Day 1 how do we represent the shape around us? course outline motivation for gathering geometry from multiple images –our eyes are two views –structure.

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Presentation transcript:

Day 1 how do we represent the shape around us? course outline motivation for gathering geometry from multiple images –our eyes are two views –structure from motion: Pollefeys Medusa mask video –sfm and camera positions: UW phototourism video –(Boujou) Reading: HZ Chapter 1; Pollefeys and Van Gool ‘From Images to 3D Models’, CACM 2002 (see website) pop quiz (for projective geometry): what is the implicit equation of the line through the points (1,2) and (3,4)? what is the intersection point of the two lines 5x+y=2 and x-2y=1?

Day 1 diagram Projective geometry quiz UW/Szeliski Phototourism video Pollefeys Medusa video Course outline Reading: HZ Ch 1 + Polle CACM

Major topics everything is about matrices projective geometry (2d and 3d) –how are points and lines encoded for simplicity of computation? what aspects of shape are preserved under imaging? how are conics and quadrics represented? how are tangents represented? how is shape at infinity encoded, for consistency of implementation? behaviour at infinity is crucial for calibration fundamental matrix –encodes epipolar geometry and 2-view geometry trifocal tensor –encodes three-view geometry camera matrix –encodes camera geometry auto-calibration with image of absolute conic –for metric reconstruction bundle adjustment –for more than 3 images and removing noise in some of the images