Overview Introduction to projective geometry I view geometry(calibration,.) 2-view geometry(stereo, motion,.) 3-and N-view geometr Autocalibration(metric reconst Application
6 Overview • Introduction to projective geometry • 1 view geometry (calibration, …) • 2-view geometry (stereo, motion, …) • 3- and N-view geometry • Autocalibration (metric reconst.) • Application
Basic geometric concepts to understand Affine Euclidean geometries (inhomogeneous coordinates) projective geometry(homogeneous coordinates) plane at infinity: attine geometry absolute conic: Euclidean geometry
7 Basic geometric concepts to understand • Affine, Euclidean geometries (inhomogeneous coordinates) • projective geometry (homogeneous coordinates) • plane at infinity: affine geometry • absolute conic: Euclidean geometry
Introduction to projective geometry Intuitive ideas from projective geometr (Formal definition of projective spaces)
8 Introduction to projective geometry • Intuitive ideas from projective geometry • (Formal definition of projective spaces)
Intuitive introduction R E=A WIth dot prod A P=R+pts at inf Naturally everything starts from the known vector space add two vector multiply any vector by any scalar zero vector - origin finite basis
9 with dot prod. n n E = A pts at inf. n n A n P = R + n R Naturally everything starts from the known vector space • add two vectors • multiply any vector by any scalar • zero vector – origin • finite basis Intuitive introduction
Vector space to affine: isomorph, one-to-one Pts, lines, parallelism vector to Euclidean as an enrichment: scalar prod Angle, distances, circles affine to projective as an extension add ideal elements Pts at infinity
10 • Vector space to affine: isomorph, one-to-one • vector to Euclidean as an enrichment: scalar prod. • affine to projective as an extension: add ideal elements Pts, lines, parallelism Angle, distances, circles Pts at infinity