Notes
Slide Show
Outline
1
Announcements
  • Project 1 artifact voting (email announce later today)
  • Project 2 out today (help session at end of class)
  • IMPORTANT:  choose Proj 2 partner and SIGNUP for panorama equip TODAY:
    • http://www.cs.washington.edu/htbin-post/admin/preserve.cgi/www/htdocs/education/courses/cse576/panorama
2
Mosaics
  • Today’s Readings
    • R. Szeliski and H.-Y. Shum. Creating full view panoramic image mosaics and texture-mapped models, Computer Graphics (SIGGRAPH'97), pages 251-258, August 1997
    • J. F. Blinn, Jim Blinn's Corner: Compositing, Part 1: Theory, IEEE Computer Graphics and Application, 14(5), Sept. 1994, pp 83-87
3
Image Mosaics



  •    +        +   …   + =
4
How to do it?
  • Basic Procedure
    • Take a sequence of images from the same position
      • Rotate the camera about its optical center
    • Compute transformation between second image and first
      • Lucas & Kanade registration
    • Shift the second image to overlap with the first
    • Blend the two together to create a mosaic
    • If there are more images, repeat


5
Aligning images
  • How to account for warping?
    • Translations are not enough to align the images
    • Photoshop demo
6
Image reprojection
  • The mosaic has a natural interpretation in 3D
    • The images are reprojected onto a common plane
      • idea:  replace camera with slide projector, project onto new PP
    • The mosaic is formed on this plane
7
Image reprojection
  • Basic question
    • How to relate two images from the same camera center?
      • how to map a pixel from PP1 to PP2
8
Image reprojection
  • Observation
    • Rather than thinking of this as a 3D reprojection, think of it as a 2D image warp from one image to another
9
Homographies
  • Perspective projection of a plane
    • Lots of names for this:
      • homography, texture-map, colineation, planar projective map
    • Modeled as a 2D warp using homogeneous coordinates
10
Image warping with homographies


11
Panoramas
  • What if you want a 360° field of view?
12
Cylindrical projection
    • Map 3D point (X,Y,Z) onto cylinder
13
Cylindrical reprojection
  • How to map from a cylinder to a planar image?
14
Cylindrical reprojection
  • Map image to cylindrical coordinates
    • need to know the camera focal length
15
Cylindrical panoramas
  • Steps
    • Reproject each image onto a cylinder
    • Blend
    • Output the resulting mosaic
16
Cylindrical image stitching
  • What if you don’t know the camera rotation?
    • Solve for the camera rotations
      • Note that a rotation of the camera is a translation of the cylinder!
      • Use Lukas-Kanade to solve for translations of cylindrically-warped images
17
Full-view Panorama
18
Different projections are possible
19
Project 2 (out today)
  • Take pictures on a tripod (or handheld)
  • Warp to cylindrical coordinates
  • Automatically compute pair-wise alignments
  • Correct for drift
  • Blend the images together
  • Crop the result and import into a viewer
20
Image Blending
21
Feathering
22
Effect of window size
23
Effect of window size
24
Good window size
25
Pyramid blending
26
Image warping
  • Given a coordinate transform (x’,y’) = h(x,y) and a source image f(x,y), how do we compute a transformed image g(x’,y’) = f(h(x,y))?
27
Forward warping
  • Send each pixel f(x,y) to its corresponding location
  •            (x’,y’) = h(x,y) in the second image
28
Forward warping
  • Send each pixel f(x,y) to its corresponding location
  •            (x’,y’) = h(x,y) in the second image
29
Inverse warping
  • Get each pixel g(x’,y’) from its corresponding location
  •            (x,y) = h-1(x’,y’) in the first image
30
Inverse warping
  • Get each pixel g(x’,y’) from its corresponding location
  •            (x,y) = h-1(x’,y’) in the first image
31
Forward vs. inverse warping
  • Q:  which is better?


  • A:  usually inverse—eliminates holes
    • however, it requires an invertible warp function—not always possible...
32
Other types of mosaics
  • Can mosaic onto any surface if you know the geometry
    • See NASA’s Visible Earth project for some stunning earth mosaics
      • http://earthobservatory.nasa.gov/Newsroom/BlueMarble/
33
Path Images
34
Pushbroom image
35
Cyclograph
36
Some path image references
  • Manifold mosaics:
    • S. Peleg and J. Herman. Panoramic mosaics by manifold projection. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 997, pp. 338-343,(extended version in PAMI 2000)
      • http://www.cs.huji.ac.il/labs/vision/papers/cvpr97-manifold.pdf
  • Stereo Panoramas
    • S. Peleg, Y. Pritch, and M. Ben-Ezra, Cameras for Stereo Panoramic Imaging, CVPR'00, 2000, pp. 208-214.
      • http://www.cs.huji.ac.il/~peleg/papers/cvpr00-stereocamera.pdf
    • S. M. Seitz and J. Kim, The Space of All Stereo Images, Proc. Intl. Conf. on Computer Vision (ICCV) , 2001, pp. 307-314.
      • http://grail.cs.washington.edu/projects/stereo/
  • Concentric Mosaics
    • H.-Y. Shum and L.-W. He, Rendering with concentric mosaics, Proc.  SIGGRAPH, 1999, pp. 299—306.
      • http://www.research.microsoft.com/users/lhe/papers/cm-siggraph99.pdf