Method for auto-stereoscopic image display with a wavelength filter array
View Patent ↗A method of spatial visualization in which several views are decomposed into bits of partial information, which are made optically visible by image rendering elements. Neighboring image rendering elements emit light of different wavelengths or wavelength ranges. Propagation directions for the light are given by wavelength filters such that an observer will see predominantly bits of partial information of a first selection of views with one eye and predominantly bits of partial information of a second selection with the other eye. At least one image rendering element is simultaneously allocated bits of partial information from at least two different views. The allocation is made in such a way that the wavelength of the partial information is always equal to the wavelength, or lies in the wavelength range, of the light emitted by the allocated image rendering element.
1. A method of spatial visualization of a scene or an object on the basis of several views (A c ) of the scene or object, in which
the views (A c ) are decomposed, on matrices (R c ) with columns (k) and rows (l), into many bits of partial information (a ckl ) characterized by their wavelengths, with c=1, . . . ,n, where (n) designates the total number of views,
the bits of partial information (a ckl ) are displayed in optically visible form by image rendering elements (α ij ) arranged in a matrix of columns (i) and rows (j),
making neighboring image rendering elements (α ij ) emit light of different wavelengths (λ) or of different wavelength ranges (Δλ),
propagation directions for the emitted light are defined by an array of many individual wavelength filters (β pq ) arranged in columns (p) and rows (q), which are transparent to different wavelengths (λ) or different wavelength ranges (Δλ) and which are arranged in front of or behind the matrix of image rendering elements (α ij ), so that every one image rendering element (α ij ) corresponds with several allocated wavelength filters (β pq ) or every one wavelength filter (β pq ) corresponds with several allocated image rendering elements (α ij ) in such a way that each straight line connecting the centroid of the cross-section area of a visible segment of the image rendering element (α ij ) and the centroid of the cross-section area of a visible segment of the wavelength filter (β pq ) corresponds to a propagation direction, so that an observer from every viewing position will see predominantly bits of partial information from a first selection of views (A c ) with one eye, and predominantly bits of partial information from a second selection of views (A c ) with the other eye, wherein
at least one image rendering element (α ij ) is allocated bits of partial information (a ckl ) from at least two different views (A c ) simultaneously,
this allocation being made in such a way that the wavelength of the partial information (a ckl ) always equals the wavelength (λ), or lies in the wavelength range (Δλ), of the light emitted by the allocated image rendering element (α ij ).
2. The method as set forth in claim 1 , in which
the bits of partial information (a ckl ) are allocated to the image rendering elements (α ij ) according to the rule
α
i
j
=
∑
c
∑
k
∑
l
a
c
k
1
·
g
c
k
l
i
j
where
(g) is a fifth-order tensor, the elements (g cklij ) of which are real numbers and act as weighting factors that determine the weight of the respective partial information (a ckl ) in an image rendering element (α ij ).
3. The method as set forth in claim 1 , in which
the index k is equaled to i and the index l is equaled to j,
the bits of partial information (a ckl ) are allocated to the image rendering elements (α ij ) according to the rule
α
i
j
=
∑
c
a
c
i
j
g
c
i
j
(
d
f
)
by which procedure
each image rendering element (α ij ) is allocated bits of partial information (a cij ) from identical positions (i, j) only in the matrices (R c ) of the views (A c ), and in which
(d f ) is a density factor, which can adopt real numbers as values and which states the number of views from which bits of partial information (a cij ) are, on average, allocated to one image rendering element (α ij ), with the weighted sum of the bits of partial information (a cij ) allocated to each image rendering element (α ij ) being normalized at 1.
4. The method as set forth in claim 3 , in which the weighting factors (g cij ) are established by the rule
d
f
·
g
cij
=
δ
(
(
Rnd
[
(
i
+
j
-
1
)
·
d
f
]
-
1
)
mod
n
+
1
-
c
)
·
[
Frac
(
(
i
+
j
-
1
)
·
d
f
)
·
δ
(
δ
(
Frac
[
(
i
+
j
-
1
)
·
d
f
]
)
)
+
δ
(
Frac
[
(
i
+
j
-
1
)
·
d
f
]
)
]
+
δ
(
(
Rnd
[
(
i
+
j
-
2
)
·
d
f
]
-
1
+
δ
(
Frac
[
(
i
+
j
-
2
)
·
d
f
]
)
)
mod
n
+
1
-
c
)
·
[
1
-
Frac
[
(
i
+
j
-
2
)
·
d
f
]
]
+
∑
i
-
Rnd
[
(
i
+
j
-
2
)
·
d
f
]
+
δ
(
Frac
[
(
i
+
j
-
2
)
·
d
f
]
)
+
1
Rnd
[
(
i
+
j
-
1
)
·
d
f
]
-
1
δ
(
[
t
-
1
]
mod
n
+
1
-
c
)
in which
the density factor (d f ) is equal for all image rendering elements (α ij ) and adopts a value greater than 1,
δ(x) is a function that satisfies the conditions δ(x=0)=1 and δ(x≠0)=0,
Rnd(x) is a function that, for arguments x≧0, supplies the next higher integer as a function value if the part of the arguments (x) after the decimal point is not equal to zero, and otherwise supplies the argument (x) itself,
“mod” designates the residual class relative to a divisor,
Frac(x) is a function that, for arguments x≧0, supplies the part of the argument (x) after the decimal point as a function value, and
(t) is an integer, and the sum is assigned the value “zero” if the upper summation limit is smaller than the lower summation limit.
5. The method as set forth in claim 1 in which the density factor (d f ) is established according to the rule
d f =f
and (f) is a positive real number determined according to the rule
f
=
d
a
z
+
d
a
in which
(z) is the distance between the matrix of image rendering elements (α ij ) and the array of wavelength filters (β pq ), and
(d a ) is a selectable viewing distance, which essentially corresponds to the mean of all distances, possible throughout the viewing space, between the matrix of image rendering elements (α ij ) and an observer or a viewing position.
6. The method as set forth in claim 3 , in which
the weighting factors are established according to the rule
g
cij
∑
t
=
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
δ
(
[
i
+
j
+
t
-
1
+
Int
(
n
2
)
]
mod
n
+
1
-
c
)
·
{
1
d
f
(
i
,
j
)
δ
[
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
-
t
]
·
Frac
(
d
f
(
i
,
j
)
-
1
2
)
+
1
d
f
(
i
,
j
)
δ
[
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
+
t
]
·
Frac
(
d
f
(
i
,
j
)
-
1
2
)
+
1
d
f
(
i
,
j
)
δ
(
δ
[
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
-
t
]
+
δ
[
Rnd
(
d
f
(
i
,
j
)
-
1
2
)
+
t
]
)
}
in which
the density factor (d f ) depends on the position (i, j) in the matrix of the image rendering elements (α ij ).
7. The method as set forth in claim 6 , in which the density factor (d f ) is described by the function
d
f
=
ⅇ
[
-
(
ⅈ
+
j
-
Int
[
i
+
j
n
]
-
n
n
+
1
2
)
2
]
c
peak
+
d
f
offset
in which
c peak is a selectable, real and positive parameter,
d f offset is a selectable, real and positive parameter, which causes a shift of the function values towards higher values, and
the function Int(x), supplies, as a function value, the greatest integer that does not exceed the argument (x).
8. A Method of spatial visualization of a scene or an object on the basis of several views (A c ) of the scene or object, comprising the steps of
decomposing the views (A c ), on matrices (R c ) with columns (k) and rows (l), into many bits of partial information (a ckl ) characterized by their wavelengths, with c=1, . . . ,n, where (n) designates the total number of views,
displaying the bits of partial information (a ckl ) in optically visible form by image rendering elements (α ij ) arranged in a matrix of columns (i) and rows (j),
such that neighboring image rendering elements (α ij ) emit light of different wavelengths (λ) or of different wavelength ranges (Δλ),
defining propagation directions for the emitted light by lenticulars,
wherein
at least one image rendering element (α ij ) is allocated bits of partial information (a ckl ) from at least two different views (A c ) simultaneously,
this allocation being made in such a way that the wavelength of the partial information (a ckl ) always equals the wavelength (λ), or lies in the wavelength range (Δλ), of the light emitted by the allocated image rendering element (α ij ).
9. The method of spatial visualization of a scene or an object on the basis of several monochrome views (A c ) of the scene or object, comprising the steps of
decomposing the views (A c ) on matrices (R c ) with columns (k) and rows (l), into many bits of partial information (a ckl ), with c=1, . . . ,n, where (n) designates the total number of views,
displaying the bits of partial information (a ckl ) in optically visible form by image rendering elements (α ij ) arranged in a matrix of columns (i) and rows (j),
making all image rendering elements (α ij ) emit light of the same wavelengths (λ) or of the same wavelength ranges (Δλ),
defining propagation directions for the emitted light by one or several arrays of many individual wavelength filters (β pq ) arranged in columns (p) and rows (q), which are transparent to different wavelengths (λ) or different wavelength ranges (Δλ) and which are arranged in front of or behind the matrix of image rendering elements (α ij ), so that every one image rendering element (α ij ) corresponds with several allocated wavelength filters (β pq ) or every one wavelength filter (β pq ) corresponds with several allocated image rendering elements (α ij ) in such a way that each straight line connecting the centroid of the cross-section area of a visible segment of the image rendering element (α ij ) and the centroid of the cross-section area of a visible segment of the wavelength filter (β pq ) corresponds to a propagation direction, so that an observer from every viewing position will see predominantly bits of partial information from a first selection of views (A c ) with one eye, and predominantly bits of partial information from a second selection of views (A c ) with the other eye, wherein
at least one image rendering element (α ij ) is allocated bits of partial information (a ckl ) from at least two different views (A c ) simultaneously.
10. The method as set forth in claim 4 , wherein the density factor (d f ) is equal for all image rendering elements (α ij ) and adopts a value between 1.3 and 2.0.
11. The method as set forth in claim 8 , in which
the index k is equaled to i and the index l is equaled to j,
the bits of partial information (a ckl ) are allocated to the image rendering elements (α ij ) according to the rule
α
i
j
=
∑
c
a
c
i
j
g
c
i
j
(
d
f
)
and in which
the weighting factors are established according to the rule
g
cij
=
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
inv
(
Frac
(
e
ya
)
)
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
e
ya
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
inv
(
Frac
(
e
ye
)
)
·
(
Frac
(
e
ye
)
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
e
ye
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
inv
(
Frac
(
e
ye
)
)
·
(
Frac
(
e
ye
)
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
r
ye
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
inv
(
Frac
(
e
ya
)
)
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
e
ya
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
q
k
)
)
)
+
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
ye
)
)
·
Frac
(
e
ye
)
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
e
ye
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
q
k
)
)
)
+
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
ya
)
)
·
Frac
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
e
ya
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
q
k
)
)
)
where e xa , e xe , e ya and e ye are auxiliary variables that apply to the relations
e xa =i·d fx +offset ex
e xe =( i+ 1)· d fx +offset ex
e ya =j·d fy +offset ey
e ye =( j+ 1)· d fy +offset ey
and, a sum is assigned the value of zero if the upper summation limit is smaller than the lower summation limit.
12. The method as set forth in claim 9 , in which
the index k is equaled to i and the index l is equaled to j,
the bits of partial information (a ckl ) are allocated to the image rendering elements (α ij ) according to the rule
α
i
j
=
∑
c
a
c
i
j
g
c
i
j
(
d
f
)
and in which
the weighting factors are established according to the rule
g
cij
=
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
inv
(
Frac
(
e
ya
)
)
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
e
ya
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
inv
(
Frac
(
e
ye
)
)
·
(
Frac
(
e
ye
)
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
e
ye
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
inv
(
Frac
(
e
ye
)
)
·
(
Rnd
(
e
ya
)
)
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
e
ye
)
)
)
+
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
inv
(
Frac
(
e
ya
)
)
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
e
ya
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
1
d
fx
·
d
fy
δ
inv
(
Frac
(
e
xa
)
)
·
(
Rnd
(
e
xa
)
-
e
xa
)
·
δ
(
c
-
EZ
(
Int
(
e
xa
)
,
Int
(
q
k
)
)
)
+
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
ye
)
)
·
Frac
(
e
ye
)
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
e
ye
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
xe
)
)
·
Frac
(
e
xe
)
·
δ
(
c
-
EZ
(
Int
(
e
xe
)
,
Int
(
q
k
)
)
)
+
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
inv
(
Frac
(
e
ya
)
)
·
Frac
·
(
Rnd
(
e
ya
)
-
e
ya
)
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
e
ya
)
)
)
+
∑
q
k
=
Rnd
(
e
ya
)
Int
(
e
ye
-
1
)
∑
p
k
=
Rnd
(
e
xa
)
Int
(
e
xe
-
1
)
1
d
fx
·
d
fy
·
δ
(
c
-
EZ
(
Int
(
p
k
)
,
Int
(
q
k
)
)
)
wherein e xa , e xe , e ya and e ye are auxiliary variables that apply to the relations
e xa =i·d fx +offset ex
e xe =( i+ 1)· d fx +offset ex
e ya =j·d fy +offset ey
e ye =( j+ 1)· d fy +offset ey
and, a sum is assigned the value of zero if the upper summation limit is smaller than the lower summation limit.