Cameras and Projectors

1. Cameras and Projectors Hao Jiang Computer Science Department Boston College Oct. 2, 2007 CS335 Principles of Multimedia Systems

2. Cameras and Projectors • Cameras and projectors have been intensively used in many different multimedia applications. • It is important to understand techniques to manipulate these devices. • We will study basic methods about • calibration, • image warping and blending, • and other issues in building a camera/projector system. CS335 Principles of Multimedia Systems

3. Example Application: Projector Geometry Distortion Compensation Automatically correcting projector geometry distortion using a camera and projector system. CS335 Principles of Multimedia Systems

4. Camera / Projector Geometry Model • Camera and projector can be modeled as a pinhole imaging system. Object Point Optical Center Focal length Optical axis Image point Image Plane CS335 Principles of Multimedia Systems

5. Camera Geometry Model • A camera projects a 3D point onto a 2D point in a image. y x 3D point (X, Y, Z) in camera’s frame is (X’,Y’,Z’) (Ox, Oy) f x = (f X’/Z’)/dx + Ox = fx X’/Z’ + Ox y = (f Y’/Z’)/dy + Oy = fy Y’/Z’ + Oy dx and dy are width and height of an image pixel CS335 Principles of Multimedia Systems

6. Homogenous Coordinate • The homogenous coordinate of a 3D point (x,y,z) is (X,Y,Z,W) where X/W = X, Y/W=Y and Z/W=Z. • The homogenous coordinate of a 2D point (x,y) is (X,Y,W) where X/W = x, Y/W=Y. • We can convert a 3D point from one frame to another, by simply T*P, where T is a 4x4 matrix and P is the homogeneous coordinate of the 3D point. CS335 Principles of Multimedia Systems

7. Camera Matrix • Using homogenous coordinate, the camera projection can be represented as X a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 x Y P = A3x4 = A P p = ~ y Z w W A3x4 is a 3 rows and 4 columns matrix, called Where camera matrix. CS335 Principles of Multimedia Systems

8. Projection from a Plane to Another Plane Z X Y P p Since p = A P We have O a11 a12 a14 a21 a22 a24 a31 a32 a34 x y w X Y 1 = ~ p = H p’ H is defines a Homography. CS335 Principles of Multimedia Systems

9. The Projector Model • Projector shares similar model with a camera. • The only difference is that a projector projects a flat object that emits lights based on a computer image onto an image plane, the screen. • Based on the previous analysis about planar object projection, the image from the computer and the one projected on the screen are related by a homography. CS335 Principles of Multimedia Systems

10. The Camera-Projector System r H2*r H1*p Image on the screen q p H2*H1*p Camera image Image sent to projector CS335 Principles of Multimedia Systems

11. Calibration • We would like to compute H1 and H2. • We project marker points on the screen and form equations a11Xn + a12Yn + a14 a31Xn + a32Yn + a34 a21Xn + a22Yn + a24 a31Xn + a32Yn + a34 = xn n = 1 .. N = yn a34=1 CS335 Principles of Multimedia Systems

12. Image Adjustment (I) Image on the screen Assume that the viewer is close to the camera. H2*H1*p H1*p q p The desired Image. Pre-warping Camera image Projector image Each p is projected to the camera image and the color is determined by color interpolation in the desired image. CS335 Principles of Multimedia Systems

13. Image Adjustment (II) Image on the screen The desired image Estimate H2 using screen corners projections. H2*H1*p H1*p Pre-warping Camera image Project image Pre-warp image based on the desired image on the screen. CS335 Principles of Multimedia Systems

14. Projection onto Arbitrary Surfaces • We have learned how to deal with projector distortion using a planar screen. • We can extend the method into other types of surfaces, such as cylinder or spheres. • We need a relative dense mesh grid to capture the local deformation model. CS335 Principles of Multimedia Systems

15. Titled Large Screen Display CS335 Principles of Multimedia Systems

16. Titled Large Screen Display • LCD or CRT are still not easy to be made as large as a wall. • Titling multiple projector images into a large screen display is flexible and relatively cheap. • The shortcoming is we need to align the images from different projectors in both geometry and color. • Manually adjusting the projectors is a tedious task. • Camera project system can be used to solve the problem. CS335 Principles of Multimedia Systems

17. Titled Images 3 2 4 Calibration Patterns 1 (Projector to Camera Homography can be computed based on these patterns) 6 7 8 5 9 11 10 12 Projector images The camera view CS335 Principles of Multimedia Systems

18. Large Screen Projection projector image 3 p pcamera = Hqprojector 3 2 4 The big image q 1 6 7 8 5 9 11 10 12 Projector images The camera view CS335 Principles of Multimedia Systems

19. Edge and Color Alignment • Colors of different projectors are usually different. A color calibration and adjustment procedure is needed. • Blending Color(p) = a Color(2,p) + (1-a)Color(3,p) 3 2 p a is determined by the dominance of 2 or 3. CS335 Principles of Multimedia Systems

20. Blending • The size of the blending region has to be carefully selected • If the region is too small, large scale structures will show abrupt changes. If it is too big, small structures (edges, dots) will overlap in a big region and therefore will result in blur (ghost) images. a 1-a Blending region CS335 Principles of Multimedia Systems

21. Multi-band Blending • Multi-band blending can be used to address the problem. • In multi-band blending, • images are filtered into different bands. • The mask is also low-pass filtered to generate mask for each band images. • Images are blending in each channel. • The blended images are summed up to get the final result. CS335 Principles of Multimedia Systems

22. Image Pyramids The Gaussian Pyramid CS335 Principles of Multimedia Systems

23. Image Pyramids The Laplacian Pyramid CS335 Principles of Multimedia Systems

24. Image Pyramids The Gaussian pyramid of the mask CS335 Principles of Multimedia Systems

25. Multi-band Blending Multi-band blending CS335 Principles of Multimedia Systems

26. Multi-band Blending CS335 Principles of Multimedia Systems

27. System Issues of Large Screen Display • Large screen projection needs multiple projectors working simultaneously. • The first structure uses share memory system such as SGI Oynx2, thatemploys a shared-memory model. A single program can have different threads writing OpenGL primitives into different pipes while reading from a single shared database and synchronizing display update over shared flags. • The second structure is PC cluster, in which each PC handles one projector. This framework is much cheaper but the synchronization is a challenge problem. CS335 Principles of Multimedia Systems

28. Applications • Visualization and Collaboration IEEE Computer Graphics and Applications, 2000 CS335 Principles of Multimedia Systems

29. Immersive Reality • The CAVE (University of Illinois at Chicago) IEEE Computer Graphics and Applications, 2000 CS335 Principles of Multimedia Systems

30. Projection for Augmented Environment Anton Treskunov and Jarrell Pair, PROJECTOR-CAMERA SYSTEMS FOR IMMERSIVE TRAINING, ASC06 CS335 Principles of Multimedia Systems

31. Input Methods for Large Screens • It presents challenges for traditional input methods. • Possible HCI methods include: • Pointing devices, including 3D tracking, passive optical (video) tracking, ultrasonic tracking, mice, and tablet interfaces; • User tracking, for point-of-view rendering or for gaze directed interaction, via optical tracking or electromagnetic tracking; • Handheld devices, providing control interfaces that can be out of band from the display; • Voice commands with audio feedback; • And haptics interfaces. CS335 Principles of Multimedia Systems

32. Multiple Camera System • Multiple camera system can capture video from different locations simultaneously. • Stereo system has been widely used for inferring the “depth” of objects. CS335 Principles of Multimedia Systems

33. 3D reconstruction from Multiple Views CS335 Principles of Multimedia Systems

34. Application of Multi-camera Imaging • Image based rendering • The Matrix CS335 Principles of Multimedia Systems

35. Cameras in the Matrix CS335 Principles of Multimedia Systems

36. Camera Calibration Toolboxes • OpenCV • Matlab Calibration Toolbox • http://www.vision.caltech.edu/bouguetj/calib_doc/ • Multiple Camera Calibration • http://cmp.felk.cvut.cz/~svoboda/SelfCal/ CS335 Principles of Multimedia Systems