Similarity and Affine Invariant Distances Between 2D Point Sets

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


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 languageAmerican English
Pages (from-to)810-814
Number of pages5
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number8
StatePublished - 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.


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


Dive into the research topics of 'Similarity and Affine Invariant Distances Between 2D Point Sets'. Together they form a unique fingerprint.

Cite this