# Advanced Computer Vision - PowerPoint PPT Presentation

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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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1
• 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!