Similarity and Affine Invariant Distances Between 2D Point Sets

Michael Werman; Daphna Weinshall

doi:10.1109/34.400572

Similarity and Affine Invariant Distances Between 2D Point Sets

Michael Werman, Daphna Weinshall

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

95 Scopus citations

Abstract

We develop expressions for measuring the distance between 2D point sets, which are invariant to either 2D affine transformations or 2D similarity transformations of the sets, and assuming a known correspondence between the point sets. We discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images. We then give a general (metric) definition of the distance between images, which leads to the same expressions for the similarity and affine cases. This definition avoids ad hoc decisions about normalization. Moreover, it makes it possible to compute the distance between images under different conditions, including cases where the images are treated asymmetrically. We demonstrate these results with real and simulated images.

Original language	English
Pages (from-to)	810-814
Number of pages	5
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	17
Issue number	8
DOIs	https://doi.org/10.1109/34.400572
State	Published - Aug 1995

Bibliographical note

Funding Information:
This research was sponsored by the U.S. Office of Naval Research under Grant N00014-93-1-1202, R&T Project Code 4424341-01.

Keywords

2D affine invariance
2D similarity invariance
Image matching
image metric
pattern analysis

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10.1109/34.400572

Cite this

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title = "Similarity and Affine Invariant Distances Between 2D Point Sets",

abstract = "We develop expressions for measuring the distance between 2D point sets, which are invariant to either 2D affine transformations or 2D similarity transformations of the sets, and assuming a known correspondence between the point sets. We discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images. We then give a general (metric) definition of the distance between images, which leads to the same expressions for the similarity and affine cases. This definition avoids ad hoc decisions about normalization. Moreover, it makes it possible to compute the distance between images under different conditions, including cases where the images are treated asymmetrically. We demonstrate these results with real and simulated images.",

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Similarity and Affine Invariant Distances Between 2D Point Sets

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