## Geometric Pattern Matching: A Performance Study (1999)

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Citations: | 14 - 1 self |

### BibTeX

@MISC{Gavrilov99geometricpattern,

author = {Martin Gavrilov and Piotr Indyk and Rajeev Motwani and Suresh Venkatasubramanian},

title = {Geometric Pattern Matching: A Performance Study},

year = {1999}

}

### Years of Citing Articles

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### Abstract

In this paper, we undertake a performance study of some recent algorithms for geometric pattern matching. These algorithms cover two general paradigms for pattern matching; alignment and combinatorial pattern matching. We present analytical and empirical evaluations of these schemes. Our results indicate that a proper implementation of an alignmentbased method outperforms other (often asymptotically better) approaches.

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Citation Context ...ny) transformations mapping (p1;p2) close to (q1;q2) (the details will be given shortly) 4. Search for T 2T such that dH(T (P );Q) (1 + ) . Step 1 of the algorithm can be performed in O(n log n) time =-=[PS85]-=-. We now discuss in detail the implementation of Step 2-4. 3.1 Step 2: Extracting Candidate Pairs The three schemes di er in their implementation of Step 2. Basic Alignment (BA): This is essentially t... |

705 | A survey of image registration techniques
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Citation Context ...arest neighbor in Q. This problem has many applications in areas such asmodel-based object recognition [Wol90], pharmacophore identi cation [FKL + 97], vehicle tracking [GL96], and image registration =-=[Bro92]-=-. In this paper, we will consider two-dimensional pattern matching. A comprehensive study of these problems was initiated by Alt, Mehlhorn, Wagener, and Welzl [AMWW88], and was followed by other work ... |

125 | Discrete geometric shapes: Matching, interpolation, and approximation
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(Show Context)
Citation Context ... by other work [CGH + 93, HKK92, Ruc93, Box96, IR96]. Unfortunately, the algorithms presented in this body of work turn out to be fairly impractical. In fact, as noted in the survey by Alt and Guibas =-=[AG96]-=- and in the paper by Goodrich et al [GMO94], these algorithms are likely to This work was supported by a Stanford Graduate Fellowship and NSF Award CCR-9357849, with matching funds from IBM, Mitsubish... |

88 |
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Citation Context ...ents this work. However, an exact comparison of our running times with those obtained in these works is not very meaningful, because the problems being solved are di erent. Huttenlocher and Rucklidge =-=[HR93]-=- consider the problem of computing the Hausdor 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 determi... |

72 | Geometric pattern matching under Euclidean motion - Chew, Goodrich, et al. - 1997 |

70 |
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Citation Context ...ting convolutions of binary vectors over ( ; +) [Ind98]. We use the 2 For the sake of brevity, we will not present performance comparisons for these two schemes. NTL package developed by Victor Shoup =-=[Sho]-=- that implements various operations on nite elds, including fast polynomial multiplication (which we use to implement convolution). 5 Running Time Analysis In this section we present analytical estima... |

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Citation Context ...e from P to Q is de ned as the maximum over all points p 2 P of the distance between p and its nearest neighbor in Q. This problem has many applications in areas such asmodel-based object recognition =-=[Wol90]-=-, pharmacophore identi cation [FKL + 97], vehicle tracking [GL96], and image registration [Bro92]. In this paper, we will consider two-dimensional pattern matching. A comprehensive study of these prob... |

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Citation Context ...). In our recent paper [IMV99], we give a more detailed analysis of the alignment scheme, presenting an algorithm that approximates the Hausdor distance under the model de ned by He ernan and Schirra =-=[HS94]-=-, where the goal is to obtain a solution close to a prede ned threshold . In addition, our work [IMV99] also presented a new paradigm which obtains the best known algorithms for the approximate versio... |

40 | Geometric matching under noise: Combinatorial bounds and algorithms
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- 1999
(Show Context)
Citation Context ...all constant factors using a natural heuristic which aligns a xed pair of points from the pattern to all point pairs from the image; the running time of the algorithm is O(kn 2 ). In our recent paper =-=[IMV99]-=-, we give a more detailed analysis of the alignment scheme, presenting an algorithm that approximates the Hausdor distance under the model de ned by He ernan and Schirra [HS94], where the goal is to o... |

36 | Pattern matching for spatial point sets
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Citation Context ...ains the best known algorithms for the approximate version of the problem by transforming it to combinatorial pattern matching; independently, a similar paradigm was presented by Cardoze and Schulman =-=[CS98]-=-. For a point set P , let the diameter of P , diam(P) = maxp1;p22P kp1 , p2k. If the diameters of both P and Q are bounded (say by ), then the running times of these algorithms are respectively O(n(n ... |

30 | Faster algorithms for string matching problems: matching the convolution bound
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(Show Context)
Citation Context ... q 2 Q, and some rotation such that each of the pattern strings matches with its corresponding text string. The subset matching algorithm involves computing convolutions of binary vectors over ( ; +) =-=[Ind98]-=-. We use the 2 For the sake of brevity, we will not present performance comparisons for these two schemes. NTL package developed by Victor Shoup [Sho] that implements various operations on nite elds, ... |

30 | Reliable and efficient pattern matching using an affine invariant metric - Hagedoorn, Veltkamp - 1999 |

28 | Tree pattern matching and subset matching in randomized O(n log^3 m) time - Cole, Hariharan - 1997 |

28 |
Practical methods for approximate geometric pattern matching under rigid motion
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Citation Context ...x96, IR96]. Unfortunately, the algorithms presented in this body of work turn out to be fairly impractical. In fact, as noted in the survey by Alt and Guibas [AG96] and in the paper by Goodrich et al =-=[GMO94]-=-, these algorithms are likely to This work was supported by a Stanford Graduate Fellowship and NSF Award CCR-9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundatio... |

27 | Combinatorial and experimental results for randomized point matching algorithms - Irani, Raghavan - 1996 |

21 | Deterministic superimposed coding with applications to pattern matching - Indyk - 1997 |

14 |
Improved algorithms for robust point pattern matching and applications to image registration
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Citation Context ... because the problems being solved are di erent. Huttenlocher and Rucklidge [HR93] consider the problem of computing the Hausdor 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 di erent. 2 Preliminar... |

12 |
Interactive model-based vehicle tracking
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Citation Context ...e distance between p and its nearest neighbor in Q. This problem has many applications in areas such asmodel-based object recognition [Wol90], pharmacophore identi cation [FKL + 97], vehicle tracking =-=[GL96]-=-, and image registration [Bro92]. In this paper, we will consider two-dimensional pattern matching. A comprehensive study of these problems was initiated by Alt, Mehlhorn, Wagener, and Welzl [AMWW88],... |

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6 | Rapid: randomized pharmacophore identi cation for drug design - Finn, Kavraki, et al. - 1997 |

4 | Point set pattern matching in 3-d - Boxer - 1996 |

3 |
Congruence, similiarity, and symmetries of geometric objects
- Alt, Melhorn, et al.
- 1988
(Show Context)
Citation Context ...ng [GL96], and image registration [Bro92]. In this paper, we will consider two-dimensional pattern matching. A comprehensive study of these problems was initiated by Alt, Mehlhorn, Wagener, and Welzl =-=[AMWW88]-=-, and was followed by other work [CGH + 93, HKK92, Ruc93, Box96, IR96]. Unfortunately, the algorithms presented in this body of work turn out to be fairly impractical. In fact, as noted in the survey ... |

2 | bounds for the complexity of the Hausdorff distance - Lower - 1993 |

1 |
Reliable and e cient pattern matching using an a ne invariant metric
- Hagedoorn, Veltkamp
- 1997
(Show Context)
Citation Context ...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 di erent. 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 d... |

1 |
Lower bounds for the complexityof the Hausdor distance
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(Show Context)
Citation Context ...ning times: for example, for jP j = k and jQj = n, the running time of the algorithm of Chew et al [CGH + 93] is ~O(k 3 n 2 ); in < 3 , the bounds are signi cantly worse. Indeed, work on lower bounds =-=[Ruc93]-=- seems to indicate that the large running times cannot be avoided in the worst case. Signi cant improvements in running times came from considering the natural relaxation of the problem to approximati... |

1 | FKL + 97 - IEEE - 1998 |

1 | Rapid: Randomized pharmacophore identification for drug design - Gardner, Lawton - 1997 |