Multiple View Geometry and Geometric Reconstruction Problems

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Multiple View Geometry andGeometric
Reconstruction Problems

• Given images, reconstruct
• Scene geometry (structure)
• Camera positions (motion)

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X
x1
x2
x3
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Problem Formulation
Cost function Geometrically statistically
meaningful
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Sublevel set is convex function is quasi-convex
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Direction (unit) vectors from cameras (blue) to
points (black) are given Find the positions of
the cameras and points.
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This does not happen in strictly quasi-convex
optimization problems.
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Further Example of Quasi-Convex
Optimization Flexible Object Tracking Joint
work with Mathieu Salzman (Lausanne)
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More Examples