A model of the effect of image motion in the Radon transform domain

One of the most fundamental properties of the Radon (projection) transform is that shifting of the image results in shifted projections. This useful property relates translational motion in the image to simple displacement in the projections. It is far from clear, however, how more general types of motion in the image domain will be manifested in the projections. In this paper, we present a model for this phenomenon in the general case; namely, we develop a generalization of the shift property of the Radon transform. We study various properties of the apparent projected motion implied by the model, and study the case of affine motion in particular. We also present illustrative examples, and briefly discuss the inverse problem implied by the forward model developed herein, along with some possible applications.

[1]  Peyman Milanfar,et al.  Two-dimensional matched filtering for motion estimation , 1999, IEEE Trans. Image Process..

[2]  Stefano Alliney,et al.  Digital Image Registration Using Projections , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Wesley E. Snyder,et al.  Application of the one-dimensional Fourier transform for tracking moving objects in noisy environments , 1982, Comput. Vis. Graph. Image Process..

[4]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[5]  Cameron J. Ritchie,et al.  Respiratory compensation in projection imaging using a magnification and displacement model , 1996, IEEE Trans. Medical Imaging.

[6]  Jerry L. Prince.  Tomographic reconstruction of 3-D vector fields using inner product probes , 1994, IEEE Trans. Image Process..

[7]  Peyman Milanfar,et al.  Projection-based, frequency-domain estimation of superimposed translational motions , 1996 .

[8]  Stephen J. Norton.  Unique tomographic reconstruction of vector fields using boundary data , 1992, IEEE Trans. Image Process..

[9]  J. Michael Fitzpatrick,et al.  The existence of geometrical density-image transformations corresponding to object motion , 1988, Comput. Vis. Graph. Image Process..

[10]  Hans Braun,et al.  Tomographic reconstruction of vector fields , 1991, IEEE Trans. Signal Process..

[11]  J. Marsden,et al.  Elementary classical analysis , 1974 .

[12]  Peyman Milanfar,et al.  A moment-based variational approach to tomographic reconstruction , 1996, IEEE Trans. Image Process..

[13]  S. Deans.  The Radon Transform and Some of Its Applications , 1983 .