US7901093B2  Modeling light transport in complex display systems  Google Patents
Modeling light transport in complex display systems Download PDFInfo
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 US7901093B2 US7901093B2 US11/623,016 US62301607A US7901093B2 US 7901093 B2 US7901093 B2 US 7901093B2 US 62301607 A US62301607 A US 62301607A US 7901093 B2 US7901093 B2 US 7901093B2
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Abstract
Description
Rcptr′=T Rprjct′
where T is called the light transport matrix. It is to be understood that since each projection pixel j results in a light ray that is scattered across the entire image sensor array 29 of real camera 25, each sensor pixel i within the image sensor array 29 will have a differently valued light transport coefficient for each projection pixel j. Therefore, each projection pixel j will result in a column of (m×n) individual light transport coefficients, one for each sensor pixel i of the camera's image sensor array 29. Since there are (p×q) projection pixels j in real projector 21, light transport matrix T will have (p×q) columns [one for each projection pixel j] and (m×n) rows [one for each sensor pixel i] of individual light transport coefficients. Thus, light transport matrix T will necessarily be huge, consisting of (p×q×m×n) individual light transport coefficient values.
Vcptr″=T^{T }Vprjct″
Remarkably, the duality transformation between the real light transport matrix, T, and its dual light transport matrix, T^{T}, is the transpose matrix operation known in the art of matrix computation.
Rcptr′=T Rprjct′
is exactly the j^{th }column of matrix T. It is to be understood that since the resolution of real projector 21 is likely to be lower than the resolution of real camera 25, the single light beam emitted from the j^{th }projection pixel under test may fall across several sensor pixels i of image sensor array 29.
[i.e. S1⊂{1, . . . , (p×q)}]
maps to a corresponding set of columns (one per projection pixel) in light transport matrix T. Furthermore, it is assumed that the first set of projection pixels S1 includes target projection pixel j, i.e. the target pixel under test.
[i.e. S1∩S2={j}]
Let Rcptr_S2 be a second image captured by real camera 25 of a projected image created by the simultaneous activation of the second set of projection pixels S2. The light transport coefficients of the j^{th }column of light transport matrix T (which corresponds to the target projection pixel under test, i.e. correspondents to j) may be directly obtain from real captured images Rcptr_S1 and Rcptr_S2 by identifying the one light ray footprint (i.e. similar to light ray footprint 50 in
Tj≈MIN(Rcptr_S1, Rcptr_S2)
where Tj is the j^{th }column of matrix T, and “MIN” indicates that the lower valued sensor pixel (i.e. the darker pixel having a lower captured light intensity value) in Rcptr_S1 and Rcptr_S2 is retained, and the higher valued (i.e. brighter) sensor pixel is discarded. In this way, the only high intensity values that are retained correspond to a lit footprint common to both S1 and S2.
[i.e. L⊂{1, . . . , (m×n)}]
common to captured image Rcptr_S1 and Rcptr_S2 that corresponds to the target projector pixel, j. It should again be noted that the target projection pixel, j, is the intersection of projection pixel sets S1 and S2, (i.e. j is the only projection pixel common to both sets S1 and S2), such that
S1∩S2={j}
Therefore, among the captured image pixels (in both Rcptr_S1 and Rcptur_S2) that do not correspond to the target projection pixel, j, [i.e. those sensor pixels not in set L, i.e. ∉L], at least one of the compared, captured sensor pixels in either Rcptr_S1 or Rcptr_S2 will not have received light. Since sensor pixels receiving light will be brighter than sensor pixels not receiving light, the operation MIN(Rcptr_S1, Rcptr_S2), provides an image where only pixels in set L [i.e. ∈L] are lit, which is a good approximation of Tj, i.e. the j^{th }column in matrix T.
Rprjct_Sy_{—}1, . . . , Rprjct_Sy_q and Rprjct_Sx_{—}1, . . . , Rprjct_Sx_p
where each image Rprjct_Sy_1, . . . , Rprjct_Sy_q is paired with any of images Rprjct_Sx_1, . . . , Rprjct_Sx_p such that each set of paired images shares only one projection pixel in common, such that
∀j ∈{1, . . . , (p×q)}∃Rprjct_{—} Sy _{—} a, Rprjct_{—} Sx _{—} b Rprjct_{—} Sy _{—} a∩Rprjct_{—} Sx _{—} b={j}
The above formula being interpreted to mean that for all projection pixels j in {1 . . . (p×q)} there exist a pair of projection images, each having a differently constructed pattern such that the intersection of the constructed patterns intersect at a single point corresponding to a common projection pixel. A basic example of such pairs of constructed patterns would be projected pairs of vertical light beams and horizontal light beams. In this case, the intersection of a captured image of a vertical line and a captured image of a horizontal line would include all the sensor pixels i that correspond to a target projection pixel, j, (i.e. pixels i that lie within a light ray footprint created by a light ray emitted from projection pixel j).
Vcptr″=T^{T }Vprjct″
Since the virtual image sensor array 27″ in the virtual camera 21″ corresponds in actuality to real imaging projection array 27 of real projector 21, it is convenient to use the same index j to denote any virtual sensor pixel within Vcptr″ obtained by virtual camera 21″. Therefore, a relationship between each virtual projection pixel j in a virtual captured image versus a corresponding row of elements in T^{T }may be denoted as
Vcptr″(j)=T ^{T} _{j }Vprjct″
where T^{T} _{j }refers to the j^{th }row in T^{T}.
SVcptr″(G)={a∀z ∈{1, . . . , (p×q)}T _{COL} _{ — } G(a)≧T T _{COL} _{ — } z (a)}
Since in general ∥SVcptr″(G)∥<<(p×q), it takes significantly less time to compute:
than to compute:
Vcptr″(j)=T ^{T} _{j }Vprjct″
Up=λHUc
where λ is a scalar and H is the 3×3 homography transformation matrix (as known in the art) of which the bottom right entry is set to 1. The pair of corresponding coordinates provide 3 linear equations, where one of them determines the scalar and the other two are used to determine H, the homography transformation matrix. Since there are 8 unknown entries in 3×3 matrix H, given the correspondence of between N coordinate points (where N≧4) on the checker board, the homography between the projectorview image and the camera image can be recovered by solving the 2N linear equations. The greater the number of N, the lower the error relating coordinate points between the projectorview and the camera image.
AI=IA=IA
If matrix A were a matrix of order m by n, then the premultiplicative identify matrix I would be of order m by m, while the postmultiplicative identify matrix I would be of order n by n.
{hacek over (T)}r=Tr/(∥Tr∥)^{2} , r=1, 2, 3, . . . , pq
where {hacek over (T)}r is the r^{th }column of {hacek over (T)}. Since the operation ∥Tr∥ defines the square root of the sum of the squares of all values in column r of matrix T, the square of ∥Tr∥ is simply the sum of the squares of all the values in column r. That is,
By dividing each value entry in column r by the sum of the squares of all the values entries in column r, operation {Tr/(∥Tr∥)^{2}} has the effect of normalizing the value entries in column r of matrix T. If one now takes the transpose of {hacek over (T)}r, i.e. flips it on its side such that the first column becomes the top row and the last column becomes the bottom row, the result will be rows of elements that are the normalized values of corresponding columns of elements in T. Therefore, for every column in T, one has the following result:
({hacek over (T)}r ^{T})×(Tr)=1
and
({hacek over (T)}r ^{T})×(Tg)=0, for r≠g
In other words, multiplying a column of T with a corresponding row in {hacek over (T)}r^{T }always results in numeral 1, and as one multiplies all the columns in T with the corresponding row in {hacek over (T)}r^{T}, one produces a matrix with numeral 1's along its diagonal, and one may place zeroes everywhere else.
c_{1}=T_{1}p_{1 }
and
c_{2}=T_{2}p_{2 }
In order to simulate projected image p_{1 }from front projector P1 using immersive projector P2, one needs c_{1 }(i.e. the captured, projected image from front projector P1) to be the same as c_{2 }(i.e. the captured, projected image from immersive projector P2), i.e. one needs
c_{2}=c_{1 }
which lead to the relation:
T_{2}p_{2}=T_{1}p_{1 }
solving for p_{2}, one obtains the following relation:
p_{2}=(T_{2} ^{−1})(T_{1}p_{1})
c_{3}=T_{3}p_{3 }
which results in
p _{3}=(T _{3} ^{−1})×(c _{3})
Consequently, one can build a virtual model of display surfaces of room 111. The virtually modeled room 111″, shown in
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