BibTeX entry

@PHDTHESIS{200205Bin_Luo,
  AUTHOR={Bin Luo},
  TITLE={Statistical Methods for Point Pattern Matching},
  SCHOOL={University of York},
  MONTH=May,
  YEAR=2002,
  URL={http://www.bmva.org/theses/2002/2002-luo.pdf},
}

Abstract

Point pattern matching is a topic of pivotal importance in computer vision. Its applications can be found in many areas such as pose estimation, stereo matching, three-dimensional reconstruction and motion tracking. There are two kinds of point pattern matching technique. Alignment aims to estimate the transformation parameters. Correspondence is concerned with point labelling. In this thesis, we aim to develop a unified statistical framework to solve the point set alignment and correspondence problems. The starting point is to develop a robust corner detector which extracts features which can be used to represent salient image structure. We choose corners as the feature points for matching in this thesis since they are the dominant ones in many types of images. Based on a magneto-static analogy of images, we demonstrate that corners are located at the saddle points of the magnitude of the vector potential. We describe a template-based method for locating the saddle-points. The second contribution is to cast the problem of point-set alignment via Procrustes analysis is cast into a maximum framework using the EM algorithm. The aim is to improve the robustness of Procrustes alignment to noise and clutter. By constructing a Gaussian mixture model over the missing correspondences between individual points, we show how alignment can be realised by applying singular value decomposition to a weighted point correlation matrix. The method can be used to match unlabelled point-sets of different size. We extend the method to non-rigid transformations using point distributions models. The point distribution models can then be aligned to incomplete point-sets when prior knowledge concerning point correspondence is unknown. Since this is a problem posed in terms of hidden variables (the correspondences), we couch the recovery of maximum likelihood alignment parameters using the apparatus of the EM algorithm. Thirdly, we show how point correspondence matching may be realised using a relational graph matching process. We make two novel contributions. Commencing from a probability distribution for matching errors, we show how a problem of graph- matching can be posed as a maximum likelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph-nodes in a matrix framework. Here we demonstrate that the method offers comparable performance advantages over more computationally demanding methods. Finally, a unified matching framework is developed which integrates both point set alignment and correspondence. The utility measure underpinning the work is the cross-entropy between probability distributions for alignment and correspondence assignment errors. We show how alignment parameters and correspondence probabilities can be located using dual singular value decompositions.