Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 690262, 11 pages
Research Article

Construction of Affine Invariant Functions in Spatial Domain

1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2Department of Mathematics G. Castelnuovo, University of Rome la Sapienza, Piazzale, Aldo Moro 2, 00185 Rome, Italy

Received 17 January 2012; Accepted 9 March 2012

Academic Editor: Bin Fang

Copyright © 2012 Jianwei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Affine invariant functions are constructed in spatial domain. Unlike the previous affine representation functions in transform domain, these functions are constructed directly on the object contour without any transformation. To eliminate the effect of the choice of points on the contour, an affine invariant function using seven points on the contour is constructed. For objects with several separable components, a closed curve is derived to construct the affine invariant functions. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the constructed affine invariant functions can be used for object classification.