R. J. Gardner and P. Milanfar, "Reconstruction of convex bodies from brightness functions," Discrete Comput. Geom., 29:279-303, 2003.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....support function. 1. Introduction The problem of reconstruction of a convex body from the areas of its shadows, goes back to A. D. Aleksandrov [Al1] who proved that an origin symmetric convex body K in R is uniquely defined by the volumes of its projections. Recently R. Gardner and P. Milanfar [GM] provided an algorithm for reconstruction of an origin symmetric convex body K from the volumes of its projections. It is plausible that there exist an explicit formula, connecting the support function of K with volumes of its shadows. The similarities between sections and projections, pointed out ....

R. J. Gardner, P. Milanfar, Reconstruction of convex bodies from brightness functions. Discrete Comput. Geom. 29 (2003), Vol. 2, 279--303.

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R. J. Gardner and P. Milanfar, "Reconstruction of convex bodies from brightness functions," Discrete Comput. Geom., 29:279-303, 2003.

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R. J. Gardner and P. Milanfar, \Reconstruction of convex bodies from brightness functions", Disc. Comput. Geom., to appear.

....estimation problem. The brightness function data is very weak, so we have to use a constrained CRLB on the shape parameters to form the confidence regions. Algorithms for reconstructing the shape of a convex object from multiple measurements of its brightness function were developed in [2] and [3]. The Cramer Rao bound analysis presented here provides statistical estimates that can be used for performance evaluation of these algorithms. 1 Introduction The problem we consider is that of shape reconstruction from noisy measurements of the brightness function. The brightness function of an ....

....where f(u) is the extended Gaussian image (EGI) of the body. Integration is over the unit sphere (in two dimensions, the unit circle) The function f is actually just the reciprocal of the curvature at the point on the boundary where u is the outer unit normal vector. For more details, see [2] [3], and [4] Whether the body is smooth or not, our approach is to reconstruct an approximating polygon that best matches the measured brightness data in the leastsquares sense. For a convex polygon with N edges we have the following formula corresponding to (1) b(v) 1 k v , 2) where ....

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R. J. Gardner and P. Milanfar, "Reconstruction of convex bodies from brightness functions", Disc. Comput. Geom., to appear.

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Gardner, R.J., and P. Milanfar, Reconstruction of convex bodies from brightness functions. Manuscript (1991). 24

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