A new graph matching method for point-set correspondence using the EM algorithm and Softassign

  • Authors:

  • Gerard Sanromí;René Alquézar;Francesc Serratosa

  • Affiliations:

  • Departament d'Enginyeria Informítica i Matemítiques, Universitat Rovira i Virgili, Av. Països Catalans, 26 Campus Sescelades, 43007 Tarragona, Spain;Institut de Robòtica i Informítica Industrial, CSIC-UPC, Parc Tecnològic de Barcelona, C/Llorens i Artigas 4-6, 08028 Barcelona, Spain;Departament d'Enginyeria Informítica i Matemítiques, Universitat Rovira i Virgili, Av. Països Catalans, 26 Campus Sescelades, 43007 Tarragona, Spain

  • Venue:
  • Computer Vision and Image Understanding
  • Year:
  • 2012

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Abstract

Finding correspondences between two point-sets is a common step in many vision applications (e.g., image matching or shape retrieval). We present a graph matching method to solve the point-set correspondence problem, which is posed as one of mixture modelling. Our mixture model encompasses a model of structural coherence and a model of affine-invariant geometrical errors. Instead of absolute positions, the geometrical positions are represented as relative positions of the points with respect to each other. We derive the Expectation-Maximization algorithm for our mixture model. In this way, the graph matching problem is approximated, in a principled way, as a succession of assignment problems which are solved using Softassign. Unlike other approaches, we use a true continuous underlying correspondence variable. We develop effective mechanisms to detect outliers. This is a useful technique for improving results in the presence of clutter. We evaluate the ability of our method to locate proper matches as well as to recognize object categories in a series of registration and recognition experiments. Our method compares favourably to other graph matching methods as well as to point-set registration methods and outlier rejectors.