.123 55 1.122 56 1.132
57 1.136 58 1.14 59 1.144
Derivation of X
[0073] tan ( q ) = x + w c #1 c tan ( q - f 2 ) = w #2 f 2 = atan (
ds 2 c ) #3 ##EQU00009## [0074] Substituting #3 into 52 yields:
[0074] c tan ( q - atan ( ds 2 c ) ) = w #4 ##EQU00010## [0075]
Substituting #4 into #1 yields:
[0075] tan ( q ) = ( x + c tan ( q - atan ( 1 2 ds c ) ) ) c #5
##EQU00011## [0076] Solving #5 for x yields:
[0076] x = ( tan ( q ) - tan ( q - atan ( 1 2 ds c ) ) ) c #6
##EQU00012## [0077] Equation of an ellipse expressed in terms of x,
y, a, & b:
[0077] ( a 2 - x ) 2 ( a 2 ) 2 + y 2 ( b 2 ) 2 = 1 #1 ##EQU00013##
[0078] Solving #1 for positive values of y yields:
[0078] y = b x a - x 2 #2 ##EQU00014## [0079] Let: [0080] x:=0, 0,
1 . . . 2 [0081] a:=4 [0082] b=2 [0083] as shown in FIG. 27.
Plotting y as a function of x, as shown in FIG. 28, yields:
TABLE-US-00002 [0083] x y = b x a - x a ##EQU00015## 0 0 0.1 0.312
0.2 0.436 0.3 0.527 0.4 0.6 0.5 0.661 0.6 0.714 0.7 0.76 0.8 0.8
0.9 0.835 1 0.866 1.1 0.893 1.2 0.917 1.3 0.937 1.4 0.954 1.5 0.968
1.6 0.98 1.7 0.989 1.8 0.995 1.9 0.999 2 1
[0084] Derivation of ap in Terms of Observable Quantities
ap = r sin ( r 2 ) # 1 a = [ tan [ q + ( r 2 ) ] - tan [ q - ( r 2
) ] ] c #2 ##EQU00016## [0085] Solving #1 for f/2 yields:
[0085] 1 / 2 = asin ( r ap ) #3 ##EQU00017## [0086] Substituting #3
into #2 yields the following implicit equation:
[0086] a = ( tan ( q + asin ( r ap ) ) - tan ( q - asin ( r ap ) )
) c #4 ##EQU00018## [0087] Guess value: ap:=20 [0088] Given
[0088] a = ( tan ( q + asin ( r ap ) ) - tan ( q - asin ( r ap ) )
) c ##EQU00019## [0089] ap(a, q, r, c):=Find(ap) [0090] Example:
[0091] a:=50, 51 . . . 100
[0091] q := .pi. 4 ##EQU00020## [0092] r:=9 [0093] c:=82
[0094] The solution for these values is plotted in FIG. 24.
[0095] Augmented Complex General Sphere Derivation
dp = ( tan ( q + atan ( ds 2 c ) ) + tan ( - q + atan ( ds 2 c ) )
) c #1 a = dp #2 ##EQU00021## [0096] Substituting #2 into #1
yields:
[0096] a = ( tan ( q + atan ( ds 2 c ) ) + tan ( - q + atan ( ds 2
c ) ) ) c #3 2 y = ds c + t cos ( q ) c #4 ##EQU00022## [0097]
Solving #4 for ds and substituting the result into #3 yields:
[0097] a = [ tan [ q - atan [ y [ ( - 1 - 1 c t cos ( q ) ) c ] ] ]
+ tan [ - q - atan [ y [ ( - 1 - 1 c t cos ( q ) ) c ] ] ] ] c #5 t
= c ( 1 - cos ( q ) ) #6 ##EQU00023## [0098] Substituting #6 into
#5 and simplifying yields:
[0098] a = [ tan [ q - atan [ y [ [ - 1 - ( 1 - cos ( q ) ) cos ( q
) ] c ] ] ] + tan [ - q - atan [ y [ [ - 1 - ( 1 - cos ( q ) ) cos
( q ) ] c ] ] ] ] c #7 ##EQU00024## [0099] From the ellipse
derivation . . .
[0099] y = b x a - x a #8 ##EQU00025## [0100] Substituting #8 into
#7 yields:
[0100] [ a = [ tan [ q - atan [ b x a - x [ a [ [ - 1 - ( 1 - cos (
q ) ) cos ( q ) ] c ] ] ] ] ] c ] + [ tan [ - q - atan [ b x [ a -
x [ a [ [ - 1 - ( 1 - cos ( q ) ) cos ( q ) ] c ] ] ] ] ] ] c #9
##EQU00026## [0101] From the derivation of x . . .
[0101] x = ( tan ( q ) - tan ( q - atan ( 1 2 ds c ) ) ) c #10
##EQU00027## [0102] Solving #10 for ds yields:
[0102] ds = 2 tan atan ( x - c tan ( q ) ) c + q c #11 ##EQU00028##
[0103] Substituting #11 into #3 yields
[0103] a = [ tan [ 2 q + atan [ ( x - c tan ( q ) ) c ] ] + ( x - c
tan ( q ) ) c ] c #12 Solving #12 for x & simplifying yields :
x = [ 1 2 ( a sin ( q ) cos ( q ) + c + i - a 2 cos ( q ) 2 + a 2
cos ( q ) 4 - c 2 ) ( sin ( q ) cos ( q ) ) 1 2 ( a sin ( q ) cos (
q ) + c - i - a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 ) ( sin ( q )
cos ( q ) ) ] #13 ##EQU00029## [0104] Substituting the first
solution of #13 into #9 yields:
[0104] a = [ tan [ q - atan [ 1 2 b 2 a sin ( q ) cos ( q ) + c + i
- a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 ( sin ( q ) cos ( q ) ) a
- 1 2 ( a sin ( q ) cos ( q ) + c + i - a 2 cos ( q ) 2 + a 2 cos (
q ) 4 - c 2 ) ( sin ( q ) cos ( q ) ) [ a [ [ - 1 - ( 1 - cos ( q )
) cos ( q ) ] c ] ] ] ] ] c + #14 [ tan [ - q - atan [ 1 2 b 2 a
sin ( q ) cos ( q ) + c + i - a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c
2 ( sin ( q ) cos ( q ) ) a - 1 2 ( a sin ( q ) cos ( q ) + c + i -
a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 ) ( sin ( q ) cos ( q ) ) [
a [ [ - 1 - ( 1 - cos ( q ) ) cos ( q ) ] c ] ] ] ] ] c delta = a 2
- x #15 ##EQU00030## [0105] Substituting the first solution of #13
Into #15 and simplifying yields:
[0105] delta = - 1 2 ( c + i - a 2 cos ( q ) 2 + a 2 cos ( q ) 4 -
c 2 ) ( sin ( q ) cos ( q ) ) #16 ##EQU00031## [0106] Solving #14
for q [0107] Guess value: [0108] Given
[0108] a = [ tan [ q - atan [ 1 2 b 2 a sin ( q ) cos ( q ) + c + i
- a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 ( sin ( q ) cos ( q ) ) a
- 1 2 ( a sin ( q ) cos ( q ) + c + i - a 2 cos ( q ) 2 + a 2 cos (
q ) 4 - c 2 ) ( sin ( q ) cos ( q ) ) [ a [ [ - 1 - ( 1 - cos ( q )
) cos ( q ) ] c ] ] ] ] ] c + [ tan [ - q - atan [ 1 2 b 2 a sin (
q ) cos ( q ) + c + i - a 2 cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 (
sin ( q ) cos ( q ) ) a - 1 2 ( a sin ( q ) cos ( q ) + c + i - a 2
cos ( q ) 2 + a 2 cos ( q ) 4 - c 2 ) ( sin ( q ) cos ( q ) ) [ a [
[ - 1 - ( 1 - cos ( q ) ) cos ( q ) ] c ] ] ] ] ] c
##EQU00032##
[0109] In FIG. 6, another arrangement of the system of the present
invention is depicted wherein the radiation source 27 is located at
a fixed distance from the selected object 21 and sufficiently far
so that magnification is not significant. However, the recording
medium 31 is allowed to be shifted, displaced, and tilted relative
to the selected object 21 and an original or desired projection
plane 37. In this arrangement, there are seven degrees of freedom
(two translational degrees of freedom for the radiation source 27
and 2 translational, 1 displacement, and 2 tilting degrees of
freedom for the recording medium 31). Therefore, a fiducial
reference having at least seven degrees of freedom is needed to
solve the system. Accordingly, a fiducial reference comprising at
least four point-size reference markers can be used to determine
the position of the radiation source relative to the selected
object 21 and the recording medium 31.
[0110] In FIG. 7, yet another arrangement of the system of the
present invention is depicted wherein the distance between the
object 21 and the radiation source 27 is sufficiently large so that
magnification can be ignored and wherein the recording medium 31 is
free to shift laterally relative to the object 21 and the desired
or original projection plane 37. In this arrangement, there are
four degrees of freedom (two translational degrees of freedom for
the radiation source 27 and two translational degrees of freedom
for the recording medium 31). Therefore, a fiducial reference
having at least four degrees of freedom is necessary to completely
determine the system. Accordingly, a fiducial reference comprising
at least two point-size reference markers can be used to determine
the position of the radiation source relative to the selected
object 21 and the recording medium 31. This relatively constrained
system may be useful in three-dimensional reconstructions of
transmission electron micrographs produced from video projections
subtending various degrees of specimen tilt and exhibiting various
amounts of arbitrary and unpredictable lateral shift due to
intrinsic instability associated with the instrument's electron
lenses.
[0111] Referring to FIG. 1, the radiation source 27 may be either a
portable or a stationary X-ray source. However, the radiation
source 27 is not limited to an X-ray source. The specific type of
source 27 which is utilized will depend upon the particular
application. For example, the present invention can also be
practiced using magnetic resonance imaging (MRI), ultrasound,
visible light, infrared light, ultraviolet light, or
microwaves.
[0112] In the embodiment shown in FIG. 10, the source 227 is a
hand-held X-ray source, similar to that described above in
reference to source 127, except that a low power laser aiming
device 250 and an alignment indicator 251 are provided to insure
that the source 227 and the recording medium 231 are properly
aligned. In addition, a radiolucent bite block 218 is provided to
constrain the detector 231 relative to the object 221, thereby
constraining the system to three degrees of freedom (two
translational and one displacement for the radiation source 227
relative to the object 221 and detector 231). Consequently, the
fiducial reference 222 can be fixed directly to the bite block 218.
When the source 227 is properly aligned with the recording medium
231, radiation emanating from the aiming device 250 impinges on the
recording medium 231. In response to a measured amount of radiation
impinging on the recording medium 231, a signal is sent to activate
the alignment indicator 251 which preferably produces a visible
and/or auditory signal. With the alignment indicator 251 activated,
the X-ray source 245 can be operated at full power to record a
projected image. In addition, the source 227 can optionally
comprise a collimator 247 to collimate the radiation from the X-ray
source and/or a transparent scatter shield 252 to protect the
operator from scattered radiation. In lieu of the scatter shield
252, the operator can stand behind a radiopaque safety screen when
exposing the patient to radiation from the source 227. A handle 248
and trigger 246 may be provided to facilitate the handling and
operation of the source 227. The source 227 is connected to a
computer/high voltage source 228 and an amplifier 260 for
controlling operation of the device.
[0113] In one embodiment, the aiming device 250 comprises an X-ray
source operated in an ultra-low exposure mode and the projected
image is obtained using the same X-ray source operated in a
full-exposure mode. Alternatively, a real-time ultra-low dose
fluoroscopic video display can be mounted into the handle 248 of
the source 227 via a microchannel plate (MCP) coupled to a CCD. The
video display switches to a lower gain (high signal-to-noise) frame
grabbing mode when the alignment is considered optimal and the
trigger 246 is squeezed more tightly.
[0114] An alternate embodiment of an aiming device in accordance
with the present invention is shown in FIG. 22. The aiming device
850 comprises a laser source 857 and a radiolucent angled mirror
858 which produces a laser beam, illustrated by dashed line 859,
which is concentric with the radiation emanating from the source
827. The alignment indicator 851 comprises a radiolucent spherical
surface 861 which is rigidly positioned relative to the detector
831 by a C-arm 829 that is plugged into the bite block 818. When
the aiming device 850 is aimed such that the laser beam 859
impinges upon the spherical surface 861, the specular component of
the laser beam 859 is reflected by the spherical surface 861.
Accordingly, proper alignment of the source 827, the object 821,
and the detector 831 is obtained when the reflected portion of the
laser beam 859 is within a small solid angle determined by the
position of the aiming device 850. Direct observation of the
reflected portion of the laser beam 859 by a detector or observer
862 can be used to verify the alignment. As shown in the figure,
the fiducial reference 822 comprises a radiolucent spacer
containing a fiducial pattern that is affixed to the detector 831.
Further, a central ring area 863 can be designated at the center of
the spherical surface 861 such that aiming the laser beam 859 at
the central ring area 863 assures an essentially orthogonal
arrangement of the source 827 and the detector 831. In addition,
replacing the concentric laser source 857 with a laser source that
produces two laser beams that are angled relative to the radiation
emanating from the source 827 permits the distance between the
source 827 and the detector 831 to be set to a desired distance,
provided that the two laser beams are constrained to converge at
the spherical surface 861 when the desired distance has been
established.
[0115] Referring again to FIG. 1, the recording medium 31 is
provided for recording the projected object image 40 of the
selected object 21 and the projected reference images, 39 and 139,
of the reference markers 23 and 123. The recording medium 31 may be
in the form of a photographic plate or a radiation-sensitive,
solid-state image detector such as a radiolucent charge-coupled
device (CCD).
[0116] In one particular embodiment depicted in FIG. 8, the
recording medium 331 comprises a CCD having a top screen 200, a
bottom screen 206 positioned below the top screen 200, and a
detector 210 positioned below the bottom screen 206. The top screen
200 is monochromatic so that a projected image projected onto the
top screen 200 causes the top screen 200 to fluoresce or
phosphoresce a single color. In contrast, the bottom screen 206 is
dichromatic, so that the bottom screen 206 fluoresces or
phosphoresces in a first color in response to a projected image
projected directly onto the bottom screen 206 and fluoresces or
phosphoresces in a second color in response to fluorescence or
phosphorescence from the top screen 200. The detector 210 is also
dichromatic so as to allow for the detection and differentiation of
the first and the second colors. The recording medium 331 may also
comprise a radiolucent optical mask 202 to modulate the texture and
contrast of the fluorescence or phosphorescence from the top screen
200, a radiolucent fiber-optic spacer 204 to establish a known
projection disparity, and a radiopaque fiber-optic faceplate 208 to
protect the detector 210 from radiation emanating directly from the
radiation source.
[0117] Yet another embodiment is depicted in FIGS. 20 and 23,
wherein the detector 731 comprises a phosphor-coated CCD and the
fiducial reference 722 comprises a radiopaque rectangular frame
725. Both the detector 731 and the fiducial reference 722 are
contained within a light-tight package 756. The detector 731 and
fiducial reference 722 are preferably positioned flush with an
upper, inner surface of the package 756. The dimensions of the
frame 725 are selected such that the frame 725 extends beyond the
perimeter of the detector 731. Phosphor-coated strip CCDs 754 are
also contained within the package 756. The strip CCDs 754 are
positioned below the frame 725 such that radiation impinging upon
the frame 725 castes an image of each edge of the frame 725 onto
one of the strip CCDs 754. The positions of the frame shadow on the
strip CCDs 754 is used to determine the projection geometry. In the
embodiment shown in FIG. 9, the recording medium 431 is smaller
than the projected image of object 521. Provided that the reference
images, 39 and 139, corresponding to the reference markers, 23 and
123, can be identified on all the projected images, image slices
extending across the union of all the projected images can be
obtained. This is illustrated schematically in FIG. 9, wherein the
reference images, 39 and 139, are taken with the source 27 and the
recording medium 431 in the image positions indicated by the solid
lines. Similarly, the dashed images, 39' and 139', are taken with
the source 27' and the recording medium 431' in the positions
indicated by the dashed lines. Accordingly, image slices of an
object which casts an object image that is larger than the
recording medium 431 can be synthesized. Further, by using multiple
fiducial references spaced in a known pattern which are all linked
to the object of interest, additional regions of commonality can be
identified between multiple overlapping projection geometries, so
that a region of any size can be propagated into a single, unified
reconstruction. Thus, it is possible to accommodate an object much
larger than the recording medium used to record individual
projection images.
[0118] The present invention also relates to a method for creating
a slice image through the object 21 of FIG. 1 from a series of
two-dimensional projected images of the object 21, as shown in FIG.
2. The method of synthesizing the image slice starts at step 45.
Each step of the method can be performed as part of a
computer-executed process.
[0119] At step 47, a fiducial reference 22 comprising at least two
reference markers, 23 and 123, is selected which bears a fixed
relationship to the selected object 21. Accordingly, the fiducial
reference 22 may be affixed directly to the selected object 21. The
minimum required number of reference markers 23 is determined by
the number of degrees of freedom in the system, as discussed above.
When the fiducial reference 22 comprises reference markers 23 of a
finite size, the size and shape of the reference markers 23 are
typically recorded.
[0120] The selected object 21 and fiducial reference 22 are exposed
to radiation from any desired projection geometry at step 49 and a
two-dimensional projected image 38 is recorded at step 51.
Referring to FIG. 1, the projected image 38 contains an object
image 40 of the selected object 21 and a reference image, 39 and
139, respectively, for each of the reference markers 23 and 123 of
the fiducial reference 22.
[0121] At step 53, it is determined whether additional projected
images 38 are desired. The desired number of projected images 38 is
determined by the task to be accomplished. Fewer images reduce the
signal-to-noise ratio of the reconstructions and increase the
intensities of component "blur" artifacts. Additional images
provide information which supplements the information contained in
the prior images, thereby improving the accuracy of the
three-dimensional radiographic display. If additional projected
images 38 are not desired, then the process continues at step
60.
[0122] If additional projected images 38 are desired, the system
geometry is altered at step 55 by varying the relative positions of
(1) the radiation source 27, (2) the selected object 21 and the
fiducial reference 22, and (3) the recording medium 31. The
geometry of the system can be varied by moving the radiation source
27 and/or the recording medium 31. Alternatively, the source 27 and
recording medium 31, the selected object 21 and fiducial reference
22 are moved. When the radiation source and recording medium
produce images using visible light (e.g., video camera), the
geometry of the system must be varied to produce images from
various sides of the object in order to obtain information about
the entire object. After the system geometry has been varied, the
process returns to step 49.
[0123] After all of the desired projected images have been
recorded, a slice position is selected at step 60. The slice
position corresponds to the position at which the image slice is to
be generated through the object.
[0124] After the slice position has been selected, each projected
image 38 is projectively warped onto a virtual projection plane 37
at step 65. The warping procedure produces a virtual image
corresponding to each of the actual projected images. Each virtual
image is identical to the image which would have been produced had
the projection plane been positioned at the virtual projection
plane with the projection geometry for the radiation source 27, the
selected object 21, and the fiducial reference 22 of the
corresponding actual projected image. The details of the steps
involved in warping the projection plane 37 are shown in FIG. 3.
The process starts at step 70.
[0125] At step 72, a virtual projection plane 37 is selected. In
most cases it is possible to arrange for one of the projected
images to closely approximate the virtual projection plane
position. That image can then be used as the basis for
transformation of all the other images 38. Alternatively, as shown
for example in FIG. 4, if the fiducial reference 22 comprises more
than two co-planar reference markers 23, a plane which is parallel
to the plane containing the co-planar reference markers 23 can be
selected as the virtual projection plane 37. When the virtual
projection plane 37 is not parallel to the plane containing the
co-planar reference markers 23, although the validity of the slice
reconstruction is maintained, the reconstruction yields a slice
image which may be deformed due to variations in magnification. The
deformation becomes more prominent when the magnification varies
significantly over the range in which the reconstruction is carried
out. In such cases, an additional geometric transformation to
correct for differential magnification may be individually
performed on each projected image 38 to correct for image
deformation.
[0126] One of the recorded projected images 38 is selected at step
74 and the identity of the reference images 39 cast by each
reference marker 23 is determined at step 76. In the specialized
case, such as the one shown in FIG. 1, where spherical reference
markers 23 of the same radius are used and the relative proximal
distance of each reference marker 23 to the radiation source 27 at
the time that the image 38 was recorded is known, assignment of
each elliptical image 39 to a corresponding reference marker 23 can
be accomplished simply by inspection. Under such conditions, the
minor diameter of the elliptical image 39 is always larger the
closer the reference marker 23 is to the radiation source 27. This
is shown most clearly in FIG. 17 wherein the minor diameter of
reference image B.sub.s corresponding to reference marker B is
smaller than the minor diameter of reference image T.sub.s
corresponding to reference marker T. Alternatively, when applied to
radiation capable of penetrating the fiducial reference 22 (i.e.,
X-rays), spherical reference markers 23 which are hollow having
different wall thicknesses and hence, different attenuations can be
used. Accordingly, the reference image 39 cast by each spherical
reference marker 23 can be easily identified by the pattern of the
reference images 39. Analogously, spherical reference markers 23 of
different colors could be used in a visible light mediated
system.
[0127] The position of each reference image 39 cast by each
reference marker 23 is measured at step 78. When a spherical
reference marker 23 is irradiated by source 27, the projected
center 41 of the reference marker 23 does not necessarily
correspond to the center 42 of the reference image 39 cast by that
reference marker 23. Accordingly, the projected center 41 of the
reference marker 23 must be determined. One method of determining
the projected center 41 of the reference marker 23 is shown in FIG.
16. The variation in intensity of the reference image 39 associated
with reference marker 23 along the length of the major diameter of
the reference image 39 is represented by the brightness profile 43.
The method depicted in FIG. 16 relies on the fact that the
projected center 41 always intersects the brightness profile 43 of
the reference image 39 at, or very near, the maximum 44 of the
brightness profile 43. Accordingly, the projected center 41 of a
spherical reference marker 23 produced by penetrating radiation can
be approximated by smoothing the reference image 39 to average out
quantum mottle or other sources of brightness variations which are
uncorrelated with the attenuation produced by the reference marker
23. An arbitrary point is then selected which lies within the
reference image 39. A digital approximation to the projected center
41 is isolated by performing a neighborhood search of adjacent
pixels and propagating the index position iteratively to the
brightest (most attenuated) pixel in the group until a local
maximum is obtained. The local maximum then represents the
projected center 41 of the reference marker 23.
[0128] Returning to step 78 of FIG. 3, when the fiducial reference
22 comprises reference markers 23 of finite size, the sizes of each
image 39 cast by each reference marker 23 are also recorded. For
example, the lengths of the major and minor diameters of elliptical
reference images cast by spherical reference markers 23 can be
measured. Computerized fitting procedures can be used to assist in
measuring the elliptical reference images 39 cast by spherical
reference markers 23. Such procedures, which are well-known in the
art, may be used to isolate the elliptical reference images 39 from
the projected image 38 and determine the major and minor diameters
of the reference images 39.
[0129] Because the attenuation of a spherical reference marker 23
to X-rays approaches zero at tangential extremes, the projected
minor diameter of resulting elliptical reference images 39 will be
slightly smaller than that determined geometrically by projection
of the reference marker's actual diameter. The amount of the
resulting error is a function of the energy of the X-ray beam and
the spectral sensitivity of the recording medium 31. This error can
be eliminated by computing an effective radiographic diameter of
the reference marker 23 as determined by the X-ray beam energy and
the recording medium sensitivity in lieu of the actual
diameter.
[0130] One method of obtaining the effective radiographic diameter
is to generate a series of tomosynthetic slices through the center
of the reference marker 23 using a range of values for the
reference marker diameter decreasing systematically from the actual
value and noting when the gradient of the reference image 39 along
the minor diameter is a maximum. The value for the reference marker
diameter resulting in the maximum gradient is the desired effective
radiographic diameter to be used for computing magnification.
[0131] Further, each projected image can be scaled by an
appropriate magnification. For fiducial references 22 comprising
spherical reference markers 23, the minor diameter of the reference
image 39 is preferably used to determine the magnification since
the minor diameter does not depend on the angle between the source
27 and the recording medium 31. Accordingly, the magnification of a
spherical reference marker 23 can be determined from the measured
radius of the reference marker 23, the minor diameter of the
reference image 39 on the recording medium 31, the vertical
distance between the center of the reference marker 23 and the
recording medium 31, and the vertical distance between the
recording medium 31 and the virtual projection plane 37.
[0132] Returning to FIG. 3 with reference to FIG. 1, a projection
transformation matrix, representing a series of transformation
operations necessary to map the selected projected image 38 onto
the virtual projection plane 37, is generated at step 80. The
projection transformation matrix is generated by solving each
projected image 38 relative to the virtual projection plane 37. In
one embodiment, the positions of the co-planar reference markers 23
are used to determine the transformation matrix by mapping the
position of the reference images 39 cast by each co-planar
reference marker 23 in the projected image onto its corresponding
position in the virtual projection plane. For example, when the
fiducial reference comprises a radiopaque frame 25, the positions
of the reference-images 39 cast by the reference markers 23 formed
at the corners of the frame 25 are mapped to a canonical rectangle
having the same dimensions and scale as the frame 25. This approach
also serves to normalize the projective data. Depending on the
number of degrees of freedom, the transformation operations range
from complex three-dimensional transformations to simple planar
rotations or translations. Once the projective transformation
matrix has been generated, the matrix is used to map the projected
image 38 onto the virtual projection plane 37 at step 82.
[0133] At step 84, it is determined whether all of the projected
images 38 have been analyzed. If all of the projected images 38
have not been analyzed, the process returns to step 74, wherein an
unanalyzed image 38 is selected. If no additional projected images
38 are to be analyzed, then the process proceeds through step 85 of
FIG. 3 to step 90 of FIG. 2.
[0134] After each image has been warped onto the virtual projection
plane, an image slice through the object 21 at the selected slice
position is generated at step 90. An algorithm, such as that
described in U.S. Pat. No. 5,359,637, which is incorporated herein
by reference, can be used for that purpose. The position of the
reference image cast by the alignment marker or markers 23 in each
projected image 38 are used as the basis for application of the
algorithm to generate the image slices.
[0135] By generating image slices at more than one slice position,
a true three-dimensional representation can be synthesized.
Accordingly, it is determined whether an additional slice position
is to be selected at step 92. If an additional slice position is
not desired, the process proceeds to step 94. If a new slice
position is to be selected, the process returns to step 60.
[0136] If image slices at multiple slice positions have been
generated, the entire set of image slices is integrated into a
single three-dimensional representation at step 94. Alternative
bases for interactively analyzing and displaying the
three-dimensional data can be employed using any number of
well-established three-dimensional recording and displaying
methods.
[0137] In the embodiment shown in FIG. 19, the source 627 is an
unconstrained point source and the detector 631 is completely
constrained relative to the object 621. Accordingly, the system has
three degrees of freedom (two translational and one displacement
for the radiation source 627 relative to the object 621 and
detector 631). A beam collimator 647 can be positioned between the
source 627 and the object 621 to collimate the radiation from the
source 627. The detector 631 comprises a primary imager 632 and a
secondary imager 634 positioned a known distance below the primary
imager 632. In one embodiment, both the primary and secondary
imagers, 632 and 634, are CCD detectors. The fiducial reference 622
comprises a radiopaque shield 633 with a ring-shaped aperture 636
of known size positioned between the primary imager 632 and the
secondary imager 634.
[0138] Radiation from the source 627 passes through collimator 647,
irradiates object 621, and produces an object image on the primary
imager 632. In addition, radiation from the source 627 which
impinges upon the radiopaque shield 633 passes through the aperture
636 to produce a circular, or elliptical, reference image of the
aperture 636 on the secondary imager 634. Since the secondary
imager 634 is not used to record object images, the secondary
imager 634 can be a low quality imager such as a low resolution
CCD. Alternatively, a lower surface of the primary imager 632 can
be coated with a phosphorescent material 635, so that radiation
impinging upon the primary imager 632 causes the phosphorescent
material 635 to phosphoresce. The phosphorescence passes through
the aperture 636 to produce the reference image on the secondary
imager 634.
[0139] In operation, the reference image produced using the system
depicted in FIG. 19 can be used to determine the position of the
source 627 relative to the object 621 and the detector 631. A
circle, or ellipse, is fitted to the projected reference image. By
fitting a circle, or ellipse, to the reference image, the effect of
dead areas and/or poor resolution of the secondary imager 634 can
be eliminated by averaging. The position of the center of the
fitted circle, or ellipse, relative to the known center of the
aperture 636 is determined. The angle .alpha. of a central ray 637
radiating from the source 627 relative to the object 621 and the
detector 631 can then be determined. In addition, the length of the
minor diameter of the projected reference image is determined and
compared to the known diameter of the aperture 636 to provide a
relative magnification factor. The relative magnification factor
can then be used to determine the distance of the source 627 from
the object 621.
[0140] The center of the fitted circle can be determined as
follows. A pixel or point on the secondary imager 634 that lies
within the fitted circle is selected as a seed point. For
convenience, the center pixel of the secondary imager 634 can be
selected, since the center point will typically lie within the
fitted circle. A point R is determined by propagating from the seed
point towards the right until the fitted circle is intersected.
Similarly, a point L is determined by propagating from the seed
point towards the left until the fitted circle is intersected. For
each pixel along the arc L-R, the average of the number of pixels
traversed by propagating from that pixel upwardly until the fitted
circle is intersected and the number of pixels traversed by
propagating from that pixel downwardly until the fitted circle is
intersected is determined. Any statistical outliers from the
averages can be discarded and the average of the remaining values
calculated. This average represents the row address of the fitted
circle's center. To obtain the column address, the entire reference
image is rotated by 90.degree. and the process is repeated. The row
address and column address together represent the position of the
center of the fitted circle.
[0141] Although the above embodiments have been described in
relation to projected images of objects produced using X-rays, the
present invention is equally applicable to images produced using a
variety of technologies, such as visible light, ultrasound, or
electron microscopy images. Specifically, intermediate voltage
electron microscope (IVEM) images can be used to provide
quantitative three-dimensional ultrastructural information.
Further, the present invention can also be used to reconstruct
three-dimensional images of objects which either emit or scatter
radiation.
[0142] When IVEM images are used, the present invention allows
cellular changes to be detected and quantified in an efficient and
cost-effective manner. Quantitation of three-dimensional structure
facilitates comparison with other quantitative techniques, such as
biochemical analysis. For example, increases in the Golgi apparatus
in cells accumulating abnormal amounts of cholesterol can be
measured and correlated with biochemically measured increases in
cellular cholesterol.
[0143] When photographic images are used, it is possible to create
a true three-dimensional model of a diffusely illuminated fixed
scene from any number of arbitrary camera positions and angles. The
resulting three-dimensional image permits inverse engineering of
structural sizes and shapes, and may be expressed as a series of
topographic slices or as a projective model that can be manipulated
interactively. This capability is particularly useful in
retrofitting existing structures or quantifying three-dimensional
attributes using non-invasive methods. In addition, the present
invention can be applied to construct topological images of
geological structures by recording images of the structure created
by the sun.
[0144] It will be recognized by those skilled in the art that
changes or modifications may be made to the above-described
embodiments without departing from the broad inventive concepts of
the invention. It should therefore be understood that this
invention is not limited to the particular embodiments described
herein, but is intended to include all changes and modifications
that are within the scope and spirit of the invention as set forth
in the claims.
* * * * *