Content-adaptive parallax barriers for automultiscopic display
In exemplary implementations of this invention, two LCD screens display a multi-view 3D image that has both horizontal and vertical parallax, and that does not require a viewer to wear any special glasses. Each pixel in the LCDs can take on any value: the pixel can be opaque, transparent, or any shade between. For regions of the image that are adjacent to a step function (e.g., a depth discontinuity) and not adjacent to a sharp corner, the screens display local parallax barriers comprising many small slits. The barriers and the slits tend to be oriented perpendicular to the local angular gradient of the target light field. In some implementations, the display is optimized to seek to minimize the Euclidian distance between the desired light field and the actual light field that is produced. Weighted, non-negative matrix factorization (NMF) is used for this optimization.
1. A method for producing an actual 4D light field that approximates a target 4D light field, wherein:
(a) a pair of spatial light modulators is backlit by an incoherent light source;
(b) the pair comprises a rear modulator that displays a rear mask and front modulator that displays a front mask;
(c) a contiguous area in each of the rear and front masks, respectively, corresponds to a region of the target 4D light field that is adjacent to a depth discontinuity;
(d) in that area, the target 4D light field has an angular gradient;
(e) in that area, a parallax barrier is displayed, which parallax barrier comprises a set of more than ten slits, a majority of the slits having an orientation within 15 degrees of perpendicular to the angular gradient;
(f) the front and rear masks produce the actual 4D light field, which actual 4D light field comprises a multi-view automultiscopic display with full motion parallax;
(g) the rear and front modulators display the rear and front masks, respectively, at a frame rate that exceeds 10 Hz; and
(h) light field factorization {tilde over (L)}=FG is calculated by one or more processors,
where
argmin
F
,
G
1
2
L
-
FG
W
2
,
for
F
,
G
≥
0
,
where the reconstruction error is given by:
1
2
L
-
FG
W
2
=
∑
ijkl
[
W
∘
(
L
-
FG
)
∘
(
L
-
FG
)
]
ijkl
.
and where
◯ denotes a Hadamard product for element-wise multiplication of matrices,
w is the weight of a weighting matrix W,
F and G are N i ×T and T×N k matrices, respectively,
Column t of F and row t of G are the rear and front masks displayed during frame t, respectively,
discrete pixel indices of the rear mask are denoted as (i,j) and discrete pixel indices of the front mask are denoted as (k,l), and
the target light field L, when discretized, is given by L[i,j,k,l].
2. The method of claim 1 , wherein initial estimates {F,G} are iteratively refined as follows.
F
←
F
∘
[
(
W
∘
L
)
G
T
]
[
(
W
∘
(
FG
)
)
G
T
]
G
←
G
∘
[
F
T
(
W
∘
L
)
]
[
F
T
(
W
∘
(
FG
)
)
]
,
.
3. The method of claim 1 , wherein the automultiscopic display has a field of view, and the field of view is adapted to one or more viewers by specifying elements of the weight matrix W.
4. A method comprising, in combination:
(a) displaying 2D rear masks at a frame rate of at least 10 Hz; and
(b) displaying 2D front masks at a frame rate of at least 10 Hz;
wherein
(i) the rear masks are displayed by a rear spatial light modulator.
(ii) the front masks are displayed by a front spatial light modulator,
(iii) incoherent light from a backlight passes first through the rear modulator and then through the front modulator,
(iv) a majority of pixels in the front masks are not limited to binary opacities,
(v) for each frame, the rear and front masks are jointly optimized by using non-negative matrix factorization to approximately calculate a solution that minimizes the Euclidian distance between a 4D light field that is actually produced and a target 4D light that is sought to be produced,
(vi) a contiguous area in each of the rear and front masks, respectively, corresponds to a region of the target 4D light field that is adjacent to a depth discontinuity,
(vii) in that area, the target 4D light field has an angular gradient, and
(viii) in that area, a parallax barrier is displayed, which parallax barrier comprises a set of more than 20 slits, a majority of the slits having an orientation within 10 degrees of perpendicular to the angular gradient, and
(ix) light field factorization {tilde over (L)}=FG is calculated by one or more processors, where
argmin
F
,
G
1
2
L
-
FG
W
2
,
for
F
,
G
≥
0
,
where the reconstruction error is given by a reconstruction error formula, as follows:
1
2
L
-
FG
W
2
=
∑
ijkl
[
W
∘
(
L
-
FG
)
∘
(
L
-
FG
)
]
ijkl
.
and where
◯ denotes a Hadamard product for element-wise multiplication of matrices,
w is the weight of a weighting matrix W,
{tilde over (L)} can be decomposed as a matrix product, {tilde over (L)}=FG,
F and G are N i ×T and T×N k matrices, respectively,
Column t of F and row t of G are the rear and front masks displayed during frame t, respectively,
discrete pixel indices of the rear mask are denoted as (i,j) and discrete pixel indices of the front mask are denoted as (k,l), and
the target light field L, when discretized, is given by L[i,j,k,l].
5. The method of claim 4 , wherein initial estimates {F,G} are iteratively refined as follows.
F
←
F
∘
[
(
W
∘
L
)
G
T
]
[
(
W
∘
(
FG
)
)
G
T
]
G
←
G
∘
[
F
T
(
W
∘
L
)
]
[
F
T
(
W
∘
(
FG
)
)
]
,
.
6. The method of claim 4 , wherein the automultiscopic display has a field of view, and the field of view can be adapted to one or more viewers by specifying elements of the weight matrix W.