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Advanced Computer Vision

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Advanced Computer Vision ... The 3D positions of the corresponding scene points in some fixed coordinate ... Active vision system: robot probes. – PowerPoint PPT presentation

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Title: Advanced Computer Vision


1
Advanced Computer Vision
  • Structure from Motion

2
Structure from Motion
  • Geometric structure-from-motion problem using
    image matches to estimate
  • The 3D positions of the corresponding scene
    points in some fixed coordinate (the scene
    structure)
  • The projection matrices associated with the
    camera observing them (the motion of the points
    relative to the cameras)


3
Two Types
  • Affine structure from motion
  • Projective structure from motion

4
Basic Assumption
  • The cameras positions and possibly their
    intrinsic parameters are a priori unknown and may
    change over time.
  • Different from, say, stereopsis, where the camera
    parameters are known so we can focus on the
    correspondence problem.
  • Ignore the correspondence problem, assuming that
    the projections of n points have been matched
    across m pictures.

5
Applications
  • Image-based rendering a video clip recorded by a
    hand-held camcorder, possibly zooming during the
    shoot, is used to capture the shape of an object
    and render it under new viewing conditions.
  • Active vision system robot probes.

6
Affine Structure from Motion
2mn equations in 8m3n unknowns
Overconstrained problem, that can be solved using
(non-linear) least squares!
7
Ambiguity of Solution

So are M and P where
i
j
and
Q is an affine transformation.
8

The Projective Structure-from-Motion Problem
Given m perspective images of n fixed points P
we can write
j
2mn equations in 11m3n unknowns
Overconstrained problem, that can be solved using
(non-linear) least squares!
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