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Hausdorff Distance with k-Nearest Neighbors

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Advances in Swarm Intelligence (ICSI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7332))

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Abstract

Hausdorff distance (HD) is an useful measurement to determine the extent to which one shape is similar to another, which is one of the most important problems in pattern recognition, computer vision and image analysis. Howeverm, HD is sensitive to outliers. Many researchers proposed modifications of HD. HD and its modifications are all based on computing the distance from each point in the model image to its nearest point in the test image, collectively called nearest neighbor based Hausdorff distances (NNHDs). In this paper, we propose modifications of Hausdorff distance measurements by using k-nearest neighbors (kNN). We use the average distance from each point in the model image to its kNN in the test image to replace the NN procedures of NNHDs and obtain the Hausdorff distance based on kNN, named kNNHDs. When k = 1, kNNHDs are equal to NNHDs. kNNHDs inherit the properties of outliers tolerance from the prototypes in NNHDs and are more tolerant to noise.

This work was supported by the National Natural Science Foundation of China (NSFC), under grant number 61170057 and 60875080.

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Authors and Affiliations

  1. Key Laboratory of Machine Perception (Ministry of Education), Peking University, P.R. China

    Jun Wang & Ying Tan

  2. Department of Machine Intelligence, School of EECS, Peking University, P.R. China

    Jun Wang & Ying Tan

Authors
  1. Jun Wang
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  2. Ying Tan
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Editor information

Editors and Affiliations

  1. Key Laboratory of Machine Perception (MOE), Peking University, Department of Machine Intelligence, School of Electronics Engineering and Computer Science, Peking University, 100871, Beijing, China

    Ying Tan

  2. Department of Electrical and Electronic Engineering, Xi’an Jiaotong-Liverpool University, Suzhou, China

    Yuhui Shi

  3. Shenzhen City Key Laboratory of Embedded System Design, College of Computer Science and Software Engineering, Shenzhen University, 518060, Shenzhen, China

    Zhen Ji

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© 2012 Springer-Verlag Berlin Heidelberg

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Wang, J., Tan, Y. (2012). Hausdorff Distance with k-Nearest Neighbors. In: Tan, Y., Shi, Y., Ji, Z. (eds) Advances in Swarm Intelligence. ICSI 2012. Lecture Notes in Computer Science, vol 7332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31020-1_32

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  • DOI: https://doi.org/10.1007/978-3-642-31020-1_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31019-5

  • Online ISBN: 978-3-642-31020-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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