Camera-Based Calibration Techniques for Seamless Multi
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR
Camera-Based Calibration Techniques for Seamless Multi-Projector Displays
, Aditi Majumder
, Ruigang Yang
Abstract— Multi-projector, large-scale displays are used in scientific visualization, virtual reality and other visually intensive applications. In recent years, a number of camera-based computer vision techniques have been proposed to register the geometry and color of tiled projectionbased display. These automated techniques use cameras to
“calibrate” display geometry and photometry, computing per-projector corrective warps and intensity corrections that are necessary to produce seamless imagery across projector mosaics. These techniques replace the traditional labor-intensive manual alignment and maintenance steps, making such displays cost-effective, flexible, and accessible.
In this paper, we present a survey of different camerabased geometric and photometric registration techniques reported in the literature to date. We discuss several techniques that have been proposed and demonstrated, each addressing particular display configurations and modes of operation. We overview each of these approaches and discuss their advantages and disadvantages. We examine techniques that address registration on both planar (video walls) and arbitrary display surfaces and photometric correction for different kinds of display surfaces. We conclude with a discussion of the remaining challenges and research opportunities for multi-projector displays.
Index Terms— Survey, Large-Format Displays, Large-
Scale Displays, Geometric Alignment, Photometric Alignment, Graphics Systems, Graphics.
Expensive monolithic rendering engines and specialized light projectors have traditionally made projectorbased displays an expensive “luxury” for large-scale visualization. However, with advances in PC graphics hardware and light projector technology, it is now possible to build such displays with significantly cheaper components. Systems, such as Li et al.’s Scalable Display
Wall , Matusik and Pfister’s 3D TV , and displays constructed using Humphreys et al.’s WireGL  and Chromium  PC-cluster rendering architecture,
M. S. Brown is with the Hong Kong Univ. of Science and
A. Majumder is with the University of California, Irvine.
R. Yang is with the University of Kentucky, Lexington, KY.
Camera-based geometric registration is used to calculate image-based corrections that can generate a seamless image from several (unaligned) overlapping projectors.
have demonstrated the feasibility of cost-effective, largeformat displays assembling from many commodity projectors and PCs.
Images from a multi-projector display must be seamless, i.e., they must appear as if they were being projected from a single display device. This involves correcting for geometric misalignment and color variation within and across the different projectors to create a final image that is both geometrically and photometrically seamless. This correction process is commonly referred to as “calibration”. Calibration involves two aspects:
geometric registration and color correction. Geometric registration deals with geometric continuity of the entire display, e.g., a straight line across a display made from multiple projectors should remain straight. Photometric correction deals with the color continuity of the display, e.g., the brightness of the projected imagery should not vary visibly within the display.
Calibration can be achieved through mechanical and electronic alignment, a common approach adopted by many research and commercial systems , , ,
, . Such alignment procedures often require a specialized display infrastructure and a great deal of personnel resources, to both set up and maintain. This significantly increases the cost and effort needed to deploy such large-scale, high-resolution displays. Often, half of a display’s total cost is related to the display infrastructure, including the mounting hardware and dis-
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 2
Left: This image illustrates the geometric misalignment problem at the boundary of two overlapping projectors. The geometry is noticeably unaligned. Right: This image shows the final seamless imagery of the same projector alignment. This registration is the goal of geometric registration methods.
play screens. In addition, most reasonably sophisticated mounting hardware does not have the capability or the precision to correct non-linear distortions such as projector radial distortion and intensity non-linearities. Further, manual methods tend to be unscalable. Calibrating even a four-projector system can be severely time consuming.
Recently, techniques have been developed that use one or more cameras to observe a given display setup in a relaxed alignment, where projectors are only casually aligned. Using feedback obtained from a camera observing the display setup, the necessary adjustments to register the imagery, both in terms of geometry and color, can be automatically computed and applied through software , , , , , , , , ,
, . The key idea in these approaches is to use cameras to provide closed-loop control. The geometric misalignments and color imbalances are detected by a camera (or cameras) that monitors the contributions of multiple light projectors using computer vision techniques. The geometric- and color-correction functions necessary to enable the generation of a single seamless image across the entire multi-projector display are determined. Finally, the image from each projector is appropriately pre-distorted by the software to achieve the correction (see Figure 1). Thus, projectors can be casually placed and the resulting inaccuracies in geometries and color can be corrected automatically by the camera-based calibration techniques in minutes, greatly simplifying the deployment of projector-based displays.
In comparison with traditional systems relying on precise setups, camera-based calibration techniques provide the following advantages in particular:
More flexility. Large-format displays with camerabased calibration can be deployed in a wide variety of environments, for example, in the corner of a room, or across a column. These irregularities can cause distortions that traditional systems may find difficult to work with.
Easy to setup and maintain. Camera-based calibration techniques can completely automate the setup of large-format displays. This is particularly attractive for temporary setups in trade-shows or field environments. Labor-intensive color balancing and geometric alignment procedures can be avoided and automated techniques can be used to calibrate the display in just minutes.
Reduced costs. Since precise mounting of projectors is not necessary, projectors can be casually placed using commodity support structures (or even as simple as laying the projectors on a shelf). In addition, it is not necessary to hire trained professionals to maintain a precise alignment to keep the display functional. Further, since the color variations can also be compensated, expensive projectors with high quality optics (that assure color uniformity) can be replaced by inexpensive commodity ones.
While camera-based calibration techniques require cameras and support hardware to digitize video signals, these costs are amortized by savings from long-term maintenance costs. Overheads like warping and blending at rendering time to correct for various distortions are reduced or eliminated by the recent advances in graphics hardware.
In this paper, we present a survey of different camerabased calibration techniques. Our goal is to provide potential developers of large-format displays a useful summary of available techniques and a clear understanding of their benefits and limitations. We start with geometric registration techniques in Section II. We organize different approaches by the types of configurations addressed and the modes of operation accommodated.
We discuss techniques for planar or arbitrary display surfaces with stationary or moving viewers. We compare these approaches and point out their positive and negative points for given environments and tasks. In Section III, we focus on color correction techniques. Until recently,
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 3 expensive color measurement instruments were used to calibrate the color of such displays and the spatial variation in color was largely ignored. Recent camera-based techniques address photometric variation across such displays for surfaces with different reflectance properties.
We discuss all these methods along with their advantages and disadvantages. In Section IV, we list several representative systems that use camera-based calibration and discuss their features. In Section V, we introduce some interesting technological hardware advancements that reduce or even remove the rendering overhead that is typical in performing geometric and photometric corrections. Finally, we conclude in Section VI with a discussion of the remaining challenges that still need to be addressed for projector-based displays.
When building a multiple-projector display, two types of geometric distortion must be addressed – intra-
projection and inter-projection distortion. Intra-projector distortions are distortions within a single projector caused by off-axis projection, radial distortion, and in some cases, display on non-planar surfaces. Inter-
projector distortions are found between adjacent projectors where edge boundaries do not match. Geometric registration techniques are used to detect and correct both types of distortion (see example in Figure 2).
Camera-based display registration techniques can be divided into two categories based on the type of display surfaces addressed, either planar or non-planar. We first discuss techniques that assume a planar display surface. These are used to construct large-scale video walls. Later, we extend the discussion to arbitrary display surfaces, for example, multiple planar walls or semispherical screens. These scenarios are particularly suited for immersive displays.
A. Planar Display Surfaces
When the display surface is planar, each projector
’s image can be related to a reference frame, R, on the display surface, via a 2D planar homography (we suggest  for readers unfamiliar with homographies).
This projector-to-reference frame homography is denoted as
k where k is the index of the projector, and the subscript R denotes that the homography maps the image of
P k to the reference frame R (notation adopted from ).
To compute the homography, it is necessary to establish four point-correspondences between coordinate frames.
Using more than four point-correspondences allows a least-squares fit solution which is often desirable in the face of errors and small non-linearities. In practice, most techniques project many known features per projector to compute the homographies , , , , ,
The alignment of the projected imagery is achieved by pre-warping the image from every projector, P k the homography,
. This pre-warp can be performed directly in the rendering pipe-line  or by using a post-rendering warp .
Thus, the key is to determine the correct
k for each projector P k
. In essence, we need to establish point-correspondences between each projector and the display’s reference frame, R. This can be accomplished by using a camera (or cameras) to observe the projected imagery, as shown in Figure 3.
1) Using a Single Camera: We first consider the case when only one camera is used. Figure 3 (left) shows an example of this setup. A homography between the camera and the display reference frame R, denoted by
C, is first computed. Typically, manually selected pointcorrespondences between the camera image and known
2D points on the display surface are used to calculate
After each P k
C has been computed, projected imagery from is observed by the camera and a projector-tocamera homography for each projector k, is calculated, and denoted as homography,
. The projector-to-reference frame k
, is then derived from
, (1) where the operator × represents a matrix multiplication.
Raskar et al.  presented a system using a single camera that could compute this mapping for a 2 × 2 projector array in roughly a few seconds. In this work, a camera was first registered to the display’s reference frame manually. Each projector P k projected a checkerboard pattern that was observed by the camera.
Corners on the checkerboard pattern where determined in the camera’s image plane, establishing the point correspondences between the camera an the projector. From this information, projector-to-camera homographies
k were computed. Next, the necessary
k could be computed using Eq. 1. This allowed the projected imagery to be correctly aligned to the display reference frame.
Raskar et al. reported that this approach could align the projected imagery with sub-pixel accuracy .
More recently, techniques that do not require manually selecting points on the display surface have been introduced , . They show that planar auto-calibration, proposed by Triggs in , can be used to determine the intrinsics of an array of projectors projecting on a single plane.
While these above approaches are effective, the use of a single camera limits the scalability of these techniques
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR
Single Camera Multiple Cameras
(Left) 3 × 3 linear homographies are computed that relate the projectors to the display reference frame, R. A camera is used to observe projected imagery from each projector. (Right) For large field-of-view projector arrays, multiple cameras are used. Each camera observes a region of the display. Projector-to-camera homographies concatenated with camera-to-reference frame homographies are used to compute the necessary projector-to-reference frame mapping.
to displays composed of a larger number of projectors.
Such large displays made of 40 − 50 projectors are used in many national institutes like Sandia, Lawrence
Livermore National Laboratories and the National Center for Supercomputing Applications (NCSA) at University of Illinois at Champagne Urbana (UIUC).
To address this scalability issue, Y. Chen et al.  proposed a method that used a single camera mounted on a pan-tilt unit (PTU). The PTU allowed the camera to move such that it could see a very large field-of-view.
Controlled by a PC, the camera could be automatically moved to observe points and lines projected by the individual projectors (the experiment in  registered eight projectors). The camera could relate points and lines from each projector to the display’s global reference frame, R. A rough alignment of projectors was assumed.
This meant that projected points and lines between projectors should be aligned, but were not because of slight mis-registrations. Using the collected data from the camera a simulated annealing algorithm was used to compute each
, such that errors between the corresponding projector points and angles between the corresponding lines where minimized. Y. Chen et al. reported that this approach could achieve near pixel accuracy in projector alignment . While this approach proved to work, it suffered from being slow. Overall time to collect data from the PTU-mounted camera and to perform the simulated annealing was reported to be around one hour.
Implementation improvements can undoubtedly reduce the overall time.
2) Using Multiple Cameras: More recently, H. Chen et al.  proposed a more scalable approach that uses multiple cameras. Several cameras observing the display are related to one another by camera-to-camera homographies. A root camera
C is established as the reference frame. Adjacent cameras, i and j, are related to one another by the i
j homographies. Point correspondences are established between adjacent cameras by observing projected points from which the i
j s are computed.
Next, each camera is registered to the root camera and thus to the reference frame R. This can be done by computing a homography
, which is constructed by concatenating adjacent camera-to-camera homographies until the root camera is reached as follows (see Figure 3 (right)):
× · · · × i
j maps points in camera, j, to the reference frame R. To determine the path of this camerato-reference frame concatenation, a minimum-spanning
“homography tree” is built that minimizes registration errors in the camera-to-camera reference frame .
Each projector is now observed by one of the cameras in the system. A single camera in the setup can typically observe only 2-4 projectors from the entire display wall.
The projectors can be related to their corresponding cameras via a homography, denoted as k
, where j is the camera index and k is the projector index. Using the homography tree computed between the cameras, the projector-to-reference homography
k for a given projector k can be computed as:
, (3) where
j has been constructed using Eq. 2. Experiments in  showed that this approach can be very accurate in registering projectors. In examples using up
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 5 to 32 projectors, sub-pixel local alignment accuracies were reported. In simulation, this technique was shown to be scalable to scores of projectors and cameras. In addition, this approach took only a few minutes to reach a solution with large numbers of projectors.
B. Arbitrary Display Surfaces
The previous homography-based approaches were applicable only if the display surface is planar. Here, we discuss approaches that address non-planar display surfaces. These include surround environments such as video domes and immersive environments. In addition, these techniques are geared for very flexible deployment in existing environments, like an office, where large empty planar display surfaces may be difficult to find.
The approaches we present address two modes of operation. One that assumes a stationary viewer and one that allows a moving user (i.e., a head-tracked viewer).
These techniques can of course be applied to planar display surfaces as well.
1) Stationary Viewer: Raskar  and Surati  proposed a registration algorithm that uses a two-pass rendering technique to create seamless imagery on arbitrary display surfaces. In this approach, a single camera is placed at the location from where the viewer is supposed to observe the displayed imagery. A set of equally spaced features are projected from each projector P k and registered in the camera image plane. The projected features P k
(x, y) are typically used to form a tessellated grid in the projector space as well as the camera image space (see Figure 4). This establishes a non-linear mapping from the projector’s features P k
(x, y) to their positions in the camera’s image plane C(u, v), denoted as C(u, v) 7→ P k
To correct the displayed imagery, a two-pass rendering algorithm is used. In the first pass, the desired image to be seen by the viewer is rendered. This desired image from the first pass is then warped to the projected image based on the C(u, v) 7→ P k
(x, y) non-linear mapping.
This non-linear warp can be realized by a piecewise texturing between tessellated meshes in the projector and the camera image space. Thw warping constitutes the second rendering pass. For clarity, Figure 4 shows this procedure using only one projector. This technique will, however, produce a seamless image even when multiple overlapping projectors are observed by the camera. Note that any camera distortion (such as radial distortion) will be encoded in the C(u, v) 7→ P k
(x, y) mapping. For cameras with severe radial distortion, e.g. a camera using a fish-eye lens, this distortion will be noticeable in the resulting image created by the projector mosaic. Care should be taken to first calibrate the camera to remove such distortion. Routines to perform this calibration are typically available in computer vision software packages, such as Intel’s OpenCV .
The warp specified from the C(u, v) 7→ P k
(x, y) mapping generates a geometrically correct view from where the camera is positioned. For this reason, the camera is positioned close to where the viewer will be positioned while viewing the display. However, as the viewer moves away from this position, the imagery will begin to appear distorted. Thus, this technique is suitable for a stationary viewer only.
Yang et al.  incorporated this two-pass rendering algorithm into the University of North Carolina at Chapel
Hill’s PixelFlex display system. In the PixelFlex system, mirrors are mounted on pan-tilt units (PTU) positioned in front of the projectors. Software allows a user to dynamically modify the projectors’ spatial alignment by moving the mirrors via the PTUs. New projector configurations are registered using the technique described above. Brown et al.  incorporated the same technique into the WireGL and Chromium  rendering architecture. This allows users to deploy PC-based tiled display systems that support unmodified OpenGL applications. Both Brown et al.  and Yang et al.  reported sub-pixel projector registration when using this two-pass approach. In addition, these approaches can register the displays in a matter of minutes. Further, the non-linear warp corrects for both non-linear projector lens distortion and display surface distortion. Thus, this approach allows for very flexible display configurations
(non-rectangular projector arrangements on non-planar display surfaces). However, the need for two rendering passes can affect performance. Brown et al.  reported a drop in performance from 60 fps to 30 fps, when the second-pass warp was used on a 2 × 2 projector array using four PCs with nVidia GeForce3 cards. This overhead may be alleviated in the future by having the second-pass conducted directly on the projectors (see
Section V). In addition, this technique uses a single camera, limiting its scalability.
2) A Moving (Head-Tracked) Viewer: For a moving viewer in an arbitrary display environment, the necessary warping function between each projector and the desired image must be dynamically computed as the view changes. Raskar et al.  presented an elegant two-pass rendering algorithm to address this situation. Figure 5(a) illustrates this two-pass rendering approach. The desired image from the viewer’s position is rendered in the first pass. This image is then projected from the viewer’s point of view onto a 3D model of the display surface using projective textures. This textured 3D model is then
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 6
(Left) Projectors display features that are observed by a camera placed near the desired viewing location. (Right) The desired image is (1) rendered and then (2) warped to the projected imagery based on its mapping to the camera.
3D Display Surface 3D Global Registration
(Pass-1) Render desired image.
Project onto a 3D model of the display surface.
(Pass-2) Render texture
3D model using projectors view frusta
a) A two-pass rendering algorithm for a moving viewer and an arbitrary display surface. The first pass renders the desired image to be observed by the user. This is used as a projective texture and projected from the viewer’s point of view onto the display surface. The textured display surface is then rendered from the projector’s point of view constituting the second pass render. When projected, second pass rendered image will look correct to the viewer. (b) Stereo-camera pairs are used to determine the 3D display surfaces D
1 and D
2 and projector locations P
1 and P
. These are then registered into a common coordinate system along with the head tracker.
rendered from the view point of the projector as the second rendering pass. When projected by the projector, this second pass image will appear geometrically correct to viewer.
In this algorithm, three components must be known:
(1) a 3D model of the display surface, (2) the projectors’ locations (in the form of a view frustum with respect to the display surface) and (3) the viewer’s location (with respect to the display surface). These three components need to be registered in a common coordinate frame for the algorithm to work. Raskar et al.  presented a system that uses several cameras to determine automatically the 3D geometry of the display surface and the location of the projectors within the display environment. The data is then integrated with a head tracker to provide the third necessary component of viewer location. Figure 5(b) shows an overview of the approach.
In this system, multiple cameras are first used to form several stereo-camera pairs S i to observe the projected imagery. Typically, one stereo pair is established for each projector. Each stereo pair is calibrated using a large calibration pattern. Note that a particular camera may be a member of more than one stereo pair. Using the stereo
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 7 pair S i
, the display surface D i seen by the projector
P i can be determined using a structured-light technique.
Each recovered 3D display surface D i is represented as a
3D mesh. From D i
, the projector’s P i
’ view frustum (i.e.,
3D location) with respect to the display surface can be computed. This completes the computation of the initial unknowns of the 3-D display surface and the projector location for every projector in the display. However, each
D i and P i pair is still registered to different coordinate frames. The next step is to unify them within a common coordinate frame.
A stereo pair S i can see its corresponding projector P i and any overlapping portion from an adjacent projector
. Using 3-D point correspondences acquired in the overlapping region between two display surfaces D i and
, a rigid transformation consisting of a rotation i
, and a translation i
T j can be computed to bring D i and D j into alignment. Once the display surfaces are in alignment view frustums, P i and P j can also be computed in the same common coordinate frame. Finally, the head tracker is registered to the global coordinate frame. This can be done by registering tracker positions to 3D points on the displays surface. A rotation and translation to bring the tracker’s coordinates into alignment with the display surface can be computed. With all three necessary components registered to a common coordinate frame, the two-pass rendering algorithm for a moving user can be used to generate seamless imagery.
This approach allows flexible projector alignment and display surfaces and, hence, recovers the underlying display surface and projector locations automatically. In addition, this technique is scalable, allowing immersive displays to be deployed in a wide-range of environments.
However, due to the large number of parameters that need to be estimated (e.g. camera parameters,3D surface, projector parameters) the accuracy of this system is roughly 1-2 pixels.
More recently, Raskar et al.  presented a more efficient method to solve for a smaller set of 3D surfaces, specifically quadratic surfaces. Examples of quadric surfaces are domes, cylindrical screens, ellipsoids, and paraboloids. Such specialized surfaces are used in systems built for training and simulation purposes. For quadratic surfaces, the warping to register the images on quadric surfaces can be expressed by a parameterized transfer equation. In comparison with the full 3D reconstruction approach in , this parameterized approach has substantially fewer unknown parameters to estimate.
A registration accuracy of one pixel was reported for this method .
Digital photographs of tiled displays showing the color variation problem. (a): Example of severe photometric variation across a display made of abutting projectors. Though difficult to believe, it is true that every pixel of this display is projecting the identical input of the maximum intensity for green. (b): A tiled display made of a 3 × 5 array of fifteen projectors (10
0 in size) with perfect geometric registration, but with color variation.
In this section, we address the color variation problem.
Current commodity projectors, our target products for building large-area displays inexpensively, do not have sophisticated lens systems to assure color uniformity across the projector’s field-of-view. Thus, the color variation in multi-projector displays made of commodity projectors, can be significant. Figure 6(a) shows the severe color variation of the 40 projector display used by
NCSA of UIUC. Even after perfect geometric alignment, the color variation problem can be the sole factor in causing a ‘break’ in creating the illusion of a single large display, as shown in Figure 6(b). Thus, color variation problems need to be addressed to achieve truly seamless displays.
Color is a three-dimensional quantity defined by onedimensional luminance (defining brightness) and twodimensional chrominance (defining hue and saturation).
The entire range of luminance and chrominance that can be reproduced by a display is represented by a 3D volume called the color gamut of the display. Since color is defined by luminance and chrominance, the color variation problem involves spatial variation in both luminance and chrominance. It has been shown that most current tiled displays composed of projectors of the
same manufacturer model show large spatial variation in luminance while the chrominance is almost constant spatially , . Also, humans are at least an order of magnitude more sensitive to luminance variation than to chrominance variation. For example, humans have higher spatial and temporal frequency acuity for luminance than for chrominance; in addition, humans can resolve a higher luminance resolution than chrominance resolution. Detailed discussion of such perceptual capabilities can be found in the psychophysics literature , ,
. It has been shown that perceptually, the subproblem of photometric variation (luminance variation) is
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 8
From left: (1) Correction done by luminance matching for a display made of two abutting projectors; (2), (3), and (4) respectively: fifteen-projector tiled display, before blending, after software blending, and after optical blending using physical mask, respectively.
the most significant contributor to the color variation problem.
The color variation in multi-projector displays has been classified in three different categories .
1) Intra-Projector Variation: Luminance varies significantly across the field-of-view of a single projector. Luminance fall-off of about 40 − 80% from the center to the fringe is common in most commodity projectors. This is caused by several reasons like the distance attenuation of light and the angle at which the light from the projector falls on the screen. This also results in an asymmetric fall-off, especially with off-axis projection. The non-Lambertian nature of the screen further pronounces the problem. There are many front projection screens available that are close to Lambertian in nature. However, this is a rare property among the rear projection screens making intra-projector variation more pronounced for rear-projection systems. However, the chrominance remains almost spatially constant within a single projector.
2) Inter-Projector Variation: Luminance can vary significantly across different projectors. This is caused by differences in the properties of the projector lamps and their ages, by differences in the position and orientation of the projector with respect to the screen, and also by differences in the projector settings like brightness, contrast and zoom. However, chrominance variation across projectors is relatively much smaller and is almost negligible for same model projectors.
3) Overlap Variation: The luminance in the region where multiple projectors overlap is multiplied by the number of overlapping projectors, creating a very high brightness region. If the chrominance properties of the overlapping projectors are not close to each other, this can also lead to visible chrominance variations in the overlapped region.
However, these variations are at least an order of magnitude smaller than the luminance variation.
A related problem is that of the black offset. Any ideal display device should project no light for the red, green, and blue (RGB) input (0, 0, 0). This is true for most cathode ray tube (CRT) projectors since the electron beam inside can be switched off completely at zero. However, most commodity projectors use light blocking technology like liquid crystal display (LCD) or digital light projector (DLP), through which some light is always projected. This is called the black offset. This reduces the contrast of projectors and current technology is driven towards reducing this black offset as much as possible.
In abutting projector displays, traditionally, the color compensation was done by manipulating the projector controls (like brightness, contrast and zoom) manually using feedback from a human user on the quality of the color uniformity achieved. Unfortunately, this is a very labor-intensive process and ideal color uniformity is not always achievable given the limited control allowed to the user. Therefore, automatic color calibration methods were devised to create scalable displays.
A. Gamut Matching
This approach was the first to automate the process of using manual feedback and manipulation of controls.
A point light measuring instrument (like a spectroradiometer) ,  is used to measure the color gamut of each projector at one spatial location. The spatial variation of color within a single projector is assumed to be negligible and the colors between the different projectors are matched by a two-step process. First, a
common color gamut is identified that is the intersection of the gamuts of different projectors. This represents the range of colors that all the projectors in the display are capable of producing. Second, by assuming projectors to be linear devices, 3D linear transformations are used to convert the color gamut of each display to the common color gamut.
This method is applicable to devices that use three primary colors (most devices use red, green and blue as color primaries). Since three primary colors form a basis for describing all colors, a color in the three-primarysystem can be represented by a unique combination of the three primaries. However, some DLP projectors use a clear filter to project the grays instead of projecting the superposition of light from the red, green and
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 9 blue filters. This makes these DLP projectors behave like four primary devices (like printers that use cyan, magenta, yellow and black as primaries). Adding the fourth primary brings in linear dependencies in such systems. As a result, a color cannot be represented using unique combinations of the four primaries. The gamutmatching method depends on the linear independence of the primaries and becomes inapplicable in such fourprimary systems.  presents a solution by which a gamut-matching method can be extended to be applied to the DLP projectors.
The theoretical disadvantage of the gamut-matching method lies in the fact that there is no practical method to find the common color gamut.  presents an optimal method to find the intersection of n color gamuts in
) time. This is clearly not a scalable solution, especially for large-scale displays of over 10 projectors.
 tries to address this problem by matching only luminance across different projectors. Since most display walls are made of the same model projectors, which differ negligibly in chrominance, achieving luminance matching across different projectors can suffice. The result of this method is shown in Figure 7. However, since spatial color variation is ignored, these methods cannot produce entirely seamless displays. Further, expensive instrumentation makes these methods cost prohibitive.
A relatively inexpensive radiometer costs at least four times more than a projector. Expensive radiometers can cost as much as a dozen projectors.
B. Using a Common Lamp
Using a common lamp is a wonderful engineering feat
. In this method, the lamps of the multiple projectors are taken off and replaced by a common lamp of much higher power. Light is distributed from this common lamp to all the different projectors using optical fibres.
However, this method is cost intensive because it requires skilled labor. Further, power and thermal issues (heat generated by the high-power lamp) make this approach unscalable. So far, a maximum of nine projectors can be illuminated by a common lamp using this method. Also, this approach addresses only the color variation caused by the differences in the lamp properties. All the other kinds of variations still exist.
Blending or feathering techniques, adopted from image-mosaicing techniques, address overlapped regions and try to smooth color transitions across these regions.
The smooth transitions can be achieved by using a linear or cosine ramp which attenuate pixel intensities
Aperture blending by mounting metal masks on the optical path of the projector that attenuates the light physically.
in the overlapped region. For example, considering a pixel x in the overlap region of projectors P
1 and P
, as illustrated in Figure 8(Left). Let the contributions of these projectors at x be given by P
(x) and P
(x) respectively. When using linear ramping the intensity at x is computed by a linear combination of the intensities
(x) and P
(x) + α
(x) where α
= 1. These weights, α
1 and α
, are chosen based on the distance of x from the boundaries of the overlapped region. For example, when using a linear ramp, these functions can be chosen as,
(x) = d1 d1 + d2
(x) = d2 d1 + d2
This two-projector example can be extended to an arbitrary number of projectors . To do so, the hull, H i
, in the camera’s image plane of observed projector P i
’s pixels is computed. The alpha-weight, A m
(x), associated with projector, P m
’s pixel, x, is evaluated as follows:
(4) where α i
(m, x) = w i
(m, x) ∗ d i
(m, x) and i is the index of the projectors observed by the camera (including projector m).
In the above equation, w i
(m, x) = 1 if the camera’s observed pixel of projector P m
’s pixel, x, is inside the convex hull, H i
; otherwise, w i
(m, x) = 0. The term d i
(m, x) is the distance of the camera’s observed pixel of projector P m
’s pixel, x, to the nearest edge of
. Figure 8 (right) shows the alpha-masks created for four overlapping projectors. The alpha-masks are applied after the image has been warped. This can be performed efficiently as a single alpha-channel textured quad the size of the framebuffer.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 10
Blending Techniques: (Left) The intensity at any pixel x in the overlapped region of two projectors, P
1 and P
, is the combination of the intensity of P
1 and P
2 at x. (Right) The resulting alpha-masks computed for four projectors.
Blending can be achieved in three ways. First, it can be done in software  where the distances from the projector boundaries and the number of projectors contributing to every pixel in the overlap region can be accurately calculated using geometric calibration information.
Thus, the ramps can be precisely controlled by software.
However, this cannot attenuate the black offset, which is especially important with scientific or astronomy data, which often have black backgrounds. Alternate optical methods thus try to achieve this blending by physical attenuation of lights so that it can also affect the black offset. In one method, physical masks mounted at the projector boundaries on the optical path attenuate the light in the overlapped region , as shown in Figure
9. In another method, optical masks are inserted in front of the projection lens to achieve the attenuation . The results of blending are shown in Figure 7. Though blending methods are automated and scalable, they ignore the inter- and intra-projector spatial color variation. Also, the variation in the overlapped region is not accurately estimated. Thus, blending works well if the overlapping projectors have similar luminance ranges, which is often assured by an initial manual brightness adjustment using the projector controls. However, for displays where the luminance has a large spatial variation (like for most rear projection systems), blending results in only softening of the seams in the overlapping region, rather than removing them.
D. Camera-based Photometric Uniformity
All the methods mentioned so far address only the inter-projector or overlapped variation. None addresses the intra-projector variation that can be significant. Also, only the gamut matching method makes an effort to estimate the color response of the projectors. However, since the spatial variation in color is significant, a highresolution estimation of the color response is the only means towards an accurate solution. Thus, the use of
Fig. 10. To compute the display luminance surface of each projector, we need only four pictures per channel. Top: Pictures taken for a display made of a 2 × 2 array of 4 projectors. Bottom: The pictures taken for a display made of a 3 × 5 array of 15 projectors (both for green channel).
a camera is inevitable. However, since a camera has a limited color gamut (as opposed to a spectroradiometer), estimating the color gamut of the display at a high resolution is difficult. However, different exposure settings of a camera can be used to measure the luminance accurately and faithfully. Exploiting this fact, ,  use a camera to correct for the photometric variation (variation in luminance) across a multi-projector display. Since most current displays use the same model projectors that have similar chrominance properties, this method achieves reasonable seamlessness.
This camera-based method aims at achieving identical photometric response at every display pixel. This is called photometric uniformity. We describe the method for a single channel. All three channels are treated similarly and independently. The method comprises two steps. The first step is a one-time calibration step that uses the camera to estimate the luminance response of the multi-projector display. At the end of this step, a perprojector per-pixel map called the luminance attenuation
map (LAM) is generated. In the image correction step, the LAM is used to correct any image to be displayed.
1) Calibration: Let the display D be made of N projectors, each denoted by P j
. Let the camera used for calibration be C. First, geometric calibration is performed to find the geometric warps T
→C relating the projector coordinates (x j
, y j
) with the camera coordinates (x c
, y c
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 11
Left: The luminance surface for one projector. Middle and Right: The display luminance surface for a 2 × 2 array of a four projector and a 3 × 5 array of fifteen projectors, respectively. (all for the green channel) and T
→D relating the projector coordinates with the global display coordinate (x d
, y d
). Any of the geometric calibration methods described in Section II can be used for this purpose. After that, photometric calibration has three steps.
a) Capturing the Display Luminance Response:
Note that the camera should be in the same location as the geometric calibration method throughout this process of photometric calibration. Using the digital camera, two functions are acquired to perform photometric calibration.
The variation of the projected intensity from a channel of a projector with the variation in the input is defined by the intensity transfer function (ITF). This is commonly called the gamma function. In projectors, this function cannot be expressed by a power function and hence we prefer to call it the intensity transfer function.  shows this function to be spatially invariant i.e varies only with input and does not change from one pixel to another within the projector. Hence, the ITF for each projector is first estimated using a point light measuring instrument like a photometer at one location for each projector. However, since such instruments can be cost prohibitive,  presents a method in which the high dynamic range (HDR) imaging method developed by
Debevec and Malik  is applied to measure the ITF of all the projectors at a time using a inexpensive video camera.
Next, the display luminance surface is captured. Images with maximum luminance are projected from each projector and captured using the camera. More than one non-overlapping projector can be captured in the same image. The images taken for this purpose for a four and fifteen projector display are shown are in Figure
10. From these images the luminance surface for each projector L
P j is generated by using the warp T
Standard RGB to Y C r
C b conversion is used for this
purpose. The luminance surface from these projectors are then added up spatially using the warp T
→D to create the display luminance surface L
. The luminance surfaces generated for a projector and the whole display are shown in Figure 11.
Left: The display luminance attenuation map for a 3 × 5 array of fifteen projectors. Right: The LAM for a single projector cut out from the display LAM on the left. (both examples are for the green channel)
b) Finding the Common Achievable Response:
Next, the luminance response that can be achieved at every pixel of the display is identified. Since the dimmer pixels cannot match the brighter pixel, the common achievable response is given by
c) Generating the Attenuation Maps: The luminance attenuation map (LAM), A
, for the whole display is first generated by
, y d
, y d
¿From this display LAM, a luminance attenuation map for each projector is generated using the inverse of the warp T
. The display and projector LAMs thus generated are shown in Figure 12. This concludes the calibration.
2) Image Correction: Once the per-projector LAMs are generated, the per-projector image correction is done in two steps. These correction steps are applied to any image that is projected from the display. First, the per pixel multiplication of the image with the LAM is performed. This multiplication assumes linear ITF. In practice, however, the ITF is non-linear. To compensate for that, an inverse of the ITF is applied to the image
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 12
The top row shows the image before correction and the bottom row shows the image after luminance matching. Left and middle:
Digital photograph of a 2 × 2 array of projectors. Right: Digital photograph of a 5 × 3 array of projectors. In this case, the image after correction was taken at a higher exposure.
after the LAM is applied. The results of this method are shown in Figure 13.
The corrections required to achieved photometric uniformity or to compensate for the surface reflectance are encoded as per-pixel linear operations and a 1D color look-up-table (LUT). These form a very efficient way of representing the non-linear correction because these operations can be applied in real time using commodity graphics hardware. Recent advances in programmable graphics hardware make it possible to implement complex per-pixel operations that can run natively on the graphics processor without taking a toll on the main
CPU , . Details of how these can be used to create interactive displays are available at .
However, since this method aims at photometric uniformity, the photometric response of every pixel is matched to the ‘worst’ pixel on the display, ignoring all the ‘good’ pixels that are very much in the majority. This results in a compression in dynamic range making the method unscalable. Ongoing research  is trying to address this issue by achieving a perceptual uniformity rather than a strict photometric uniformity.
brick walls or a poster boards , for scenarios where it may not be possible to find white display surfaces. In this approach, the camera and projectors are assumed to be linear devices and the color transformation between them is expressed by a 3 × 3 matrix, V . The RGB color,
C, measured by a camera for a projector input, P , is related by the matrix multiplication C = V P .
The camera is first used to measure the response of several images projected from the projector. Each image is made of identical input at every projector pixel.
With the projector pixel inputs and the corresponding measured outputs from the camera established, V can be estimated for each pixel by solving a set of overdetermined linear equations. Once V is estimated, V
−1 is applied to the input image to generate the desired response that would look seamless on an imperfect surface. The estimated V is further refined by a continuous feedback and an estimation loop between the projector and the camera. The non-linearities of the projector and the camera are also considered to validate the assumption of linear devices. Greater details of this method are available in . This method has not yet been scaled to displays made of multiple projectors.
E. Camera-Based Compensation for Non-White Surfaces
The methods described so far can be used to compensate for color variation in a multi-projector display when projecting on a white screen. Recent work addresses the issue of using projectors to project on displays that are not necessarily white but have colors and textures, like
All of the approaches discussed in the previous sections have been used and tested in deploying various projector-based display systems. Table I provides a list of representative systems and supporting publication references. Table I lists these systems in chronological
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 13 order based on publication date and itemizes key aspects each system, including the types of display surface, the number of cameras and projectors in the system, geometric and photometric registration approach used, the number of rendering passes required, and targeted viewer mode (stationary vs. moving). Since many approaches are available for different applications and display configurations, we use this section to discuss the positive and negative aspects of the various approaches for geometric and photometric registration.
On the geometric front, restricting the display surface to be planar has many benefits. First, there are more scalable techniques to register very large arrays with sub-pixel accuracy, such as the homography tree approach . In addition, the alignment procedure using a
2D linear homography can be performed in the graphics pipeline, allowing for efficient rendering , . Planar homography-based approaches, however, can correct for only linear geometric distortions. For instance, nonlinear radial distortion introduced by a projector’s optical system cannot be corrected by this method. Yang et al.
 showed that the zoom setting of some projectors affected the radial distortion enough to introduce pixel errors in homography-based approaches. As a result, the projectors usable zoom range had to be fixed to the positions that minimize radial distortion.
The parameterized transfer equation introduced by
Raskar et al.
 extends planar surface algorithms to quadric surfaces. While some screens (i.e., dome and cylindrical screens) can be modelled as quadric surfaces, this requires precise manufacturing. For applications that use cheaper constructed surfaces that do not require head-tracking, it may still be better to use the direct mapping technique (see Section II-B.1) that can compensate for the imperfections in the display surface geometry.
For arbitrary display surfaces, the direct mapping from the camera space to the projector space is a very efficient way to generate seamless images from one fixed view location. The resulting two-pass rendering algorithm compensates for display surface distortion as well as projector lens distortion. For small arrays (4-5 projectors), this approach is very flexible and can allow quick deployment of projector-based displays in a wide range of environments. However, because this technique requires the camera to see the entire display and it is not scalable to large projector arrays.
The technique presented by Raskar et al.  for a moving user and arbitrary display surfaces involves a full 3D modeling of the display environment including the projector positions and display surface geometry.
While this approach is the most general solution to large scale display deployment, it is non-trivial to implement a robust and practical system. Due to its complexity, the best registration error reported so far is about 1-2 pixels.
For correcting the color variation problem, solutions like blending (Section III-C) do not estimate the spatial variation and hence cannot achieve entirely seamless display, especially for large displays. However, for small systems of 2 − 4 projectors, blending can achieve effective results if it is preceded by color balancing across different projectors. This color balancing can be manual or can be automated using gamut matching techniques
(Section III-A). The camera based technique (Section
III-D) can achieve reasonable photometric seamlessness across the display, which is sufficient for displays made of same brand projectors. The advantage of this method lies in its complete automation and scalability. However, the limitation of both gamut matching or photometric uniformity lies in degrading the color quality of the display in terms of dynamic range and color resolution.
Thus, achieving perceptual uniformity (rather than strict photometric uniformity) while maintaining high display quality is the current area of research. Finally, current camera-based correction do not address chrominance variation, arbitrary display geometry or a moving user, which are still active areas of research.
To correct geometric and photometric distortions in a projector-based display requires changes to be made to the desired image, which causes overhead during rendering time. This shortcoming has been ameliorated by recent advances in computer hardware. Modern graphics hardware provides a tremendous amount of image processing power. Thus, many of the correction operations can be off-loaded to the graphics board. The overhead to warp and blend a screen resolution image becomes negligible. In addition, certain correction operations can be integrated into the graphics rendering pipeline, such as the one-pass rendering algorithm for off-axis projection on planar surfaces . These approaches completely eliminate the image correction overhead when rendering 3D contents. With increasing programmability in graphics hardware, we expect that new techniques that leverage the power of programmable graphics hardware will emerge to reduce the rendering overhead in a wide range of configurations.
The need for more flexibility in projector-based displays is also being addressed by projector manufacturers.
Recent projectors are equipped with more options to adjust the projected images. For example, projectors from
EPSON provide automatic keystone correction using a built-in tilt sensor . 3D-Perception CompactView was one of the first companies to offer a projector that
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 14
HARACTERISTICS OF REPRESENTATIVE LARGE
FORMAT DISPLAYS USING CAMERA
Raskar et al. 
Y. Chen et al. 
H. Chen et al. 
Metaverse  iLamp 
Display surfaces arbitrary
♦ planar arbitrary
♥ planar multiple walls
♦ quadric surfaces number of projectors
5 number of cameras one multiple one on PTU one multiple one one/projector
Photometric correction fixed warping full 3D model color attenuation software blending simulated annealing optical blending fixed warping software blending homography tree homography full 3D model optical blending software blending software blending
Rendering passes two three one two one one two
♦ head-tracked moving viewer.
♥ static viewer (image is correct for a fixed location).
performed real-time corrective warping to the incoming video stream . This feature is used to help compensate for projection on smooth, curved surfaces, such as those in video domes. Recently, other projector manufacturers have provided similar options. The Barco Galaxy-WARP projector is also capable of performing real-time corrective warping to the incoming video stream . Both products allow for non-linear image mapping. Thus, a wide range of configurations can be accommodated without incurring any rendering overhead.
Currently, these products allow control of the nonlinear warping via user interfaces. However, it is a matter of time before an interface between the projector and camera-based registration techniques will allow this warping to be specified automatically. With the projectors performing the warping in real-time, performance overhead will not be an issue. This should be a great benefit to the current two-pass rendering algorithms.
Merging this technology with camera-based registration will truly allow a new generation of flexible and highly configurable projector-based display environments.
Camera-based calibration techniques have enabled a much wider range of configurations for projector-based displays. The capability of automatic geometric alignment and photometric correction of multiple projected images eases the setup and reduces the cost of largeformat displays. Coupled with advances in distributed rendering software and graphics hardware, the possibility of creating inexpensive and versatile large format displays using off-the-shelf components becomes a reality.
It is our hope that the information provided in this survey will provide projector-based display users a useful guide to the currently available techniques and their associated advantages and disadvantages.
Looking forward, there are a number of research topics that can further advance the state of the art.
a) Geometric Registration Quality: Registration quality is often reported as pixel registration accuracy in local overlapped regions and not in the context of the global display coordinate frame. Moreover, using the pixel as a unit of measure is ill-defined when imagery is projecting on arbitrary display surfaces or contributing projector pixels are not uniform in size. Better metrics and analytical approaches are needed to fully evaluate overall registration accuracy.
b) Color Correction: The shortcoming of the automated color correction method presented here is the severe degradation in image quality. Methods should be devised that optimize the available resources in terms of brightness and contrast of the display and achieve perceptual uniformity, which may not require strict photometric uniformity. Also, only the problem of spatial photometric variation has been addressed while assuming that most current displays have negligible chrominance variation. However, when using different model projectors, the chrominance variation cannot be ignored.
Finally, arbitrary 3D display surfaces with arbitrary reflectance properties for moving users is still to be addressed.
c) Image Resampling: Most of the geometric correction techniques involved a resampling of an original rendered image. How this resampling affects the overall resolution of the display and ways to avoid fidelity loss need to be addressed.
d) Continuous Calibration: Almost all camerabased techniques treat the calibration procedure as a preprocessing routine. The correction function derived from the calibration information remains fixed until the next calibration. During the normal operation of a display system, however, there are many factors that affect the validity of the calibration, such as vibrations, electronic
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. X, MONTH YEAR 15 drift, aging of projector light bulbs, or even transient events such as temporary occlusion of projector light. To deal with these problems, techniques could be developed to continuously monitor the projected imagery and correct any undesired distortions online. Promising works, such as continuous monitoring of display surfaces  and shadow removal , ,  have demonstrated the potential of this research area.
e) Display and User Interaction: The real-time feedback of cameras in the display environment make it possible to develop interaction techniques between the user and the display. For example, laser pointer interaction inside a camera-registered displays can be easily realized , . Significantly more ambitious goals have been set forth in UNC’s Office of the Future project  and Gross et al’s  blue-c system.
These systems aim to provide immersive 3D telecommunication environments where cameras capture realtime 3D information of users inside the display. The tightly coupled relationship between the camera and display environment offers great potential for novel user interaction metaphors within such environments.
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Michael Brown received his B.Eng. and PhD degrees, both in Computer Science, from the
University of Kentucky in 1995 and 2001, respectively. he was a visiting PhD student at the University of North Carolina at Chapel
Hill from 1998-2000. In 2001, he joined the
Computer Science faculty at the Hong Kong
University of Science and Technology. His research interests include, image processing and computer graphics.
Aditi Majumder is an Assistant Professor at the Department of Computer Science in University of California, Irvine. She received her
BE in Computer Science and Engineering from
Jadavpur University, Calcutta, India in 1996 and PhD from Department of Computer Science, University of North Carolina at Chapel
Hill in 2003.
Her research focuses large area displays, computer graphics and vision, image processing and human computer interaction. Her significant contributions include development of photometric vision techniques that use limitation of human perception to achieve seamless high-quality multi-projector displays and geometric registration of images from multi-camera sensors to create real-time panoramic video for immersive teleconferencing.
Ruigang Yang is an Assistant Professor in the
Computer Science Department at the University of Kentucky. He received his Ph.D. degree in Computer Science from University of North
Carolina at Chapel Hill in 2003. Prior to coming to UNC-Chapel Hill, he earned a M.S.
degree in Computer Science from Columbia
University in 1998.
Dr. Yang’s research interests include computer graphics, computer vision, and multimedia. He is a member of the IEEE Computer Society and ACM.
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