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Image alignment

Image alignment. Image from http://graphics.cs.cmu.edu/courses/15-463/2010_fall/. A look into the past. http://blog.flickr.net/en/2010/01/27/a-look-into-the-past/. A look into the past. Leningrad during the blockade. http://komen-dant.livejournal.com/345684.html. Bing streetside images.

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Image alignment

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  1. Image alignment Image from http://graphics.cs.cmu.edu/courses/15-463/2010_fall/

  2. A look into the past http://blog.flickr.net/en/2010/01/27/a-look-into-the-past/

  3. A look into the past • Leningrad during the blockade http://komen-dant.livejournal.com/345684.html

  4. Bing streetside images http://www.bing.com/community/blogs/maps/archive/2010/01/12/new-bing-maps-application-streetside-photos.aspx

  5. Image alignment: Applications Panorama stitching Recognitionof objectinstances

  6. Image alignment: Challenges Small degree of overlap Intensity changes Occlusion,clutter

  7. Image alignment • Two families of approaches: • Direct (pixel-based) alignment • Search for alignment where most pixels agree • Feature-based alignment • Search for alignment where extracted features agree • Can be verified using pixel-based alignment

  8. Alignment as fitting • Previous lectures: fitting a model to features in one image M Find model M that minimizes xi

  9. xi xi ' T Alignment as fitting • Previous lectures: fitting a model to features in one image • Alignment: fitting a model to a transformation between pairs of features (matches) in two images M Find model M that minimizes xi Find transformation Tthat minimizes

  10. 2D transformation models • Similarity(translation, scale, rotation) • Affine • Projective(homography)

  11. Let’s start with affine transformations • Simple fitting procedure (linear least squares) • Approximates viewpoint changes for roughly planar objects and roughly orthographic cameras • Can be used to initialize fitting for more complex models

  12. Fitting an affine transformation • Assume we know the correspondences, how do we get the transformation?

  13. Fitting an affine transformation • Linear system with six unknowns • Each match gives us two linearly independent equations: need at least three to solve for the transformation parameters

  14. Fitting a plane projective transformation • Homography: plane projective transformation (transformation taking a quad to another arbitrary quad)

  15. Homography • The transformation between two views of a planar surface • The transformation between images from two cameras that share the same center

  16. Application: Panorama stitching Source: Hartley & Zisserman

  17. Fitting a homography • Recall: homogeneous coordinates Converting fromhomogeneousimage coordinates Converting tohomogeneousimage coordinates

  18. Fitting a homography • Recall: homogeneous coordinates • Equation for homography: Converting from homogeneousimage coordinates Converting to homogeneousimage coordinates

  19. Fitting a homography • Equation for homography: 3 equations, only 2 linearly independent

  20. Direct linear transform • H has 8 degrees of freedom (9 parameters, but scale is arbitrary) • One match gives us two linearly independent equations • Four matches needed for a minimal solution (null space of 8x9 matrix) • More than four: homogeneous least squares

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