This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Affine Parameter Estimation from the Trace Transform
October 2006 (vol. 28 no. 10)
pp. 1631-1645
In this paper, we assume that we are given the images of two segmented objects, one of which may be an affinely distorted version of the other, and wish to recover the values of the parameters of the affine transformation between the two images. The images may also differ by the overall level of illumination. The multiplicative constant of such difference may also be recovered. We present a generic theoretical framework to solve this problem. In terms of this framework, other proposed methods may be interpreted. We show how, in this framework, one can recover the affine parameters in a way that is robust to various effects, such as occlusion and illumination variation. The proposed method is generic enough to be applicable also to matching two images that do not depict the same scene or object.

[1] J. Astola, P. Haavisto, and Y. Neuvo, “Vector Median Filters,” Proc. IEEE, vol. 78, pp. 678-689, 1990.
[2] J. Ben-Arie and Z. Wang, “Pictorial Recognition of Objects Employing Affine Invariance in the Frequency Domain,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp. 604-618, June 1998.
[3] R.N. Bracewell, K.Y. Chang, A.K. Jha, and Y.H. Wang, “Affine Theorem for Two Dimensional Fourier Transform,” Electronic Letters, vol. 29, no. 3, p. 304, 1993.
[4] J. Flusser and T. Suk, “A Moment Based Approach to Registration of Images with Affine Geometric Distortion,” IEEE Trans. Geoscience and Remote Sensing, vol. 32, no. 2, pp. 382-387, Mar. 1994.
[5] A. Goshtasby, “Registration of Images with Geometric Distortion,” IEEE Trans. Geoscience and Remote Sensing, vol. 26, no. 1, pp. 60-64, Jan. 1998.
[6] A. Kadyrov and M. Petrou, “The Trace Transform and Its Applications,” IEEE Trans. Pattern and Machine Intelligence, vol. 23, no. 8, pp 811-828, Aug. 2001.
[7] A. Kadyrov and M. Petrou, “Object Signatures Invariant to Affine Distortions Derived from the Trace Transform,” Image and Vision Computing, vol. 21, pp. 1135-1143, 2003.
[8] S. Kruger and A. Calway, “Image Registration Using Multiresolution Frequency Domain Correlation,” Proc. British Machine Vision Conf., pp. 316-325, 1998.
[9] L Lucchese, “A Frequency Domain Technique Based on Energy Radial Projection for Robust Estimation of Global 2D Affine Transformations,” Computer Vision and Image Understanding, vol. 81, pp. 72-116, 2001.
[10] M. Petrou and A. Kadyrov, “Affine Invariant Features from the Trace Transform,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 30-44, Jan. 2004.
[11] M. Petrou, “Image Registration: An Overview,” Advances in Imaging and Electron Physics, vol. 130, pp. 243-291, 2004.
[12] G. Stockman, S. Kopstein, and S. Benett, “Matching Images to Models for Registration and Object Detection via Clustering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, no. 3, pp. 229-241, 1982.
[13] J. Ton and A.K. Jain, “Registering Landsat Images by Point Matching,” IEEE Trans. Geoscience and Remote Sensing, vol. 27, no. 5, pp. 642-651, Sept. 1989.
[14] A. della Ventura, A. Rampini, and R. Schettini, “Image Registration by Recognition of Corresponding Structures,” IEEE Trans. Geoscience and Remote Sensing, vol. 28, pp. 305-314, 1990.
[15] Z. Yang and F.S. Cohen, “Cross-Weighted Moments and Affine Invariants for Image Registration and Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, pp. 804-814, 1999.

Index Terms:
Image registration, affine transform, trace transform, object matching, parameter estimation.
Citation:
Alexander Kadyrov, Maria Petrou, "Affine Parameter Estimation from the Trace Transform," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1631-1645, Oct. 2006, doi:10.1109/TPAMI.2006.198
Usage of this product signifies your acceptance of the Terms of Use.