This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Similarity and Affine Invariant Distances Between 2D Point Sets
August 1995 (vol. 17 no. 8)
pp. 810-814
ASCII Text
x 
 
Michael Werman, Daphna Weinshall, "Similarity and Affine Invariant Distances Between 2D Point Sets," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 810-814, August, 1995.
 
 
BibTex
x
 
@article{ 10.1109/34.400572,
author = {Michael Werman and Daphna Weinshall},
title = {Similarity and Affine Invariant Distances Between 2D Point Sets},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {17},
number = {8},
issn = {0162-8828},
year = {1995},
pages = {810-814},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.400572},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Similarity and Affine Invariant Distances Between 2D Point Sets
IS - 8
SN - 0162-8828
SP810
EP814
EPD - 810-814
A1 - Michael Werman,
A1 - Daphna Weinshall,
PY - 1995
KW - Image matching
KW - pattern analysis
KW - 2D affine invariance
KW - 2D similarity invariance
KW - image metric.
VL - 17
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

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.

[1] K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. Academic Press, 1990.
[2] G.H. Golub and C.F. Van Loan,Matrix Computations.Baltimore: Johns Hopkins Univ. Press, 1989.
[3] A. Rosenfeld and A.C. Kak,Digital Picture Processing. Academic Press, 2nd ed., 1982
[4] J. Sprinzak and M. Werman,“Affine point matching,” Pattern Recognition Letters, 1993.
[5] D. Weinshall,M. Werman,, and N. Tishby,“Stability and likelihood of views of three dimensional objects,” ECCV, pp. 24-35, 1994.

Index Terms:
Image matching, pattern analysis, 2D affine invariance, 2D similarity invariance, image metric.
Citation:
Michael Werman, Daphna Weinshall, "Similarity and Affine Invariant Distances Between 2D Point Sets," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 810-814, Aug. 1995, doi:10.1109/34.400572
Usage of this product signifies your acceptance of the Terms of Use.