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Claims  |
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Having thus described the invention, it is now claimed:
1. A diagnostic imaging apparatus for forming a three-dimensional
representation of a specimen comprising:
acquisition means for acquiring slice data indicative of a physical
property of a plurality of generally planar regions of a specimen, each
generally planar region being divided into a plurality of subregions
represented by subregion data representative of that portion of the slice
data unique thereto;
means for assigning a viewing value to subregions of at least one of the
planar slices, the viewing value being assigned in accordance with
subregion data thereof;
means for segregating at least a first one of the subregions to define a
region of interest;
means for defining a boundary of interest within the region of interest;
means for assembling image data representative of subregions of the
boundary of interest as a function of subregion data unique thereto;
scaling means for assigning a scaled value to at least a portion of the
image data, such that the image data is representative of first, second,
and third dimensions of an associated specimen; and
means for projecting the image data onto a viewing surface.
2. The diagnostic imaging apparatus of claim 1 wherein the scaling means
includes means for adjusting the scaled value in accordance with a virtual
displacement of the image data from the viewing surface.
3. The diagnostic imaging apparatus of claim 2 wherein the scaling means
further includes means for adjusting a plurality of the scaled values in
accordance with an angle of a normal to the boundary of interest in
relation to the viewing surface.
4. The diagnostic imaging apparatus of claim 1 further comprising means for
extrapolating the region of interest to at least a second generally planar
region to form at least one extrapolated region of interest.
5. The diagnostic imaging apparatus of claim 4 further comprising means for
extrapolating the boundary of interest into at least the one extrapolated
region of interest.
6. The diagnostic imaging apparatus of claim 4 further comprising means for
varying a position of the viewing surface in relation to the image data.
7. The diagnostic imaging apparatus of claim 6 wherein the acquisition
means is comprised of at least one of a magnetic resonance device and a
computed tomographic device.
8. The diagnostic imaging apparatus of claim 1 further comprising means for
extrapolating the boundary of interest to at least a second region of
interest.
9. A method of forming a three-dimensional representation of a specimen
comprising the steps of:
acquiring slice data indicative of a physical property of a plurality of
generally planar regions of a specimen, each generally planar region being
divided into a plurality of subregions represented by subregion data;
assigning a viewing value to subregions of at least one of the plurality of
generally planar slices, the viewing value being assigned in accordance
with subregion data thereof;
segregating at least a first one of the generally planar regions to form a
region of interest;
extrapolating the region of interest to at least a second generally planar
region to form at least one extrapolated region of interest;
defining a boundary around a portion of the region of interest;
assembling image data representative of subregions within the boundary of
interest as a function of subregion data unique thereto;
assigning a scaled value representative of at least a portion of the image
data, whereby image data representative of a first, second, and third
dimensions of the object is assigned; and
projecting the image data onto a viewing surface.
10. The method of claim 9 further comprising the steps of determining a
displacement of image data from the viewing surface and adjusting the
scaled value in accordance therewith.
11. The method of claim 10 further comprising the steps of determining an
angle of a normal to the boundary of interest to the viewing surface and
adjusting a plurality of the scaled values in accordance therewith.
12. The method of claim 11 further comprising the step of extrapolating the
boundary of interest to at least the one extrapolated region of interest.
13. The method of claim 12 further comprising the step of varying a
position of the viewing surface in relation to the image data.
14. A diagnostic imaging apparatus for forming a three-dimensional
representation of a specimen comprising:
acquisition means for acquiring slice data indicative of a physical
property of a plurality of generally planar regions of a specimen, each
generally planar region being divided into a plurality of subregions
represented by subregion data representative of that portion of the slice
data unique thereto;
means for assigning a viewing value to generally all subregions of at least
one of the plurality of generally planar slices, the viewing value being
assigned in accordance with subregion data thereof;
means for selectively defining a section of at least a first one of the
generally planar regions to form a region of interest;
means for defining a boundary of interest within the region of interest;
means for projecting the boundary region into other subregions;
scaling means for assigning a scaled value representative of at least a
portion of the image data, whereby image data representative of first,
second, and third dimensions of the object is assigned;
means for projecting the image data onto a viewing surface;
means for adjusting the scaled value in accordance with a virtual
displacement of the image data from the viewing surface;
means for adjusting a plurality of the scaled values in accordance with an
angle of a tangent to the boundary of interest in relation to the viewing
surface; and
means for extrapolating the region of interest to at least a second
generally planar region to form at least one extrapolated region of
interest.
15. The diagnostic imaging apparatus of claim 14 further comprising means
for extrapolating the boundary of interest into at least the extrapolated
region of interest.
16. The diagnostic imaging apparatus of claim 15 further comprising means
for varying a position of the viewing surface in relation to the image
data.
17. The diagnostic imaging apparatus of claim 16 wherein the acquisition
means is comprised of at least one of a magnetic resonance device and a
computed tomographic device.
18. A diagnostic imaging apparatus for forming a three-dimensional
representation of a specimen comprising:
acquisition means for acquiring spatially encoded slice data indicative of
a physical property of a plurality of generally planar regions of a
specimen, each generally planar region being divided into a plurality of
subregions represented by spatially encoded subregion data representative
of that portion of the slice data unique thereto;
means for assigning a viewing value to generally each subregion of each of
the plurality of generally planar slices, an assigned viewing value being
functionally related to subregion data;
partitioning means including:
means for apportioning first one of the generally planar regions to form a
first region of interest, and
means for apportioning at least a second of the generally planar regions to
form at least second region of interest;
boundary means including:
means for defining a first boundary of interest within the first region of
interest, and
means for defining a boundary of interest within at least the second region
of interest;
means for defining a position of an associated viewing surface in relation
to generally each viewing value;
scaling means for a scaling generally each viewing value in accordance with
a displacement thereof from the associated viewing surface;
means for modifying generally each viewing value in accordance with
subregion data from which it was derived; and
means for projecting the image data onto a viewing surface.
19. The diagnostic imaging apparatus of claim 18 wherein said boundary
comprises a plurality of generally parallel, linearly adjacent,
subregions.
20. The diagnostic imaging apparatus of claim 19 further comprising means
for determining potentially visible face portions of each of the data
segments, a visible face portion being defined as that portion of a data
segment which is directly projectable on the viewing surface without
obstruction by another of the data segments.
21. The diagnostic imaging apparatus of claim 20 wherein the partitioning
means includes means for apportioning the second region of interest as an
extrapolation of a partitioning from the first partitioning means.
22. The diagnostic imaging apparatus of claim 21 wherein the boundary means
includes means for defining the second boundary of interest as an
extrapolation of the first boundary of interest.
23. The diagnostic imaging apparatus of claim 22 wherein the scaling means
further includes means for adjusting a plurality of the scaled values in
accordance with an angle of a tangent to the boundary of interest in
relation to the viewing surface.
24. The diagnostic imaging apparatus of claim 23 further comprising means
for varying a position of the viewing surface in relation to the image
data.
25. The diagnostic imaging apparatus of claim 24 wherein the acquisition
means is comprised of at least one of a magnetic resonance device and a
computed tomographic device.
26. A method of forming a three-dimensional representation of a specimen
comprising the steps of:
(a) acquiring spatially encoded slice data indicative of a physical
property of a plurality of generally planar regions of a specimen, each
generally planar region being divided into a plurality of subregions
represented by spatially encoded subregion data representative of that
portion of the slice data unique thereto;
(b) assigning a viewing value to generally each subregion of each of the
plurality of generally planar slices, an assigned viewing value being
functionally related to subregion data;
(c) segregating a first one of the generally planar regions to form a first
region of interest;
(d) segregating at least a second of the generally planar regions to form
at least second region of interest;
(e) defining a first boundary of interest within the first region of
interest;
(f) defining a second boundary of interest within at least the second
region of interest;
(g) defining a position of an associated viewing surface in relation to
generally each viewing value;
(h) scaling each viewing value generally in accordance with a displacement
thereof from the associated viewing surface; and
(i) projecting the image data onto a viewing surface.
27. The method of claim 26 wherein at least one of steps (e) and (f)
includes the step of defining each boundary of interest as a plurality of
generally parallel, linear, data segments.
28. The method claim 27 further comprising the step of determining
potentially visible face portions of each of the data segments, a visible
face portion being defined as that portion of a data segment which is
directly projectable on the viewing surface without crossing another of
the data segments, prior to commencement of step (i).
29. The method of claim 28 wherein step (d) includes the step of
apportioning the second region of interest as an extrapolation of a
partitioning from step (c).
30. The method of claim 29 wherein step (e) includes the step of defining
the second boundary of interest as an extrapolation of the first boundary
of interest defined in step (d).
31. The method of claim 30 wherein step (h) includes the step of adjusting
a plurality of the scaled values in accordance with an angle of a tangent
to the boundary of interest in relation to the viewing surface.
32. The method of claim 31 further comprising the step of varying a
position of the viewing surface in relation to the image data prior to the
commencement of step (i).
33. A diagnostic imaging apparatus for forming a three-dimensional
representation of a specimen comprising:
acquiring means for acquiring image data representative of a
three-dimensional image of a specimen;
monitor means having a viewing area;
means for projecting the image data to the viewing area;
means for defining a cutting surface;
means for projecting the cutting surface on the viewing area;
means for dividing the image data to at least a first portion and a second
portion in accordance with the cutting surface;
means for generating modified image data representative of divided image
data; and
means for projecting the modified image data to the viewing surface.
34. The diagnostic imaging apparatus of claim 33 further comprising means
for selecting one of the portions and wherein the modified image data is
comprised of the selected portion.
35. The diagnostic imaging apparatus of claim 34 further comprising means
for varying a position of the viewing surface in accordance with the
modified image data.
36. The diagnostic imaging apparatus of claim 35 further comprising a
scaling means for assigning a scaled value to subregions of the image
data, whereby image data representative of a first, second, and third
dimension is assigned.
37. The diagnostic imaging apparatus of claim 36 wherein the scaling means
further includes means for adjusting the scaled value in accordance with a
perceived displacement of the image data from the viewing surface.
38. The diagnostic imaging apparatus of claim 37 wherein the scaling means
further includes means for adjusting a plurality of the scaled values in
accordance with an angle of a normal to the boundary of interest in
relation to the viewing surface.
39. The diagnostic imaging apparatus of claim 38 further comprising means
for deriving the three dimensional image data from a plurality generally
parallel, two dimensional images.
40. The diagnostic imaging apparatus of claim 39 wherein the means for
deriving the three dimensional image data is comprised of at least one of
a computed tomography scanner and a magnetic resonance imaging device.
41. The diagnostic imaging apparatus of claim 36 further comprising the
step of adjusting the scaled value in accordance with a perceived
displacement of the image data from the viewing surface.
42. The method of claim 41 further comprising the step of adjusting a
plurality of the scaled values in accordance with an angle of a normal to
the boundary of interest in relation to the viewing surface.
43. The method of claim 42 further comprising the step of deriving the
three dimensional image data from a plurality generally parallel, two
dimensional images.
44. A method of diagnostic imaging comprising the steps of:
acquiring image data representative of a three dimensional image of a
specimen;
projecting the image data to an associated viewing area;
defining a cutting surface;
projecting the cutting surface on the associated viewing area;
dividing the image data to at least a first portion and a second portion in
accordance with the cutting surface;
generating modified image data representative of divided image data; and
projecting the modified image data to the associated viewing surface.
45. The method of claim 44 further comprising the step of selecting one of
the portions and wherein the step of generating modified is directed to
image data comprising the selected portion.
46. The method of claim 45 further comprising the step of varying a
position of the viewing surface in accordance with the modified image
data.
47. The method of claim 46 further comprising the step of assigning a
scaled value to subregions of the image data, whereby image data
representative of a first, second, and third dimension is assigned.
48. A method of forming a three dimensional representation of a specimen
comprising the steps of:
acquiring a plurality of parallel planar slices, each slice being comprised
of spatially encoded data representative of a physical property along a
plane of a specimen;
assigning a gray scale value corresponding to spatially encoded data of one
slice;
generating a two-dimensional image of the one slice on a video display
terminal;
isolating a region of interest encompassing a selected portion of the one
slice in accordance with the image;
extrapolating the region of interest to other slices to form a box of
interest;
assigning a virtual screen location in relation to the box of interest;
selectively projecting spatially encoded data within the box of interest to
the virtual screen location; and
generating an image from projected spatially encoded data. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
This application pertains to the art of diagnostic imaging and more
particularly to three-dimensional imaging.
The invention is particularly applicable to CT scanners and will be
described with particular reference thereto although it will be
appreciated that the invention has broader application such as generating
three-dimensional diagnostic images from data acquired by magnetic
resonance imaging.
With the advent of computed tomography ("CT") and magnetic resonance
imaging ("MRI"), cross-sectional images of the human anatomy may be
generated. Data obtained by the CT or MRI scanners is assembled and a gray
scale is assigned in accordance with data obtained from a particular
section of the data.
As organs are, however, three-dimensional in reality, a series of slices or
scans must be taken, and a mental integration is required to visualize the
actual anatomy. A need was presented to place such a series of
reconstructed planar images in a more familiar format. This type of image
reformation aids physicians in their mental integration. It also aids in
filling the communication gap between radiologists, referring physicians,
collaborators, and their patients. Better planning in medical treatments
or surgical operations is resultant from this type of imaging.
In the last decade, there have been many suggested methods to reformat
cross-sectional images and present them as a three-dimensional image from
any perspective view. Essentially, five different approaches have been
tried. These include the cuberille approach, the octree approach, the ray
tracing approach, the triangulation approach, and the contour approach.
Each of these approaches, however, suffers from its own distinct
disadvantageous.
In order for a three-dimensional imaging processor to become practically
useful, a system response must be extremely fast, ideally less than one
second per frame if not real time. In the prior art systems,
implementation at such speeds could only be achieved with use of special
purpose hardware Such special purpose hardware is extremely expensive, and
is generally not cost effective. Such dedicated hardware is not usable for
other process operations except for its particular three-dimensional
reformatting.
Another disadvantage of the prior art lies particularly with the
cuberille-type approach. In such systems, preprocessing of original image
data is required as the underlying model of this approach assumes that the
three-dimensional object is composed of cubes of the same size. Since, in
fact, input data from a CT or MRI scanner is typically not cubic as the
distance between two consecutive slices is commonly much larger than the
slice of pixels or reconstructed images, resolution and accuracy is
forfeited.
The present invention contemplates a new and improved method and apparatus
which overcomes all of the above referred problems and others, and
provides a system for generating three-dimensional diagnostic images which
is simple, economical, and readily adaptable to general purpose processor
means.
SUMMARY OF THE INVENTION
In accordance with the present invention, a diagnostic imaging system for
forming a three-dimensional representation of the specimen comprises a
means for acquiring slice data indicative of a physical property of a
plurality of generally planar regions of a specimen. Each generally planar
region is divided into a plurality of subregions which are represented by
data representative of that portion of the slice data unique thereto. A
means is provided for assigning a viewing value to generally all of the
subregions of at least one of the plurality of generally planar slices.
The viewing value is assigned in accordance with the physical property of
that particular subregion. A means is provided for apportioning a planar
region to form a region of interest which encompasses a selected surface
boundary. Means is provided for selecting the surface boundary of interest
from within the region of interest, and for assembling image data
representative of the boundary of interest from a plurality of the slices.
A scaled viewing value is assigned to data of a surface of interest, the
scaled value being determined by anticipated projection onto a viewing
surface.
In accordance with another aspect of the present invention, scaled viewing
value is determined in accordance with displacement of a portion of the
surface of interest from the viewing surface.
In accordance with another aspect of the present invention, a system is
provided for selecting a region of interest from data generated from a
single slice, and means for extrapolating that region of interest to
subsequent slices.
In accordance with a still more limited aspect of the present invention,
the boundary of interest is selected from a single slice, and extrapolated
into the region of interest of subsequent slices.
In accordance with another aspect of the present invention, a position of
the viewing surface in relation to the image is variable.
In accordance with a different aspect of the present invention, a system is
provided to implement surface density imaging on a three-dimensional
image.
In accordance with yet a different aspect of the present invention, a
system is provided for slicing an image along a selected planar region to
view a cross-section of a three-dimensional imaged object.
An advantage of the present invention is that a system is provided wherein
a three-dimensional image is generated from a series of slice scans
obtained from conventional imagers.
Another advantage of the present invention is the provision of a system for
generating three-dimensional images with increased fidelity and
resolution.
Another advantage of the present invention is the provision of a system for
generating three-dimensional images which does not require specialized
hardware.
Another advantage of the present invention is the provision of a system
with which surface density of three-dimensional image may be visualized.
Still another advantage of the present invention is the provision of a
system with which cross-sectional cuttings of a three-dimensional image
may be selected and viewed.
Further advantages will become apparent to one of ordinary skill in the art
upon a reading and understanding of the following specification.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention may take physical form in certain parts and arrangements of
parts, preferred embodiments of which will be described in detail in this
specification and illustrated in the accompanying drawings which form a
part hereof and wherein:
FIG. 1 is a block diagram of a three-dimensional image generating apparatus
of the present invention and a system for representation thereof;
FIG. 2 is a diagram illustrating three-dimensional image generated in
accordance with the present invention;
FIG. 3 illustrates a segmented object and a projection thereof onto a
viewing surface;
FIG. 4 illustrates a scheme for three-dimensional image data projection
onto a viewing area;
FIG. 5 is a flow chart for facilitating generation of the three-dimensional
image of the present system;
FIG. 6 is a flow chart of the viewing operations of the present
three-dimensional viewing apparatus;
FIG. 7 is a flow chart illustrating an enhanced system for allowing surface
density information to be displayed on a generated three-dimensional
image;
FIG. 8 is a continuation flow chart of FIG. 7;
FIG. 9 illustrates a specimen image for cutting and viewing in accordance
with the present invention;
FIG. 10 illustrates a procedure for cutting an image in the system of the
present invention; and
FIG. 11 is a flow chart of the image slices operation of the present
invention.
FIG. 12 illustrates an alternate cutting operation of that described in
FIG. 11.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings wherein the showing are for the purposes of
illustrating the preferred embodiments of the invention only and not for
the purposes of limiting the same, FIG. 1 illustrates a block diagram of a
diagnostic imaging apparatus performing a three-dimensional representation
of a specimen. An acquisition means for acquiring slice data A is
interfaced with a data processor/control circuit B. As illustrated, the
acquisition means A is comprised of a CT scanner and will be described
with particular reference thereto. It will be appreciated, however, that
similar sliced data may readily be acquired by any other suitable slice
image apparatus such as an MRI device.
The CT scanner is comprised of an x-ray source 10 which projects a fan beam
of x-rays through an image circle 12 to a detector array 14. The x-ray
source 10 is variable in relation to the image circle 12 to provide
relative motion therebetween under the control of motor means 16. A
plurality of generally parallel slices is obtainable by incrementing a
subject through the image circle 12 between subsequent scans by such means
as the gearing 18. A processor 22 interfaces an x-ray tube control circuit
24 which facilitates acceleration/deceleration control of a rotating anode
of x-ray tube 10, as well as controlling generation the x-ray fan beam. An
array processor 26 works under control of a program stored in memory means
28. The array processor functions in conjunction with the processor 22,
and under programming noted below. Use of an array processor is
advantageous for rapid processing of the three-dimensional image data of
the present system.
Slice data is acquired from the acquisition means A via data acquire
circuitry 30. Images generated from the array processor 22 are
reconstructed by the image reconstruction circuitry 32. A control panel 20
allows for human interaction with the processor 22. Finally, a display
means 34 allows for viewing of a resultant image.
In the preferred embodiment, the array processor 26 is comprised of three
processor elements for facilitating rapid computation. It will be
appreciated, however, that other processing units will function adequately
when images are processed in accordance with the teachings of the present
system.
The processor takes a set of images of consecutive slices of a
three-dimensional object generated by the acquisition means A and produces
spatially encoded slice data indicative of a physical property thereof.
Means is provided for assigning a viewing value to generally all
subregions of at least one of the generally planar slices. This viewing
value is suitably a gray scale level. These images of consecutive slices
are given in a format similar to that of a conventional CT or MRI scanner.
The subject procedure for generating the three-dimensional images renders
such a generation to be particularly adaptable to conventional processors
such as the subject array processor. Three-dimensional objects under
investigation, such as bones or organs, usually extend through many
consecutive cross-sectional image slices. For instance, a set of
cross-sectional CT images would be required for investigation of a lumbar
spine since the spine extends beyond one slice's thickness. To efficiently
extract the three-dimensional object from the slice, a three-dimensional
box which is large enough to encapsulate the three-dimensional object
under investigation is initially selected This three-dimensional box,
called the box of interest ("BOI") which is smaller than a toll volume
represented by a slice set, reduces total information necessary to process
and, therefore, reduces the processing time. The BOI functions to
apportion each image slice into a two-dimensional region thereof. Each
region, referred to as a region of interest ("ROI") is in turn comprised
of a plurality of subregions which are represented by data obtained from
the data acquisition means. The ROI is preferably selected from a single
slice image, and projected or extrapolated onto subsequent slices for
practicality. It will be appreciated, however, that in certain situations
it may be desirable to select an ROI from two or more regions to encompass
a certain volume. For example, a first ROI might be selected having a
first set of dimensions, and a second ROI selected having a second set of
dimensions which are greater or less than the first, with intermediate
slices therebetween being functionally related to the dimensions of the
two dimension sets. For most purposes, however, a single ROI with a given
set of dimensions extrapolated or projected onto subsequent slices is
adequate.
After a region of interest has been defined, an object or boundary of
interest of a subject is selected from therewithin. Again, such object is
suitably selected from a single ROI from a single slice and projected onto
subsequent ROI's of the box of interest. In certain situations, however,
it is appreciated that the boundary of interest may desirably be selected
from two or more of the regions of interest.
Selection of the boundary of interest may be made by manual selection from
a display, such as by placing a cursor on that boundary, or by isolating a
particular boundary with a given gray scale level. In the preferred
embodiment, a combination of both is implemented. The region of interest
is initially generated as a planar image. A selected range of gray scales
is assigned to this region of interest and only those areas falling within
this range are then illuminated. An operator or technician then selects,
through the control panel 20 (FIG. 1) which of the surfaces or boundaries
within this range are to be taken. This is in turn projected onto
subsequent regions of the box of interest.
Turning to FIG. 2, a sample object is illustrated in a box of interest 37
which has in turn been assembled from consecutive slices. The object or
specimen 34 is sectioned in its entirety by two slices. Regions of
interest 36, 38 are selected from each slice. Each region of interest 36,
38 is itself comprised of subregion data 40 which may be referred to as a
picture element or pixel. The pixel is so named due to its use to generate
a subsequent image by assigning a unique viewing value or gray scale level
thereto which is a function of the physical property of that particular
element as gleaned from the slice imaging apparatus.
When the pixels 40 of each region of interest 36, 38 are so placed, a
volume element ("VOXEL") which is indicative of a volume property of the
subject specimen is definable.
In general, an object under investigation must undergo further processing
from the three-dimensional box which encapsulates it. In the present
system, this processing is referenced to as segmentation. Segmentation
consists of multiple computer graphics and image processing techniques
used in unison. These techniques include thresholding, contouring, and
region growing. The segmentation process allows for the image processing
to be completed on a standard processor. In segmentation, once the object
of interest is extracted from the three-dimensional box in the fashion
illustrated above, the object is represented in a concise fashion. In the
present system, the scan line representation technique is implemented. In
this technique, an object is represented by a set of segments which fill
the object volume completely. Each segment is, in turn, represented by its
two end points, the slice number in which the segment belongs, and the row
number of the segment within the slice. Turning particularly to FIG. 2(b),
it will be seen that creation of two such segments has been illustrated.
The segment 46 is created from the endpoints (pixels) 48, 50, while the
segment 56 is created from the endpoints 58, 60.
With reference to FIG. 3, the presently described three-dimensional
reformatting process is capable of generating perspective
three-dimensional images of an object 66 in any given viewing direction.
Each viewing direction is associated with a rectangle or a square viewing
surface such as 68 on which corresponding perspective three-dimensional
images are formed. This rectangle or viewing area is referred to as a
screen for the reason that the generated three-dimensional image is viewed
by displacing it on a two-dimensional viewing area. Such as that continued
in display console 34 (FIG. 1).
A perspective three-dimensional view of a three-dimensional object may be
viewed as being comprised of orthogonal projections to the screen of
points on the surface of the object onto that screen. To provide a depth
queue effect in the viewing of the generated image, the projected points
on the screen are assigned, via a scaling means, with a viewing value such
as a number representing a shade of gray, called a gray level. This
assigned gray level is inversely proportional to a shortest distance from
a corresponding point on the surface of the object along a normal to the
screen. The viewing directions is assumed to be normal to the screen. In
this framework, if two points on a surface of the object project onto the
same point of the screen, only a point closest to the screen is visible.
Moreover, points on the surface of the object which are closer to the
screen are seen painted whiter, and points on the surface which are
further away from the screen are darkened to facilitate a pseudo
three-dimensional picture.
To render the curvature of the surface of the object at a visible point,
the scaling means may alternatively or additionally include means to
assign a corresponding gray level multiplied with a weight which is a
function of a cosine of an angle of the normal to the screen and the
normal to the surface of the object that a particular point in
consideration. For an efficient implementation in terms of computational
time and computer memory, this angle is estimated from the distance of the
surrounding points in the screen to corresponding visible points on the
surface of the object. More precisely, the formula used to assign a gray
level appears below:
g=SCALE*cos.sup.m Maximum(AVERD, CUTOFF)*(K * (d-DMAX)+GMIN) FORMULA (1)
where: g=assigned gray level
d=assigned distance to viewing area
K=(GMAX-GMIN)/(DMIN-DMAX)
DMIN=0.5*DIAG
DMAG=1.5*DIAG
DIAG=the diagonal of the Box Of Interest
AVERD=sum of four numbers, each number being the minimum between MAXA and
the absolute value of the difference between the distances assigned to one
of the four opposite pairs of pixels surrounding the pixel in
consideration
GMAX, GMIN, m, MAXA, CUTOFF, and SCALE are arbitrary values depending on
the desired viewing characteristics; in the preferred embodiment, suitable
values are: GMAX=255, GMIN=-225, m=20, MAXA=25, CUTOFF=0.9919, and
SCALE=1/200
Turning again to FIG. 3, as a surface rendering is carried out by the
processors, rectangular screen 68 is divided into small squares, called
screen pixels. For a good resolution of three-dimensional views of the
object, it is advantageous to consider a screen just large enough to
contain a projection of the object. To achieve this goal, the diagonal of
the box of interest is advantageously chosen to be the side dimension of
the screen.
The magnification factor of the three-dimensional image is suitably
achieved by choosing a screen of smaller size as a number of pixels
subdividing the screen remains constant. For example, 256.times.256 pixels
or 512.times.512 pixels is suitably chosen. The number of pixels of a
screen will be referred to as the screen resolution. A change of
three-dimensional views of the object is suitably realized by changing a
position of the screen, rather than by rotation of an object itself. With
continuing to FIG. 3, such a positioning of the viewing surface 68 is
depicted in relation to the object 66. As noted above, the
three-dimensional object is represented by a set of segments. In such a
representation, a line segment belonging to the object represents a part
thereof. In a case where all slices are parallel to one another, and when
division of a slice into pixels is facilitated by rectangular grids as
illustrated in FIG. 2(c), each segment represents a parallelepiped
containing it. Dimensions of the parallelepiped 90 are as follows:
the length of the line segment 46 l;
the common side of pixels in an axial plane
of the slice w; and
a distance between the slice containing the line segment and the following
slice h.
For practical purposes, it is assumed that the union of all the
parallelepipeds associated with the segments in the object representation
is the three-dimensional object to be displayed. This assumption becomes
more and more accurate as the distance between two consecutive slices is
smaller and the nu | | |
