| M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. Technical Report RUU-CS-97-33, Dept. of Computing Science, Utrecht University, 1997. |
....major approaches to branch and bound techniques for geometric matching have emerged over the last decade. The first is an approach based on matchlists and (optionally) a depth first search strategy[4] The second is based on data structures for fast proximity searches or discrete Voronoi diagrams [14, 12, 9] and has its origins in earlier hierarchical matching schemes organized around multi resolution image analysis [3, 10] Matchlist based approaches to geometric matching are very easy to implement: all a user needs to supply is a quality of match function for a pair of features (and an upper bound ....
....a tight upper bound. For other kinds of transformations and error measures, a tight upper bound is difficult to compute, but we do not actually require a tight upper bound for the algorithm to converge. Therefore, branch and bound algorithms can be formulated using more general upper bounds (e.g. [9]) that are easier to derive. Briefly, we start by determining a bound on the location of each model point m j under any transformation T T. This bound can be expressed as any convenient geometric region, for example a bounding rectangle or a bounding circle in the image plane. For the purpose ....
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M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. Technical Report RUU-CS-97-33, Dept. of Computing Science, Utrecht University, 1997.
....of the fact that as the pattern size becomes larger, its diameter increases as well. As a result, if the pattern and the image have comparable diameters, the filtering mechanism of GRID performs extremely well. Related work. Much of the recent empirical work in geometric pattern matching [HR93, HV97, MNL98] has studied algorithms based on an exhaustive search of the transformation space (with clever pruning techniques) Our evaluation naturally complements this work. However, an exact comparison of our running times with those obtained in these works is not very meaningful, because the ....
....and Rucklidge [HR93] consider the problem of computing the Hausdorff distance from P to Q under translation (and scaling) and Mount et al. MNL98] consider the problem of image registration in which the goal is to determine whether a large overlap exists between P and Q. In the case of [HV97] the distance measure used is different. 2 Preliminaries For any point p, let R(p; r1 ; r2) denote the annulus centered at p of inner radius r1 and outer radius r2 r1 . In the sequel, we use B(p; r) to denote a two dimensional ball of radius r centered at p. We also use R(p; r1 ; r2 ) to ....
M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. Technical Report RUU-CS-97-33, Dept. of Computing Science, Utrecht University, 1997.
....whether there is a translation plus scaling that brings the partial Hausdorff distance under a given threshold is done in [30] by a progressive subdivision of transformation space. The subdivision of transformation space is generalized to a general geometric branch and bound framework in [25]. Here the optimal transformation is approximated to any desired accuracy. The matching can be done with respect to any transformation group #, for example similarity (translation, rotation, and scaling) or affine transformations (translation, rotation, scaling, and shear) The algorithm uses a ....
M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. International Journal of Computer Vision, 31(2/3):203--225, 1999.
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M. Hagedoorn and R. C. Veltkamp. Reliable and efficient pattern matching using an affine invariant metric. Technical Report RUU-CS-97-33, Dept. of Computing Science, Utrecht University, The Netherlands, 1997.
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