07 homogencoord

07 homogencoord - Projective geometry 2D Acknowledgements...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Spring 2006 Projective Geometry 2D Projective geometry- 2D Acknowledgements Marc Pollefeys: for allowing the use of his excellent slides on this topic http://www.cs.unc.edu/~marc/mvg/ Richard Hartley and Andrew Zisserman, " Multiple View Geometry in Computer Vision " Wednesday, February 3, 2010
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
..to map one 3D “plane” to “another 3D plane” Homography Wednesday, February 3, 2010
Image of page 2
y [pixels] x [pixels] ! 253 ! 55 143 342 540 738 936 1135 1333 1531 ! 94 ! 15 64 144 223 302 381 461 540 619 Wednesday, February 3, 2010
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image Alignment ! 45 31 107 183 259 336 412 488 564 640 ! 178 ! 105 ! 32 41 114 188 261 334 407 480 Wednesday, February 3, 2010
Image of page 4
Wednesday, February 3, 2010
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
http://thebrain.mcgill.ca / Mapping from retina to visual cortex ..in perspective Wednesday, February 3, 2010
Image of page 6
http://thebrain.mcgill.ca / left eye Wednesday, February 3, 2010
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Projective Geometry 2D How? Compute the keypoints Construct a description of these keypoints (including location information). E.g., a SIFT descriptor Match a set of keypoints from one image to a set of points from the other image. you need a matching criterion. Example: use Euclidean distance in the 128-dimensional feature space. prune the matches based on a model. Example. use the homography model. Using the matched points, compute the model parameters reproject, align, and blend the images together to create a larger panorama. 8 Wednesday, February 3, 2010
Image of page 8
Projective Geometry 2D This lecture we learn about such geometric projection models begin with homogeneous representation of points in space projective space and the homography model .. and more. 9 Wednesday, February 3, 2010
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Projective Geometry 2D 10 Homogeneous coordinates Homogeneous representation of lines equivalence class of vectors, any vector is representative Set of all equivalence classes in R 3 (0,0,0) T forms P 2 Wednesday, February 3, 2010
Image of page 10
Projective Geometry 2D 10 Homogeneous coordinates Homogeneous representation of lines equivalence class of vectors, any vector is representative Set of all equivalence classes in R 3 (0,0,0) T forms P 2 Homogeneous representation of points on if and only if Wednesday, February 3, 2010
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Projective Geometry 2D 10
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern