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Description  |
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BACKGROUND OF THE INVENTION
The present invention relates to stereoscopic display method and apparatus
for calculating a phase distribution from 3-dimensional information of an
object and performing a holographic stereoscopic display and, more
particularly, to stereoscopic display method and apparatus for expressing
an object as a display target by sampling points, thereby calculating a
phase distribution.
In case of obtaining phase information to display a hologram from the
3-dimensional information of an object by a computer, a very large amount
of information must be handled, so that it is hitherto demanded to reduce
a calculation amount.
Conventionally, in computer processes of phase information to display a
hologram from the 3-dimensional information of an object, as shown in FIG.
1, an object or space, which is specified by 3-dimensional information and
is displayed, is divided in a lattice shape at regular intervals and
sampling points shown by dots are set at regular intervals. A phase
distribution is calculated for every microarea of the hologram plane which
expresses the phase distribution while using a set of sampling points as a
display target. In this case, by setting the interval between sampling
points to a limit of the resolution of the human eyes, a solid image can
be displayed without deteriorating picture quality.
When the interval between sampling points of the object which are used in
the phase calculation is uniformly set to the resolution limit of the
human eyes, however, the number of sampling points is extremely large.
Processes for calculating the phase distribution for every sampling point
and adding the calculated phase distributions with respect to all of the
sampling points must be repeated for every microarea of all of the
hologram planes. There is consequently a problem such that the amount of
calculations to obtain the phase information is extremely large and it
takes a long time to calculate the phase information. To reduce the amount
of calculations for the phase information, a method of uniformly reducing
the number of sampling points is also considered. However, this causes a
problem in that the picture quality deteriorates. The resolution of the
human eyes, on the other hand, varies depending on the conditions such as
observation distance, nature of the image, and the like. The use of the
method of uniformly setting the interval between sampling points on the
basis of the highest resolution merely results in an increase in the
amount of calculation, for the phase information than it is needed, so
that such a method is not always preferable.
SUMMARY OF THE INVENTION
According to the present invention, there are provided stereoscopic display
method and apparatus for reducing the number of sampling points to
calculate phase information in a holographic stereoscopic display. First,
the invention has been made on the assumption that it is intended to
provide a stereoscopic display method comprising: a phase calculating step
of calculating a hologram phase distribution; a phase distribution
expressing step of expressing the phase distribution calculated by the
phase calculating step; and a wave front converting step of converting the
phase distribution expressed by the phase distribution expressing step
into a wave front of the light, thereby displaying a solid image. In
addition to the above processing steps, the invention further has: a
feature portion detecting step of detecting a feature portion in a display
target specified by 3-dimensional information; and a sampling point
setting step of setting sampling points at a high density into the feature
portion detected by the feature portion detecting step and setting
sampling points at a low density with respect to a non-feature portion as
a portion other than the feature portion. In the phase calculating step, a
hologram phase distribution is calculated with respect to the sampling
points set by the sampling point setting step.
The feature portion used in the specification is a portion in which a
change in gradation of an image at the edge of an object or in the plane
thereof. With respect to the feature portion, the sampling points are set
at a high density. With respect to the non-feature portion other than the
feature portion, the sampling points are set at a low density. The phase
calculating step comprises: a step of setting a region on a hologram to
calculate the phase distribution of the sampling points of the feature
portion; a step of setting a region on the hologram to calculate the phase
distribution of the sampling points of the non-feature portion so as to be
different from the region in case of the feature portion; and a step of
calculating the phase distribution every region. In this case, it is also
possible to construct in a manner such that a region in which small
regions are discretely arranged on the hologram is set as a region on the
hologram to calculate the phase distribution of the sampling points of the
non-feature portion, thereby making the sampling points in the non-feature
region blur when a hologram is displayed, so that a solid image can be
displayed as a continuous plane although the sampling points are coarse.
According to such stereoscopic display method and apparatus of the
invention as mentioned above, a density of the sampling points in the
feature portion is set to a high value and a density of the sampling
points in the non-feature portion to a low value so as to match with the
effective resolution of the human eyes and the total number of sampling
points is reduced as a whole, so that an amount of calculations for the
phase distribution can be reduced. With respect to the non-feature portion
in which the density of the sampling points is coarse, phase distributions
of the hologram planes are discretely calculated so as to cause a blur in
the reconstructed image due to a diffraction effect, thereby enabling a
continuous plane to be displayed even in case of the coarse sampling
points. Specifically speaking, a portion having a feature such as edge
portion of an object or portion of a high contrast is sampled at a high
resolution, and a smooth portion of a small contrast difference is sampled
at a low resolution. As a sampling method, a display space is divided at
regular angles around the visual point of the observer, thereby sampling
so as to set a coarse resolution as the object is far from the observer.
Further, a portion which is seen as a dark portion for the human eyes is
not sampled. By setting those sampling points, the calculation amount of
the phase information can be reduced without substantially deteriorating
the picture quality.
The above and other objects, features, and advantages of the present
invention will become more apparent from the following detailed
description with reference to the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is an explanatory diagram showing the conventional setting of
uniform sampling points;
FIG. 2 is a block constructional diagram showing an embodiment of the
invention;
FIG. 3 is a flowchart showing a procedure of a stereoscopic display method
of the invention;
FIG. 4 is an explanatory diagram of a method of separately setting sampling
points with respect to a feature portion and a non-feature portion
according to the invention;
FIG. 5 is an explanatory diagram of a method of setting sampling points by
an angle dividing method of the invention;
FIG. 6 is an explanatory diagram of a practical method of setting sampling
points of the invention;
FIG. 7 is a flowchart showing the details of a feature extracting process
in FIG. 2;
FIGS. 8A and 8B are explanatory diagrams of Laplacian operators which are
used in the extraction of a feature of a 2-dimensional image;
FIG. 9 is an explanatory diagram of Laplacian operators which are used in
the feature extraction of a 3-dimensional pixel image;
FIGS. 10A and 10B are explanatory diagrams of the feature extraction by
3-dimensional Laplacian operators;
FIG. 11 is an explanatory diagram of a display target before extracting a
feature;
FIG. 12 is an explanatory diagram of a display target whose feature was
extracted;
FIG. 13 is an explanatory diagram showing a specific example of the setting
of sampling points according to the invention based on the feature
extraction;
FIG. 14 is an explanatory diagram of a blur of an image due to a
diffraction of a hologram;
FIG. 15 is an explanatory diagram showing an angle and a positional
relation in FIG. 14;
FIGS. 16A, 16B and 16C are explanatory diagrams showing diffraction
intensity distributions due to a plurality of dot images;
FIG. 17 is an explanatory diagram showing the formation of a discrete phase
distribution to make a reconstructed image blur at a point set in a
non-feature portion of the invention;
FIGS. 18A and 18B are explanatory diagrams of a method of eliminating a
dark portion as sampling points;
FIG. 19 is an explanatory diagram of the phase distribution calculation
according to the invention; and
FIGS. 20A and 20B are explanatory diagrams in case of applying the
invention to a holographic stereogram to calculate a phase distribution on
the basis of a 2-dimensional image.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 2 shows an embodiment of a stereoscopic display apparatus of the
invention. The stereoscopic display apparatus of the invention has a
3-dimensional information forming section 10 using a CAD system or the
like. Information of an object to be stereoscopically displayed is
inputted from the 3-dimensional information forming section 10. The
information of the display target from the 3-dimensional information
forming section 10 is given to a feature extracting section 12. The
information of the display target, which need to be sampled at a
relatively high resolution, are extracted as a feature portion and the
other points are extracted as a non-feature portion. The feature portion
of the display target extracted by the feature extracting section 12 is
given to a feature sampling point setting section 14 and sampling points
are set at a high resolution. After completion of the setting of the
sampling points to the feature portion, a phase calculating region at a
hologram plane is set by a phase calculating region setting section 18. On
the other hand, the non-feature portion extracted by the feature
extracting section 12 is given to a non-feature sampling point setting
section 20. Sampling points are set at a low resolution. In a low
luminance region eliminating section 22, further, a portion which is dark
when it is seen by the human eyes is eliminated from the region in which
sampling points are set. The sampling points set in the non-feature
portion are finally given to a phase calculating region, setting section
24. A phase calculating region at the hologram plane by the sampling
points set in the non-feature portion, is set.
After the phase calculating regions of the feature portion and non-feature
portion were respectively set by the phase calculating region setting
sections 18 and 24, a phase distribution is calculated by a phase
distribution calculating section 26. Namely, phase distributions are
calculated every predetermined microregion of the hologram plane with
respect to all of the sampling points as a target. A phase distribution is
subsequently obtained by adding the results of the calculations of the
phase distributions of all of the sampling points. Such a process is
executed with respect to all of the microregions of the hologram plane.
After the phase distributions at the hologram plane were calculated by the
phase distribution calculating section 26, in a phase distribution display
section 28, the calculated phase distributions are expressed by a display
device such as a liquid crystal display or the like provided at the
position of the hologram plane. In this state, by irradiating a
reproduction light to the display device and by converting the
reproduction light into the wave front by the expressed phase
distribution, a solid image is displayed.
A flowchart of FIG. 3 shows a processing routine as a stereoscopic display
method of the invention and corresponds to a processing procedure of the
apparatus construction shown in FIG. 2. First, in step S1, 3-dimensional
information as a display target is inputted. In step S2, a feature portion
is extracted. In step S3, sampling points are set with respect to the
extracted feature portion. The details of the setting of the sampling
points in the feature portion will be clearly explained hereinlater. In
step S4, phase calculating regions at the hologram plane based on the
sampling points set in the feature portion are set. In step S5, sampling
points are set with respect to the non-feature portion. The setting of the
sampling points of the non-feature portion will be also clearly explained
hereinafter. After the sampling points of the non-feature portion were
set, the sampling points of a low luminance portion are eliminated in step
S6. In step S7, phase calculating regions at the hologram plane based on
the sampling points set in the non-feature portion are set. In the setting
of the phase calculating regions corresponding to the sampling points of
the non-feature portion, for example, they are discretely set on the
hologram plane in a checkerwise manner. By the setting of such discrete
phase calculating regions, the sampling points of the non-feature portion
in the case where the phase distribution is expressed and is converted
into the wave front are made blur, thereby enabling a continuity of the
plane to be displayed even when the interval between the sampling points
is widened. In step S8, on the basis of the setting of the phase
calculating regions of the feature portion in step S4 and the setting of
the phase calculating regions of the non-feature portion in step S7, the
phase calculation is executed with respect to all of the microregions
while setting each of the microregions on the hologram plane based on each
sampling point into one unit. In step S9, the result of the calculation of
the phase distribution calculated in step S8 is read out from, for
example, a memory or the like and displayed on a display apparatus such as
a liquid crystal device or the like. A reference light is irradiated to
the expressed phase distribution, thereby enabling a solid image to be
displayed.
FIG. 4 shows the principle for separately setting sampling points at two
different kinds of regular intervals with respect to the feature portion
and the non-feature portion for a 3-dimensional display target in the
invention. A solid body is now used as a display target 30. The display
target 30 is divided into a feature portion and a non-feature portion. As
a feature portion of the target object 30, there is an edge portion or a
portion of a high contrast. As a non-feature portion, there is a portion
of a small contrast. Namely, when an attention is paid to the angular
resolution of the human eyes, for example, the human eyes have an angular
resolution of about 1.degree. in case of an eyesight of 1.0. In the
ordinary life, an angle resolution of about 2.degree. is sufficient. When
the human being sees a moving object, it is said that the human gaze
traces a pattern such that an outline or density of an object suddenly
changes or the like. Namely, when a moving object is reproduced, it is
necessary to reproduce the moving object at a high resolution with respect
to a portion of a reproduction image, which the human gaze traces. This
means, however, that a high resolution is not always necessary with
respect to the other portions.
When a 3-dimensional image is reproduced, a portion which needs a high
resolution is defined as a feature portion and the other portion is
defined as a non-feature portion from a viewpoint of the angular
resolution of the human eyes. The edge portion or the portion of a high
contrast of the display target 30 shown in FIG. 4 are included in the
feature portion. The portion of a small contrast is included in the
non-feature portion. Therefore, with respect to the edge as a feature
portion of the display target 30, sampling points are set at fine
intervals. With respect to the other non-feature portion, sampling points
are set at coarse intervals.
As a rule in the setting of the sampling points in the invention, an angle
dividing method shown in FIG. 5 is used. According to the angle dividing
method, sampling points are set on the lines divided by a predetermined
angle around a visual point 32 of the observer. Therefore, the sampling
points are arranged at fine intervals at a plane 34 near the eyes 32 of
the observer.
The interval between the sampling points at a plane 36 that is far from the
observer increases as the positions of the sampling points are far from
the plane 36. Namely, the near plane 34 is sampled at a high resolution.
The remote plane 36 is sampled at a low resolution. It is now assumed that
as shown in FIG. 4 a distance from the visual point 32 of the observer to
a surface 38 of the display target 30 is equal to R, for example, an
interval L.sub.1 between sampling points P.sub.11 and P.sub.12 in an edge
40 as a feature portion is decided as follows.
##EQU1##
On the other hand, an interval L.sub.2 between sampling points P.sub.21 and
P.sub.22 on the plane 38 as a non-feature portion which are adjacent to
the sampling points P.sub.11 and P.sub.12 of the edge 40 is decided as
follows.
##EQU2##
As will be obviously understood from the equations (1) and (2), according
to the invention, with respect to the feature portion, the sampling points
are set at the interval which are determined by the equation (1). With
respect to the non-feature portion, the sampling points are set at the
interval which is half of the above interval as shown in the equation (2).
By setting the sampling points such that the feature portion is set to the
high resolution and the non-feature portion is set to a low resolution as
mentioned above, the number of sampling points can be reduced as a whole
and an amount of calculations of the phase distributions which are
executed with respect to the hologram plane on the basis of the sampling
points can be reduced.
FIG. 6 shows a method of setting sampling points for a more specific
display target according to the invention. A hologram display surface 42
is set in a proper display space. The hologram display surface 42 can be
realized by expressing the phase distribution calculated by using, for
example, a liquid crystal device or the like. As will be obviously
understood from the equations (1) and (2), the interval between the
sampling points is proportional to the distance R from the visual point of
the observer 32 to the display object. Namely, as the observer 32 is at a
distance that is close to the display object, fine sampling points must be
set. However, when the observer is excessively close to the display
object, it is hard to see the solid image. Therefore, the observer
generally observes the display object from a remote distance of about 300
mm. Such a distance is called a least distance of distinguished vision at
which the display object can be clearly seen.
Reference numerals 46 and 48 in FIG. 6 denote regions in which a solid
image can be stereoscopically displayed by the hologram display surface
42. The distance R, however, from the observer 32 to the display object is
variable and cannot be unconditionally decided. When the observer 32
observes the display object, accordingly, the observation region is
divided into the region 46 in which the least distance of distinguished
vision can be assured and the region 48 in which the display object is
seen from a position where the observer is away from the display object by
at least the least distance of distinguished vision or more. Since the
observer 32 cannot put the visual point to a position which exceeds the
hologram display surface 42, the region 48 is a region that is away from
the object by the least distance of distinguished vision or more in the
case where the eyes come into contact with the hologram display surface 42
and the object is seen in this state. In the case where the region is
divided into the regions 46 and 48 as mentioned above, with respect to the
region 46, for instance, the distance R is set to a fixed value of (R=300
mm). With respect to the feature portion and the non-feature portion, the
intervals L.sub.1 and L.sub.2 between the sampling points are set in
accordance with the following equations.
L.sub.1 =(1/2).times.300.times.tan {(1/60).degree.}=0.044 [mm]
L.sub.2 =(1/2).times.300.times.tan {(1/30).degree.}=0.087 [mm]
where, R=300 [mm] (constant)
With respect to the dotted region 48 which cannot be distinguished by the
observer, when it is now assumed that the distance from the hologram
display surface is set to R', the intervals L.sub.1 and L.sub.2 between
the sampling points are set in accordance with the following equations.
L.sub.1 =(1/2)R'.times.tan{(1/60).degree.}=1.5.times.10.sup.-4 R' [mm]
L.sub.2 =(1/2)R'.times.tan{(1/30).degree.}=2.9.times.10.sup.-4 R' [mm]
where, R'>300 [mm]
Namely, with respect to the region 48, the interval between the sampling
points is set at a resolution that is inversely proportional to the
distance R' from the hologram display surface 42. An extracting process of
a feature portion according to the invention in a display object for
setting sampling points by different resolutions will now be described in
detail.
A flowchart of FIG. 7 shows the details of the feature portion extracting
process shown in step S2 in FIG. 3. The 3-dimensional data inputted as a
display target is used as a target and luminance data is first formed
every pixel in step S201. The luminance data is constructed by luminance
information and 3-dimensional coordinate information. In step S202, a
difference operator which is known as a reference mask for detection of a
difference is set. In step S203, an overlap calculation of the operator
and the luminance data, namely, the product sum calculation is executed in
a state in which the difference operators have been defined while setting
each of the 3-dimensional pixel data as a target pixel. In step S204, a
comparing process to discriminate whether the value obtained by the
overlap calculation is equal to or larger than a predetermined threshold
value or not. In step S205, the portion having the overlap position
exceeding the threshold value is produced as feature portion data.
FIGS. 8A and 8B show operators as reference masks which are used in the
quadratic differential operation (Laplacian operation) as an example of
the edge extracting process of a 2-dimensional image. The Laplacian
operator in FIGS. 8A and 8B is constructed by (3.times.3) mask patterns
and the quadratic differential operations are executed in two directions
of X and Y axes. Namely, "-2" is set into the central reference image
setting position per one direction, so that "-4" is set for two
directions. FIG. 8B shows the Laplacian operator which is used in the
quadratic differential operations in eight directions in which the
directions of 45.degree. are further added. Since "-2" is set per one
direction, "-8" is set into the setting portion of the central target
pixel.
According to the invention, since a feature extraction is performed for the
3-dimensional luminance data as a target, for example, a 3-dimensional
Laplacian operator 50 as shown in FIG. 9 is prepared on the basis of the
Laplacian operators in the 2-dimensional image as shown in FIGS. 8A and
8B. That is, in case of a solid image, since the luminance data is
ordinarily expressed in a form of pixel, "-26" is set into the central
pixel to be set into the target pixel of the target 3-dimensional data
constructed by (3.times.3.times.3=27) pixels as shown in FIG. 10A. "1" is
set into the other pixels. The value of -26 of the central pixel is a
value to execute the quadratic differential operations with respect to 13
directions comprising the directions of the 3-dimensional coordinates and
the directions of 45.degree..
FIG. 11 shows the display target 30 which is used to extract a feature. A
light/dark pattern 52 of a larger luminance change than that of the
peripheral portion, for example, is displayed on one of the surfaces of
the display target 30. When the feature extraction is executed by using
the 3-dimensional Laplacian operator 50 with regard to the 3-dimensional
luminance data of the display target shown in FIG. 11, the edges of the
display object 30 and the region of the light/dark pattern 52 can be
extracted as a feature portion as shown in FIG. 12.
FIG. 13 shows an example of the setting of sampling points in the feature
portion, and non-feature portion, which were detected by the feature
extracting process by using the 3-dimensional Laplacian operator. Each dot
on the display target 30 indicates the sampling point. As shown in the
diagram on the left side of a left upper corner 54, in the edge portion
detected as a feature portion, sampling points are set at the fine
interval L.sub.1, and in the flat plane portion excluding the edge
portion, sampling points are coarsely set at the interval L.sub.2 which is
twice as large as the interval L.sub.1. In the edge detection by the
Laplacian operator, a slight width occurs in the edge portion, so that the
sampling points are finely set in the edge portion and a portion near it.
In case of FIG. 12, sampling points are set at the fine interval L.sub.1
with respect to the edge and one line adjacent to the edge.
As mentioned above, with respect to the feature portion of the display
target, points are arranged at the resolution limit of the human eyes in
the reproducing mode, so that such sampling points are seen as a contour
in case of the edge and sampling points are seen as points at which a
boundary line is continuous in case of the light and dark portion. With
respect to the points which are displayed as a non-feature portion,
however, since its resolution is equal to or less than the resolution
limit of the human eyes, there is a possibility such that those points are
seen as discrete points in the reproduction of an image. According to the
invention, however, with respect to the reproduction points of the
non-feature portion, they are seen on the continuous plane by using a blur
of a hologram image.
As shown in FIG. 14, in case of trying to reproduce the points by a
hologram 56 having an opening width D, a blur of the image appears due to
a diffraction limit. An extent x of the blur is expressed by
x=2.lambda.R/D (3)
Namely, the blur extent x is determined by the opening D of the hologram
56, the distance R to the reproduction image, and the wavelength .lambda.
of the reproduction light. As shown in FIG. 15, it is now assumed that it
is intended to reconstruct an image by a plane 58 locating at the position
of the distance R from the visual point 32 and the points P.sub.1 and
P.sub.2 of a pitch interval d. The interval d between the points P.sub.1
and P.sub.2 is expressed as follows by using an angle 8 from the visual
point 32.
d=2Rtan(.theta./2).div.R.theta. (4)
On the other hand, an intensity distribution function F by the diffraction
is expressed as follows as shown in FIG. 16(A). Theref | | |
