A new Radon transform result

A convex elliptical region of the plane supports a positive-valued function of two variables whose Radon transform depends only on the slope of the integrating line: any two parallel lines that intersect the ellipse generate equal line integrals of the function. It is somewhat surprising that such a...

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Bibliographic Details
Main Authors: Marzetta, T.L., Shepp, L.A.
Format: Conference Proceeding
Language:English
Subjects:
Image analysis
Image motion analysis
Image sequence analysis
Image sequences
Integral equations
Motion detection
Noise figure
Nonlinear filters
Object detection
Signal to noise ratio
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Summary:A convex elliptical region of the plane supports a positive-valued function of two variables whose Radon transform depends only on the slope of the integrating line: any two parallel lines that intersect the ellipse generate equal line integrals of the function. It is somewhat surprising that such a function exists. It is even more surprising, as we show in this paper, that the elliptical region is the only convex compact planar set that supports such a function. We discovered this result while attempting to extend an analytical solution technique for a 2-D integral equation that figures in a certain problem of motion detection in a noisy image sequence.
DOI:10.1109/ICIP.1997.648014