Stereo Vision

Egon ElbreHans Mäesalu

general stuff about this 3D thing

why?

applications

gamesmoviessimulatorsroboticsproduct presentationsarchitecture visualizationvirtual television studiosvirtual presence for video communicationsgeneral virtual reality applications

Single-View Geometry

orthographic projection

perspective projection

IRL

simple camera projection

just think of it as magic

extrinsic/intrinsic camera calibration matrix

finding 3D point with triangulation

assuming we know where the cameras are

finding a depth map

image rectification

finding matchingpoints simpler

rectification gives us

step 1 - get the pictures

step 2 - find some interesting points

step 3 - guess similar points

step 4 - remove outliers (RANSAC)

RANSACRANdom SAmpling Consensus

rectify

disparity map

demo video

Introduction to Epipolar Geometry

terminology

F(undamental)-matrix

E(ssential)-matrix

and finally...

reconstruction from two views only

1. identify a number (at least 8) of point correspondences2. form linear equations based on x'TFx=0 formula3. find the solution F for those equations4. compute P, P' camera matrices from F5. given to cameras P, P' and corresponding point pairs

triangulate the 3D point X

we know how to do 1 and 5we won't discuss 2, 3 as it's about solving some linear equations and no one will remember it after the lecture anywayabout 4 - well that's complicated

note! can't be done uniquely due to some ambiguity

further reading

"Multiple View Geometry in Computer Vision", Richard Hartley and Andrew Zisserman"Uncertain Projective Geometry: Statistical Reasoning for Polyhedral Object Reconstruction", Stephan Heuel"Computer Vision: Algorithms and Applications", Richard Szelinski"Learning OpenCV", Gary Bradski and Adrian Kaehler