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Lecture 18: Single-view modeling, Part 2

CS4670 / 5670 : Computer Vision. Noah Snavely. Lecture 18: Single-view modeling, Part 2. Announcements. Project 3 due this Thursday by 11:59pm Demos on Friday (?) Project 3 artifacts due this Friday by 11:59pm Take-home prelim out Friday, due Wednesday 10/24 by the beginning of class

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Lecture 18: Single-view modeling, Part 2

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  1. CS4670 / 5670 : Computer Vision Noah Snavely Lecture 18: Single-view modeling, Part 2

  2. Announcements • Project 3 due this Thursday by 11:59pm • Demos on Friday (?) • Project 3 artifacts due this Friday by 11:59pm • Take-home prelim out Friday, due Wednesday 10/24 by the beginning of class • Please don’t post on Piazza about the prelim, just email the staff

  3. Quiz from last time • How do you compute the image-space line l passing through two points p and q? • How do you compute the image-space point p at the intersection of two lines l and m?

  4. Comparing heights Vanishing Point

  5. Measuring height 5.4 5 Camera height 4 3.3 3 2.8 2 1 How high is the camera?

  6. Measuring height without a ruler

  7. Measuring height without a ruler Z C ground plane • Compute Z from image measurements • Need more than vanishing points to do this

  8. The cross ratio • A Projective Invariant • Something that does not change under projective transformations (including perspective projection) The cross-ratio of 4 collinear points P4 P3 P2 P1 • Can permute the point ordering • 4! = 24 different orders (but only 6 distinct values) • This is the fundamental invariant of projective geometry

  9. scene cross ratio C image cross ratio Measuring height  T (top of object) t r R (reference point) H b R B (bottom of object) vZ ground plane scene points represented as image points as

  10. Measuring height t v H image cross ratio vz r vanishing line (horizon) t0 vx vy H R b0 b

  11. v t1 b0 b1 Measuring height vz r t0 vanishing line (horizon) t0 vx vy m0 b • What if the point on the ground plane b0 is not known? • Here the guy is standing on the box, height of box is known • Use one side of the box to help find b0 as shown above

  12. 3D Modeling from a photograph St. Jerome in his Study, H. Steenwick

  13. 3D Modeling from a photograph

  14. 3D Modeling from a photograph Flagellation, Piero della Francesca

  15. 3D Modeling from a photograph video by Antonio Criminisi

  16. 3D Modeling from a photograph

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