Patent Application
20080024683
In the following Detailed Description, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. In this regard, directional terminology, such as “top,” “bottom,” “front,” “back,” etc., may be used with reference to the orientation of the Figure(s) being described. Because components of embodiments of the present invention can be positioned in a number of different orientations, the directional terminology is used for purposes of illustration and is in no way limiting. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following Detailed Description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.
In one embodiment, image display system 100 includes image frame buffer 104, sub-frame generator 108, projectors 112A-112C (collectively referred to as projectors 112), camera 122, and calibration unit 124. Image frame buffer 104 receives and buffers image data 102 to create image frames 106. Sub-frame generator 108 processes image frames 106 to define corresponding image sub-frames 110A-110C (collectively referred to as sub-frames 110). In one embodiment, for each image frame 106, sub-frame generator 108 generates one sub-frame 110A for projector 112A, one sub-frame 110B for projector 112B, and one sub-frame 110C for projector 112C. The sub-frames 110A-110C are received by projectors 112A-112C, respectively, and stored in image frame buffers 113A-113C (collectively referred to as image frame buffers 113), respectively. Projectors 112A-112C project the sub-frames 110A-110C, respectively, onto target surface 116 to produce displayed image 114 for viewing by a user.
Image frame buffer 104 includes memory for storing image data 102 for one or more image frames 106. Thus, image frame buffer 104 constitutes a database of one or more image frames 106. Image frame buffers 113 also include memory for storing sub-frames 110. Examples of image frame buffers 104 and 113 include non-volatile memory (e.g., a hard disk drive or other persistent storage device) and may include volatile memory (e.g., random access memory (RAM)).
Sub-frame generator 108 receives and processes image frames 106 to define a plurality of image sub-frames 110. Sub-frame generator 108 generates sub-frames 110 based on image data in image frames 106. In one embodiment, sub-frame generator 108 generates image sub-frames 110 with a resolution that matches the resolution of projectors 112, which is less than the resolution of image frames 106 in one embodiment. Sub-frames 110 each include a plurality of columns and a plurality of rows of individual pixels representing a subset of an image frame 106.
Projectors 112 receive image sub-frames 110 from sub-frame generator 108 and, in one embodiment, simultaneously project the image sub-frames 110 onto target 116 at overlapping and spatially offset positions to produce displayed image 114. In one embodiment, display system 100 is configured to give the appearance to the human eye of high-resolution displayed images 114 by displaying overlapping and spatially shifted lower-resolution sub-frames 110 from multiple projectors 112. In one form of the invention, the projection of overlapping and spatially shifted sub-frames 110 gives the appearance of enhanced resolution (i.e., higher resolution than the sub-frames 110 themselves).
A problem of sub-frame generation, which is addressed by embodiments of the present invention, is to determine appropriate values for the sub-frames 110 so that the displayed image 114 produced by the projected sub-frames 110 is as close in appearance as possible as to how the high-resolution image frame (e.g., image frame 106) from which sub-frames 110 are derived would appear if displayed directly.
Projector tone curves generally vary from projector to projector. In conventional multi-projector tiled systems, the luminance (L) response of the individual projectors is generally adjusted so as to achieve an image that is seamless in appearance. To achieve this seamless appearance, the luminance responses of the projectors are generally downwardly adjusted to match the luminance response of the weakest projector(s). As such, the minimum luminance (LMIN) provided by each of the projectors is adjusted to equal the LMIN value of the projector having the highest LMIN value, and the maximum luminance (LMAX) provided by each of the projectors is adjusted to equal the LMAX value of the projector having the lowest LMAX value. In other words, with conventional multi-projector tiled systems, the luminance range provided by each of the projectors is adjusted so as to substantially equal the worst combination of the group of multiple projectors. As such, although conventional multi-projector tiled systems increase the resolution of a projected image by increasing the number of pixels employed to display the image, image brightness is sacrificed because the full brightness range of the projectors is not utilized.
In contrast, with a superimposed projector system according to one embodiment of the present invention, the brightness of the desired image ranges from a minimum luminance value (LMIN), which is substantially equal to the sum of the minimum luminance values provided by each of the projects, to a maximum luminance value (LMAX), which is substantially equal to the sum of the maximum luminance values provided by each of the projectors. As such, a superimposed projector system according to one embodiment of the present invention can render a desired image using substantially the full brightness range of the projectors.
In addition to varying between projectors, the luminance response of a single projector is typically non-linear in response to varying gray level inputs. Also, the luminance response of a given projector to a single gray level may vary spatially across the projected image. If these luminance variances are not accounted for, the superimposed multiple projector display system may not be able to utilize the full luminance range when projecting a desired image.
As such, in one embodiment, as will be described in greater detail below, the present invention provides a system and method that accounts for luminance variations between the multiple superimposed projectors when generating sub-frame values for each of the component projectors. By generating sub-frame values in this fashion, an image display system in accordance with one embodiment of the present invention, such as image display system 100, is able to utilize substantially the full combined brightness range of the multiple projectors when displaying a desired image. In one embodiment, the present invention provides algorithms to account for variations in the luminance of a projected image from multiple superimposed projectors.
Additionally, the bit-depth of images projected by conventional multi-projector tiled systems is generally limited to the bit depth of the individual component projectors. For example, a tiled system having two M-bit projectors is generally able to project 2M unique levels. As such, two 8-bit projectors are able to project 256 unique levels.
As will be described in greater detail below, by dithering the sub-frames differently for each of the component projectors as described herein, such as by employing jointly designed dither arrays for each of the component projectors, an overlapping projection system in accordance with one embodiment of the present invention is able to project a maximum number of unique intensity levels which is substantially equal to a sum of the unique intensity levels capable of being projected by each of the component projectors. For example, an overlapping projection system in accordance with one embodiment of the present invention employing two M-bit projectors is able to project up to 2(2M)−1 bits (e.g. two superimposed 8-bit projectors are able to project up to 511 unique levels). Additionally, as mentioned above and described in greater detail below, an overlapping projection system in accordance with one embodiment of the present invention accounts for luminance variations between component projectors and individual spatial luminance variations of each component projector.
It will be understood by a person of ordinary skill in the art that functions performed by sub-frame generator 108 may be implemented in hardware, software, firmware, or any combination thereof. The implementation may be via a microprocessor, programmable logic device, or state machine. Components of the present invention may reside in software on one or more computer-readable mediums. The term computer-readable medium as used herein is defined to include any kind of memory, volatile or non-volatile, such as floppy disks, hard disks, CD-ROMs, flash memory, read-only memory, and random access memory.
Also shown in
In one embodiment, display system 100 includes a camera 122 and a calibration unit 124, which are used in one form of the invention to automatically determine a geometric mapping between each projector 112 and the reference projector 118, as described in further detail below with reference to
In one form of the invention, image display system 100 includes hardware, software, firmware, or a combination of these. In one embodiment, one or more components of image display system 100 are included in a computer, computer server, or other microprocessor-based system capable of performing a sequence of logic operations. In addition, processing can be distributed throughout the system with individual portions being implemented in separate system components, such as in a networked or multiple computing unit environment.
In one embodiment, display system 100 uses two projectors 112.
In one embodiment, as illustrated in
As illustrated in
In one form of the invention, sub-frames 110 have a lower resolution than image frames 106. Thus, sub-frames 110 are also referred to herein as low-resolution images or sub-frames 110, and image frames 106 are also referred to herein as high-resolution images or frames 106. It will be understood by persons of ordinary skill in the art that the terms low resolution and high resolution are used herein in a comparative fashion, and are not limited to any particular minimum or maximum number of pixels.
In one form of the invention, display system 100 produces a superimposed projected output that takes advantage of natural pixel misregistration to provide a displayed image 114 with a higher resolution than the individual sub-frames 110. In one embodiment, image formation due to multiple overlapped projectors 112 is modeled using a signal processing model. Optimal sub-frames 110 for each of the component projectors 112 are estimated by sub-frame generator 108 based on the model, such that the resulting image predicted by the signal processing model is as close as possible to the desired high-resolution image to be projected.
In one embodiment, sub-frame generator 108 is configured to generate sub-frames 110 based on the maximization of a probability that, given a desired high resolution image, a simulated high-resolution image that is a function of the sub-frame values, is the same as the given, desired high-resolution image. If the generated sub-frames 110 are optimal, the simulated high-resolution image will be as close as possible to the desired high-resolution image. The generation of optimal sub-frames 110 based on a simulated high-resolution image and a desired high-resolution image is described in further detail below with reference to
In one embodiment, process 230 proceeds directly to 245. Alternatively, in one embodiment, process 230 proceeds to 242 and 244, as described below. At 242, a simulated high-resolution image frame is formed based on the low resolution sub-frames of each of the projectors. In one embodiment, formation of the simulated high-resolution image frame includes applying a luminance profile of each projector to the corresponding low-resolution sub-frame. A description of one embodiment for determining luminance profiles for each projector is described in greater detail below with respect to
At 244, the low-resolution sub-frames of the projectors are iteratively updated based on an error between the high-resolution image frame and the simulated high-resolution image frame until a desired convergence condition is satisfied. In one embodiment, the convergence condition comprises a predetermined number of iterations. In one embodiment, the convergence condition comprises substantially minimizing the error between the high-resolution and the simulated high-resolution image frames. The iterative process of generating the low-resolution sub-frames is described in greater detail below with respect to
At 245, a dither array, or dither mask, is determined for each projector (e.g. projectors 112A-112C) of the multi-projector display system (e.g. multi-projector display system 100 of
At 246, the dither array (see 320 Tk of
For each additional high-resolution image frame 106, 238 through 248 are repeated to form a corresponding projected image 114 on the target surface 116. If no additional high-resolution images are to be projected, process 230 is complete, as illustrated at 250. It is noted that the determination of the luminance profile and the dither array for each component projector, as described above at 242 and 245, need only be performed once for each projector. In one embodiment, this initial determination may be performed at manufacture. In one embodiment, the luminance profile and the dither array of each component projector may be adjusted or re-calibrated after the initial determination.
As indicated at 254, in one embodiment, the processes of 245, 246, and 248 are together described as dithering the intensity levels of each low-resolution sub-frame to one of the unique intensity levels of the associated projector differently for each projector to form a dithered low-resolution sub-frame such that the dithered low-resolution sub-frames, when simultaneously projected in an overlapping fashion, form a projected image representative of the high resolution image and having a maximum number of unique projection levels substantially equal to a sum of the maximum number of unique intensity levels of all projectors of the multi-projector display system.
Two of the sixteen pixels of the sub-frame 110 shown in
Rk=HkDTYk Equation I
The low-resolution sub-frame pixel data (Yk) is expanded with the up-sampling matrix (DT) so that the sub-frames 110 (Yk) can be represented on a high-resolution grid. The interpolating filter (Hk) fills in the missing pixel data produced by up-sampling. In the embodiment shown in
Relative geometric distortion between the projected component sub-frames 110 is due to the different optical paths and locations of the component projectors 112. A geometric transformation is modeled with the operator, Fk, which maps coordinates in the frame buffer 113 of the kth projector 112 to the frame buffer 120 of the reference projector 118 (
In one embodiment, the geometric mapping (Fk) is a floating-point mapping, but the destinations in the mapping are on an integer grid in image 304 (Rkref). Thus, it is possible for multiple pixels in image 302 (Rk) to be mapped to the same pixel location in image 304 (Rkref), resulting in missing pixels in image 304 (Rkref). To avoid this situation, in one form of the present invention, during the forward mapping (Fk), the inverse mapping (Fk−1) is also utilized as indicated at 305 in
In another embodiment of the invention, the forward geometric mapping or warp (Fk) is implemented directly, and the inverse mapping (Fk−1) is not used. In one form of this embodiment, a scatter operation is performed to eliminate missing pixels. That is, when a pixel in image 302 (Rk) is mapped to a floating point location in image 304 (Rkref), some of the image data for the pixel is essentially scattered to multiple pixels neighboring the floating point location in image 304 (Rkref). Thus, each pixel in image 304 (Rkref) may receive contributions from multiple pixels in image 302 (Rk), and each pixel in image 304 (Rkref) is normalized based on the number of contributions it receives.
A relative luminance profile, Lk, models the linearized spatial luminance response of the kth component projector 112 relative to the combined luminance response of all component projectors 112. The determination of relative luminance profile Lk is described in greater detail below with respect to
A superposition/summation of the weighted-warped images 305 (Rkwgt) of each the component projectors 112 forms a hypothetical or simulated high-resolution image 306 (X-hat) in the reference projector frame buffer 120, as represented in the following Equation II:
{circumflex over (X)}=ΣLkFkRk Equation II
In one embodiment, as illustrated by the dashed line in
If the simulated high-resolution image 306 (X-hat) in the reference projector frame buffer 120 is identical to the given (desired) high-resolution image 308 (X), the system of component low-resolution projectors 112 would be equivalent to a hypothetical high-resolution projector placed at the same location as the reference projector 118 and sharing its optical path. In one embodiment, the desired high-resolution images 308 are the high-resolution image frames 106 (
In one embodiment, if the simulated high-resolution image 306 (X-hat) in the reference projector frame buffer 120 deviates too far from the desired high-resolution image 308 (X), the sub-frames 110 (Yk) are updated iteratively according to the following Equation III:
Y
k
(N+1)
=Y
k
(n)
+αDH
k
T
F
k
T
L
k
T
{X−{circumflex over (X)}} Equation III:
In this fashion, the sub-frame 110 (Yk) for each component projector 112 is iteratively adjusted based on each projector's relative contribution to the simulated high-resolution image 306 (X-hat).
In one embodiment, the data of sub-frames 110 (Yk) for each component projector 112 is iteratively adjusted (such as described above with respect to Equation III or as described in greater detail below) until optimal sub-frame data (Yk*) for each of the sub-frames 110 (Yk) is determined which results in simulated high-resolution image 306 (X-hat) being substantially equal to desired high-resolution image 308 (X). The iteratively adjusted sub-frames comprising the optimal sub-frame data (Yk*) for each component projector 112 are illustrated in
According to one embodiment of the present invention, once determined, the optimal sub-frame data (Yk*) for each of the optimal sub-frames 310 (Ykopt) is adjusted on a pixel-by-pixel basis by the corresponding dither array 320 (Tk), as indicated by operator 322, to generate a dithered sub-frame 324 (Ykdth) for each component projector 112. Example embodiments of processes for determining dither arrays 320 (Tk) are described below and illustrated by
The dithered sub-frames 324 (Ykdth) are then provided to the component projectors 112 for projection. However, because the luminance values of the dithered sub-frames 324 (Ykdth) of each of the component projectors 112 comprise linearized relative values, the values cannot be input directly to the corresponding projector for projection and are gamma-corrected prior to providing the data values to the corresponding component projector 112 for projection. By employing an appropriately designed dither array 320 (Tk) for each of the corresponding component projectors 112, the bit-depth of overlapped projection system 100 is increased.
In one embodiment, the deviation of the simulated high-resolution image 306 (X-hat) from the desired high-resolution image 308 (X) is modeled as shown in the following Equation IV:
X={circumflex over (X)}+η Equation IV
As shown in Equation IV, the desired high-resolution image 308 (X) is defined as the simulated high-resolution image 306 (X-hat) plus η, which in one embodiment represents zero mean white Gaussian noise.
The solution for the optimal sub-frame data (Yk*) for the sub-frames 110 is formulated as the optimization given in the following Equation V:
Thus, as indicated by Equation V, the goal of the optimization is to determine the sub-frame values (Yk) that maximize the probability of X-hat given X. Given a desired high-resolution image 308 (X) to be projected, sub-frame generator 108 (
Using Bayes rule, the probability P(X-hat|X) in Equation V can be written as shown in the following Equation VI:
The term P(X) in Equation VI is a known constant. If X-hat is given, then, referring to Equation IV, X depends only on the noise term, η, which is Gaussian. Thus, the term P(X|X-hat) in Equation V will have a Gaussian form as shown in the following Equation VII:
To provide a solution that is robust to minor calibration errors and noise, a “smoothness” requirement is imposed on X-hat. In other words, it is assumed that good simulated images 306 have certain properties. The smoothness requirement according to one embodiment is expressed in terms of a desired Gaussian prior probability distribution for X-hat given by the following Equation VIII:
In another embodiment of the invention, the smoothness requirement is based on a prior Laplacian model, and is expressed in terms of a probability distribution for X-hat given by the following Equation IX:
The following discussion assumes that the probability distribution given in Equation VIII, rather than Equation IX, is being used. As will be understood by persons of ordinary skill in the art, a similar procedure would be followed if Equation IX were used. Inserting the probability distributions from Equations VII and VIII into Equation VI, and inserting the result into Equation V, results in a maximization problem involving the product of two probability distributions (note that the probability P(X) is a known constant and goes away in the calculation). By taking the negative logarithm, the exponents go away, the product of the two probability distributions becomes a sum of two probability distributions, and the maximization problem given in Equation V is transformed into a function minimization problem, as shown in the following Equation X:
The function minimization problem given in Equation X is solved by substituting the definition of X-hat from Equation II into Equation X and taking the derivative with respect to Yk, which results in an iterative algorithm given by the following Equation XI:
Y
k
(N+1)
=Y
k
(n)
−Θ{DH
k
T
F
k
T|({circumflex over (X)}(n)=X)+β2∇2{circumflex over (X)}(n)|} Equation XI
Equation XI may be intuitively understood as an iterative process of computing an error in the reference projector 118 coordinate system and projecting it back onto the sub-frame data. In one embodiment, sub-frame generator 108 (
To begin the iterative algorithm defined in Equation XI, an initial guess, Yk(O), for the sub-frames 110 is determined.
The initial guess, Yk(0), for sub-frames 110 is determined from high-resolution frame 308 (X). In one embodiment, the initial guess for the sub-frames 110 is determined by texture mapping the desired high-resolution frame 308 onto the sub-frames 110. In one form of the invention, the initial guess is determined from the following Equation XII:
Y
k
(0)
=DB
k
F
k
T
X Equation XII
Thus, as indicated by Equation XII, the initial guess (Yk(0)) is determined by performing a geometric transformation (FkT) on the desired high-resolution frame 308 (X), and filtering (Bk) and down-sampling (D) the result. The particular combination of neighboring pixels from the desired high-resolution frame 308 that are used in generating the initial guess (Yk(0)) will depend on the selected filter kernel for the interpolation filter (Bk).
In another form of the invention, as illustrated by
Y
k
(0)
=DF
k
T
X Equation XIII
Equation XIII is the same as Equation XII, except that the interpolation filter (Bk) is not used.
Several techniques are available to determine the geometric mapping (Fk) between each projector 112 and the reference projector 118, including manually establishing the mappings, or using camera 122 and calibration unit 124 (
F
2
=T
2
T
1
−1 Equation XIV
In one embodiment, the geometric mappings (Fk) are determined once by calibration unit 124, and provided to sub-frame generator 108. In another embodiment, calibration unit 124 continually determines (e.g., once per frame 106) the geometric mappings (Fk), and continually provides updated values for the mappings to sub-frame generator 108.
At 334, an inverse of the luminance curve determined above at 332 is applied to a series of input values to generate a series of pre-corrected input values. The series of pre-corrected input values are applied to the selected projector such that the selected projector functions as a linearized light projection device. The luminance output of the selected projector in response to the series of pre-corrected input values is captured with a digital camera or other suitable image capturing device. Based on the image data values captured by the camera at each of the pre-corrected input values, the gamma curve of the camera is determined.
In one embodiment, the luminance curve of each of the component projectors 112 is determined and each projector is employed to project a same series of pre-corrected data values. The corresponding luminance values captured by the camera are then integrated to determine the gamma curve (at 334) of the camera to thereby reduce potential effects resulting from noise.
At 336, data values representative of a selected gray level are applied to and projected by a first component projector 112 of the imaging system 100. At 338, the projected output of the component projector 112 in response to the selected gray level input is captured by the camera. The gamma curve of the camera, as determined at 334, is applied to the captured luminance values to linearize the captured luminance values.
Process 330 proceeds to 340 where the linearized luminance values are “warped” to the high-resolution grid, which is also referred to herein as projector space. Generally, the resolution of the camera does not match the resolution of the high-resolution image which is desired to be projected, with the number of pixels of the image captured by the camera generally being less than the number of pixels of the desired high resolution image. As such, at 340, an up-sampling matrix, an interpolating filter, and a geometric mapping (similar to Fk, Hk, and DT described above by Equations I and II with respect to formation of images Rk and Rref) are applied to the output data captured by the camera to expand and map (commonly referred to as “warping”) the captured image to the high-resolution grid and generate an absolute linear luminance profile (Lk′) for the component projector 112. Alternatively, a texture mapping method, as is well-known in the art, can be employed to map the output data captured by the camera from the coordinate system of the camera to the coordinate system of the desired high resolution image.
At 342, process 330 queries whether the projector whose absolute linear luminance profile L′k was just determined at 340 is the final component projector 112 of image display system 100. If the answer to the query is “no”, process 330 returns to 336 and repeats 336 through 340 to determine the absolute linear luminance profile L′k of the next component projector 112 of image display system 100.
If the answer to the query at 342 is “yes”, process 330 proceeds to 344 where the absolute linear luminance profile, Lk, of each of the component projectors 112 are normalized across space to determine the relative luminance profile (Lk) for each component projector 112. The relative luminance profile, Lk, for each projector is employed as described above with respect to
In one embodiment of process 330, in lieu of warping the output data captured by the camera “up to” the high-resolution grid at 340, the absolute linear luminance profile, Lk′, for each component projector 112 is formed by warping the output data captured by the camera “down to” the low-resolution sub-frame coordinate system. The absolute linear luminance profiles, Lk′, are then normalized at 344 such that the relative luminance profile, Lk, for each component projector 112 is with respect to the low-resolution sub-frame coordinate system in lieu of the high-resolution grid. In such an embodiment, with reference to
In one embodiment, as illustrated at 346, process 330 adjusts the luminance values captured by the camera at 338 to compensate for any spatial variance that may exist in the camera's image sensor. Similar to the spatial variance described above with respect to component projectors 112, there may also be a spatial variance across the camera's image sensor. In one embodiment, to determine the camera's spatial variance, a known “flat-field” luminance field is provided and captured with the camera. The luminance values captured by the camera in response to the known flat-field are then linearized using the camera's gamma curve, as determined at 334 above, to determine an absolute linear spatial variance (VC) of the camera. At 346, an inverse of the absolute linear spatial variance (VC−1) of the camera is applied to the linearized luminance values determined at 338 to adjust for any spatial variance contributions of the camera. These adjusted linearized luminance values are then “warped” to a desired reference grid or coordinate system as described at 340.
In one embodiment of the present invention, as illustrated by
At least a portion of projected light from each of the component projectors 112 results from ambient light contributions, which is in addition to light projected in response to received image data. As such, due to ambient light, a certain amount of light will be projected by each component projector 112 of image display system 100 even when in an “off” state. During operation, such ambient light contributions can affect the quality of the projected image.
As such, in one embodiment of the present invention, a process similar to that for determining the relative luminance profile, Lk, for each component projector 112 as described above with respect to
In one embodiment, with respect to
The image formation process for modeling sub-frames 110 (Zk) is similar to that for generating sub-frames Yk as described above with respect to
In a fashion similar to that described above by Equation II, a summation of the warped images 404 (Rref) of each of the component projectors 112 forms a hypothetical or simulated-high resolution image 406 (X-hat). However, unlike Equation II and the image formation process of
If the simulated high-resolution image 406 (X-hat) in the reference projector frame buffer 120 is identical to the given (desired) high-resolution image 408 (X), the system of component low-resolution projectors 112 would be equivalent to a hypothetical high-resolution projector placed at the same location, as the reference projector 118 and sharing its optical path. In one embodiment, the desired high-resolution images 408 are the high-resolution image frames 106 (
In one embodiment, if the simulated high-resolution image 406 (X-hat) in the reference projector frame buffer 120 deviates too far from the desired high-resolution image 408 (X), an iterative process (similar to that described above by Equation III) is employed to determine values for sub-frames 110 (Zk) which will form desired high-resolution image 408(X). In one embodiment, this iterative process is represented by the following Equation XV:
Z
k
(n+1)
=Z
k
(n)
+αDH
k
T
F
k
T
{X−{circumflex over (X)}} Equation XV:
Since the values of the sub-frames Zk of each of the component projectors 112 comprise linearized absolute luminance values, sub-frames Zk cannot be directly provided to the corresponding projector for projection. As such, when the simulated high-resolution image 406 (X-hat) is determined to be substantially equal to the desired high-resolution image 408 (X), the values of sub-frames Zk are translated or mapped to provide data values for projection by the corresponding component projector 112 based on the projector's luminance curve (i.e. gamma curve). In one embodiment, this mapping or translation is represented by the following Equation XVI:
Z
k
′=P
k
−1
Z
k Equation XVI
In one embodiment, the operator Pk−1 is based on the gamma curve, and on an absolute linear luminance profile corresponding to the kth projector, similar to the luminance curve and absolute linear luminance profile Lk as described respectively at 332 and 344 by process 330 of
To begin the image formation process described above by
Based on the gamma value, sub-frame generator 108 performs a de-gamma operation (γ−1) to form the desired high-resolution frame 407 (X″) with pixels having linearized data values. The linearized data values of frame 407 (X″) are mapped to absolute linear luminance values within the full luminance range of the component projectors 112 (from ΣLMIN to ΣLMAX, as described above) to form a desired high-resolution image frame 408 (X).
In one embodiment, the linearized data values of each pixel of frame 407 (X″) are mapped with respect to a full luminance range of each pixel of the projector system. In one embodiment, the linearized data values of each pixel of frame 407 (X″) are mapped with respect to a full luminance range of all pixels of the projector system such that the relative “brightness” of the pixels with respect to one another remains the same. In one embodiment, in a fashion similar to that described above with regard to the process of
The initial guess, Zk(0), for sub-frames 110 is determined from desired high-resolution frame 408 (X). In one embodiment, the initial guess for the sub-frames 110 is determined by texture mapping the desired high-resolution frame 408 onto the sub-frames 110. In one form of the invention, the initial guess is determined in a fashion similar to the described above by Equation XII. In one embodiment, the initial guess is determined in a fashion similar to that described above by Equation XIII.
Techniques for determining dither arrays (Tk) for component projectors 112 of overlapped image display system 100 are described below with respect to
One dithering technique, sometimes referred to as an “ordered” dithering, employs a dither array or matrix composed of dither values corresponding to the unique levels of the display device and which are arranged in a particular pattern (e.g. Hilbert pattern). A pixel level of an image to be displayed is compared to a dither level at a corresponding position in the dither array and the pixel level is adjusted or “dithered” to one of the unique available projection levels based on the comparison. Each pixel is compared to only one value in the dither array. If the size of the image to be displayed is greater than the size of the dither array, some methods “tile” the smaller dither array across the image so as to dither the entire image.
As an example, consider an image having 512 gray levels (i.e. a 9-bit image having unique levels ranging from 0 to 511) to be displayed by a display device, such as a projector, capable of providing 256 unique levels (i.e. an 8-bit device). In one instance, the 256 unique levels of the projector are assigned to those of the image such that the projector provides 256 unique levels ranging between 0 and 512 (e.g. 0, 2, 4, . . . , 510). The upper and lower bounds of each of the 512 image levels are determined based on the number of unique levels available from the projector. For example, a pixel having a level of 5 has lower and upper bounds of 4 and 6 with respect to the 256 unique projection levels. A dither array having 256 values corresponding to the unique levels of the projector (e.g. 0, 2, 4, . . . , 510) is employed to select between the upper and lower bounds for each pixel of the image. As an example, if a pixel has a value of “295” and a dither value at the corresponding position in the dither array is “200”, the upper bound (i.e. “296”) is selected as the pixel's “dithered” value. However, if the dither value at the corresponding position in the dither array is “300” rather than “200”, the lower bound (i.e. “294”) is selected as the pixel's dithered value.
With regard to the overlapping or superimposed multi-projector image display system of one embodiment of the present invention, such as image display system 100 of
As such, by employing jointly designed dither arrays for each of the component projectors of an overlapping projection system in accordance with one embodiment of the present invention, the bit-depth of the projection system can be increased. For example, a multi-projector system employing two M-bit projectors is able to project up to 2(2M)−1 unique levels. For instance, two superimposed 8-bit projectors are able to project up to 511 unique levels.
A dither array 502 (Tk) for a selected one of the component projectors 112 (e.g. component projector 112A) is applied to the corresponding optimal low-resolution sub-frames 310 (Ykopt), as indicated by an operator 503, to generate a dithered low-resolution sub-frame 504 (Ykdth) for the selected component projector. In one embodiment, as described above, dither array 502 (Tk) includes dither or threshold values corresponding to each of the unique levels which can be displayed by the selected one of the component projectors, with the dither values being arranged in a desired pattern. In one embodiment, the desired pattern is initially a random pattern, with the desired pattern subsequently being iteratively updated as described in greater detail below. With regard to process 500, applying dither array 502 (Tk) to the corresponding low-resolution sub-frames 310 (Ykopt) includes comparing each value of low-resolution sub-frame 310 (Ykopt) to a corresponding value in dither array 502 (Tk) in a fashion similar to the “ordered” dithering process described above.
In one embodiment, where the selected component projector is an M-bit projector, dither array 502 (Tk) includes 2M unique dither values. In one embodiment, the size of dither array 502 (Tk) matches the size of the corresponding optimal low-resolution sub-frames 310 (Ykopt) and includes multiple entries of each of the dither values. For example, where the optimal low-resolution sub-frame 310 (Ykopt) is a 1024×768 frame and the selected component projector is an 8-bit projector (i.e. 256 unique levels), dither array 502 (Tk) is a 1024×768 array and includes 3,072 dither entries for each of the 256 unique dither values (e.g. 0, 1, 2, . . . , 255), which are arranged in a desired pattern. In one embodiment, dither array 502 (Tk) is smaller in size and is “tiled” across optimal low-resolution sub-frame 310 (Ykopt).
An image formation model, such as the image formation model of
Generation of up-sampled image 301, high-resolution image 302 (Rk), warped image 304 (Rkref), and weighted-warped image 305 (Rkwgt) are performed in a fashion similar to that described above with respect to
In one embodiment, as illustrated, dithered high-resolution frame 506 (X-hatdth) is compared to simulated high-resolution image frame 306 (X-hat) which is generated using optimal low-resolution sub-frames 310′ (Ykopt) for each component projector 112, including the selected component projector. When the dithered low-resolution sub-frame 504 (Ykdth) of the selected component projector is optimized, the dithered high-resolution frame 506 (X-hatdth) formed by dithered low-resolution sub-frame 504 (Ykdth) of the selected projector and the optimal low-resolution sub-frames 310 (Ykopt) of the remaining component projectors will be as close as desired (e.g. within an acceptable error) to simulated high-resolution image frame 306 (X-hat). Various error metrics may be employed to determine how close dithered high-resolution frame 506 (X-hatdth) is to simulated high-resolution image frame 306 (X-hat), such as, for example, mean square error and weighted mean square error techniques.
In one embodiment, similar to that described above with respect to simulated high-resolution image frame 306 (X-hat) and desired high-resolution image frame 308 (X), if dithered high-resolution frame 506 (X-hatdth) deviates too far from simulated high-resolution image frame 306 (X-hat), the pattern of dither or threshold values of dither array 502 (Tk) is iteratively adjusted based on the determined error until an optimal dither array 502 (Tk) is determined that results in dithered high-resolution frame 506 (X-hatdth) being as close as possible to simulated high-resolution image frame 306 (X-hat) (see 320 (Tk) of
Various techniques may be employed to efficiently adjust the pattern of dither or threshold values of dither array 502 (Tk), such as, for example, swap and toggle techniques. One example of a mean-preserving dither matrix is described by the following publications: R. Ulichney, “Method of Increasing Apparent Amplitude Resolution and Correcting Luminance Non-Uniformity in Projected Displays”, IEEE International Workshop on Projector-Camera Systems (PROCAMS-2003); and R. Ulichney, “Halftoning”, Wiley Encyclopedia of Electrical and Electronic Engineering, Vol. 8, pp. 588-600, John Wiley and Sons, Inc., 1999, each of which are herein incorporated by reference.
In one embodiment, dithered high-resolution frame 506 (X-hatdth) is subtracted on a pixel-by-pixel basis from the simulated high-resolution image frame 306 (X-hat) at a subtraction stage 508. In one embodiment, the resulting image error data (Δ) 510 is filtered by a human visual system (HVS) weighting filter (W) 512. In one embodiment, HVS weighting filter (W) 512 filters error image data (Δ) 510 based on characteristics of the human visual system. In one embodiment, (HVS) weighting filter (W) 512 reduces or eliminates low-frequency errors (to which the human visual system is most sensitive). The mean squared error of the filtered data is then determined at a stage 514 to provide a measure of how close dithered high-resolution frame 506 (X-hatdth) is to simulated high-resolution image frame 306 (X-hat).
At 556, one projector of the component projectors 112 is selected, such as component projector 112A, for example. At 558, dither array 502 (Tk) having an initial dither pattern is determined for the selected component projector 112. In one embodiment, the initial dither pattern is a random pattern. At 560, dither array 502 (Tk) is applied to the optimal sub-frame 310 (Ykopt) of the selected component projector 112 to generate dithered sub-frame 504 (Ykdth) for the selected component projector. Initially, dither array 502 (Tk) will have an initial dither pattern (e.g. random pattern) as determined at 558, but will otherwise have a dither pattern as adjusted at 568 below.
At 562, an image formation model such as described above with respect to
If the answer to the query at 566 is “no”, process 550 proceeds to 568 where the dither pattern of dither array 502 (Tk) is adjusted based on an error between dithered high-resolution image 506 (X-hatdth) and simulated high resolution image 306 (X-hat), such as described above with respect to
If the answer to the query at 566 is “yes”, process 550 proceeds to 570 where the present dither array 502 (Tk) is selected as the dither array for the selected one of the component projectors 112 (e.g component projector 112A). In one embodiment, the present dither array 502 (Tk) is selected as the dither array for the selected one of the component projectors 112 and stored at a memory therein. At 572, process 550 queries whether a dither array has been determined for each of the projectors of the multi-projector display system. If the answer to the query at 572 is “no”, process 550 proceeds to 574 where a next one of the component projectors 112 is selected and returns to 558. If the answer to the query at 572 is “yes”, process 550 is complete, as illustrated at 576.
With regard to process 550, it is noted that the dither array 502 (Tk) of each component projector 112 is independently calculated. In other words, when determining dither array 502 (Tk) for a selected component projector 112, the dither array 502 (Tk) for only the selected projector 112 is employed to form a corresponding dithered low-resolution sub-frame 504 (Ykdth), so that the dithered high-resolution image 506 (X-hatdth) is formed based on the dithered low-resolution sub-frame 504 (Ykdth) of the selected component projector and the optimal low-resolution sub-frames 310′(Ykopt) of the remaining, non-selected, component projectors 112. As such, a dither array 502 (Tk) of one component projector 112 does not affect the determination of a dither array 502 (Tk) of another component projector 112.
At 592, the dither array 502 (Tk) of the selected component projector 112 (e.g. component projector 112A), as determined at 554 through 570, is employed to generate the dither arrays 502 (Tk) of the remaining, non-selected component projectors 112 (e.g. 112B, 112C, etc.). In one embodiment, different shifts, orientations, and inversions of dither array 502 (Tk) of the selected component projector 112 are employed to generate dither arrays 502 (Tk) for the remaining, non-selected component projectors 112. For example, in one embodiment, a 90-degree rotation of the determined dither array 502 (Tk) of the selected component projector (e.g. component projector 112A) is employed to generate a dither array 502 (Tk) of one of the remaining component projectors (e.g. component projector 112B). In one embodiment, a gray-level inversion of the determined dither array 502 (Tk) of the selected component projector (e.g. component projector 112A) is employed to generate a dither array 502 (Tk) of one of the remaining component projectors (e.g. component projector 112B). Any number of such techniques or combinations of such techniques can be employed to form dither arrays 502 (Tk) for the remaining component projectors from dither array 502 (Tk) of the selected component projector. Upon generating dither arrays 502 (Tk) for the remaining component projectors at 592, process 590 is complete, as indicated at 594.
As such, with regard to process 590, it is noted that the dither arrays 502 (Tk) of component projectors 112 are “coupled” to one another. In other words, a change in the dither array 502 (Tk) of the selected component projector 112 (e.g. component projector 112A) affects the dither arrays 502 (Tk) of the remaining component projectors 112 (e.g. component projectors 112B, 112C, etc.).
At 606, dither arrays 502 (Tk) having an initial dither pattern are determined for each of the component projectors 112. In one embodiment, the initial dither pattern for each dither array 502 (Tk) is a random pattern. In one embodiment, the initial dither pattern is the same for each dither array 502 (Tk) for each of the component projectors 112. In another embodiment, the initial dither pattern is different (e.g. random) for each dither array 502 (Tk) for each of the component projectors 112.
At 608, the dither array 502 (Tk) for each component projector is applied to the corresponding optimal sub-frame 310 (Ykopt) determined at 604 to generate a dithered sub-frame 504 (Ykdth) for each of the component projectors 112. At 610, one projector of the component projectors 112 is selected, such as component projector 112A, for example.
At 612, an image formation model such as described above with respect to
At 614, the dithered high-resolution image 506 (X-hatdth) generated at 612 is compared to simulated high resolution image 306 (X-hat) determined at 604. At 616, based on the comparison at 614, it is queried whether dithered high-resolution image 506 (X-hatdth) is optimal relative to simulated high resolution image 306 (X-hat).
If the answer to the query at 616 is “no”, process 600 proceeds to 618 where the dither pattern of dither array 502 (Tk) for the selected component projected 112 is adjusted based on an error between dithered high-resolution image 506 (X-hatdth) and simulated high resolution image 306 (X-hat), such as described above with respect to
At 620, a new dithered low-resolution sub-frame 504 (Ykdth) for the selected component projector 112 is generated by applying the adjusted dither array 502 (Tk) to the corresponding optimal low-resolution sub-frame 310 (Ykopt). Process 600 then returns to 612 where a new dithered high-resolution image 506 (X-hatdth) is generated using the new dithered low-resolution sub-frame 504 (Ykdth) for the selected component projector 112, and 614 and 616 are repeated.
If the answer to the query at 616 is “yes”, process 600 proceeds to 622 where the present dither array 502 (Tk) is set as the dither array for the selected one of the component projectors 112 (e.g component projector 112A). In one embodiment, the present dither array 502 (Tk) is set as the dither array for the selected one of the component projectors 112 and stored at a memory therein.
At 624, process 600 queries whether a dither array 502 (Tk) has been determined for each of the component projectors 112 of the multi-projector display system 100. If the answer to the query at 624 is “no”, process 600 proceeds to 626 where a next one of the component projectors 112 is selected and repeats the above described process so as to determine an optimal dither array 502 (Tk) for the next projector. If the answer to the query at 624 is “yes”, an optimal dither array 502 (Tk) has been determined for each of the component projectors, thereby completing process 600, as illustrated at 628.
With regard to process 600, it is noted that the dither arrays 502 (Tk) of the component projectors 112 are jointly determined. As described above, when determining dither array 502 (Tk) for a selected component projector 112, the dither arrays 502 (Tk) for the non-selected projectors 112 are employed in the formation of the dithered high-resolution image 506 (X-hatdth). As such, with regard to process 600, a change in the dither array 502 (Tk) of each component projector 112 affects the dither arrays 502 (Tk) of the other component projectors 112 of multi-projector image display system 100.
It is noted that
In summary, by employing jointly designed dither arrays (Tk) for each of the component projectors of multi-projector image display system as described herein, such as component projectors 112 of image display system 100, the bit-depth of the image display system can be increased.
Although described herein primarily in terms of employing dither matrices to dither the low-resolution sub-frames of each component projector, other methods or processes may be employed so long as the low-resolution sub-frames of each component projector are dithered differently from one another. Examples of such processes include, for example, applying a different quantization algorithm to each low-resolution sub-frame and introducing noise differently into each low-resolution sub-frame.
One form of the present invention provides an image display system 100 with multiple overlapped low-resolution projectors 112 coupled with an efficient real-time (e.g., video rates) image processing algorithm for generating sub-frames 110. In one embodiment, multiple low-resolution, low-cost projectors 112 are used to produce high resolution images 114 at high lumen levels, but at lower cost than existing high-resolution projection systems, such as a single, high-resolution, high-output projector. One form of the present invention provides a scalable image display system 100 that can provide virtually any desired resolution and brightness by adding any desired number of component projectors 112 to the system 100.
In some existing display systems, multiple low-resolution images are displayed with temporal and sub-pixel spatial offsets to enhance resolution. There are some important differences between these existing systems and embodiments of the present invention. For example, in one embodiment of the present invention, there is no need for circuitry to offset the projected sub-frames 110 temporally. In one form of the invention, the sub-frames 110 from the component projectors 112 are projected “in-sync”. As another example, unlike some existing systems where all of the sub-frames go through the same optics and the shifts between sub-frames are all simple translational shifts, in one form of the present invention, the sub-frames 110 are projected through the different optics of the multiple individual projectors 112. In one form of the invention, the signal processing model that is used to generate optimal sub-frames 110 takes into account relative geometric distortion among the component sub-frames 110, and is robust to minor calibration errors and noise.
It can be difficult to accurately align projectors into a desired configuration. In one embodiment of the invention, regardless of what the particular projector configuration is, even if it is not an optimal alignment, sub-frame generator 108 determines and generates optimal sub-frames 110 for that particular configuration.
Algorithms that seek to enhance resolution by offsetting multiple projection elements have been previously proposed. These methods assume simple shift offsets between projectors, use frequency domain analyses, and rely on heuristic methods to compute component sub-frames. In contrast, one form of the present invention utilizes an optimal real-time sub-frame generation algorithm that explicitly accounts for arbitrary relative geometric distortion (not limited to homographies) between the component projectors 112, including distortions that occur due to a target surface 116 that is non-planar or has surface non-uniformities. One form of the present invention generates sub-frames 110 based on a geometric relationship between a hypothetical high-resolution reference projector 118 at any arbitrary location and each of the actual low-resolution projectors 112, which may also be positioned at any arbitrary location.
In one embodiment, image display system 100 is configured to project images 114 that have a three-dimensional (3D) appearance. In 3D image display systems, two images, each with a different polarization, are simultaneously projected by two different projectors. One image corresponds to the left eye, and the other image corresponds to the right eye. Conventional 3D image display systems typically suffer from a lack of brightness. In contrast, with one embodiment of the present invention, a first plurality of the projectors 112 may be used to produce any desired brightness for the first image (e.g., left eye image), and a second plurality of the projectors 112 may be used to produce any desired brightness for the second image (e.g., right eye image). In another embodiment, image display system 100 may be combined or used with other display systems or display techniques, such as tiled displays.
Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific embodiments shown and described without departing from the scope of the present invention. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Therefore, it is intended that this invention be limited only by the claims and the equivalents thereof.
