← Parminces
Hartley & Zisserman, 2nd Edition (2003)

Multiple View Geometry
in Computer Vision

The definitive reference on projective geometry for vision, rebuilt chapter by chapter as interactive lessons. From homogeneous coordinates to auto-calibration, with live simulations at every step.

16
Chapters
60+
Simulations
100+
Quizzes
Part 0: Background — Projective Geometry, Transformations & Estimation
Chapter 1

A Tour of Multiple View Geometry

Projective geometry everywhere, camera projections, reconstruction from views, the big picture.

Chapter 2

Projective Geometry & Transformations of 2D

Homogeneous coordinates, points, lines, conics, transformation hierarchy, the line at infinity.

Chapter 3

Projective Geometry & Transformations of 3D

Planes, lines, quadrics in 3-space, the plane at infinity, the absolute conic.

Chapter 4

Estimation — 2D Projective Transformations

DLT algorithm, cost functions, MLE, normalization, RANSAC robust estimation.

Chapter 5

Algorithm Evaluation & Error Analysis

Performance bounds, covariance estimation, Monte Carlo methods, MLE residuals.

Part I: Camera Geometry & Single View Geometry
Chapter 6

Camera Models

Pinhole model, calibration matrix K, finite cameras, projective cameras, cameras at infinity.

Chapter 7

Computation of the Camera Matrix P

DLT for cameras, geometric error, restricted estimation, radial distortion.

Chapter 8

More Single View Geometry

Vanishing points, vanishing lines, camera calibration from a single view, IAC.

Part II: Two-View Geometry
Chapter 9

Epipolar Geometry & the Fundamental Matrix

Epipoles, epipolar lines, the fundamental matrix F, the essential matrix E, special motions.

Chapter 10

3D Reconstruction of Cameras & Structure

Projective reconstruction theorem, stratified reconstruction, reconstruction ambiguity.

Chapter 11

Computation of the Fundamental Matrix F

8-point algorithm, normalization, RANSAC for F, degeneracies, image rectification.

Chapter 12

Structure Computation — Triangulation

Linear triangulation, geometric error, optimal triangulation, line reconstruction.

Chapter 13

Scene Planes & Homographies

Plane-induced homographies, computing F from homography, the infinite homography.

Part III & IV: Three-View & N-View Geometry
Chapter 15

The Trifocal Tensor

Line incidence, point transfer, tensor notation, fundamental matrices from three views.

Chapter 18

N-View Computational Methods

Bundle adjustment, factorization algorithm, projective factorization, sequence reconstruction.

Chapter 19

Auto-Calibration

Absolute dual quadric, Kruppa equations, stratified self-calibration, rotating cameras.