Computer Vision and Machine Learning Winter School ENS Lyon 2010 Camera geometry and image alignment Josef Sivic http://www.di.ens.fr/~josef INRIA, WILLOW, ENS/INRIA/CNRS UMR 8548 Laboratoire d’Informatique, Ecole Normale Supérieure, Paris With slides from: O. Chum, K. Grauman, S. Lazebnik, B. Leibe, D. Lowe, J. Philbin, J. Ponce, D. Nister, C. Schmid, N. Snavely, A. Zisserman Outline Part I - Camera geometry – image formation •  Perspective projection •  Affine projection •  Projection of planes Part II - Image matching and recognition with local features •  Correspondence •  Semi-local and global geometric relations •  Robust estimation – RANSAC and Hough Transform Motivation: Stitching panoramas Feature-based alignment outline Feature-based alignment outline Extract features Feature-based alignment outline Extract features Compute putative matches Feature-based alignment outline Extract features Compute putative matches Loop: •  Hypothesize transformation T (small group of putative matches that are related by T) Feature-based alignment outline Extract features Compute putative matches Loop: •  Hypothesize transformation T (small group of putative matches that are related by T) •  Verify transformation (search for other matches consistent with T) Feature-based alignment outline Extract features Compute putative matches Loop: •  Hypothesize transformation T (small group of putative matches that are related by T) •  Verify transformation (search for other matches consistent with T) 2D transformation models Similarity (translation, scale, rotation) Affine Projective (homography) Why these transformations ???