An algorithm for reconstructing convex bodies from their projections
نویسندگان
چکیده
منابع مشابه
Reconstructing hv-Convex Polyominoes from Orthogonal Projections
Tomography is the area of reconstructing objects from projections. In discrete tomography an object T we wish to reconstruct may be a set of cells of a multidimensional grid. We perform measurements of T , each one involving a projection that determines the number of cells in T on all lines parallel to the projection’s direction. Given a finite number of such measurements, we wish to reconstruc...
متن کاملConvex-Bodies with Similar Projections
By examining an example constructed by Petty and McKinney, we show that there are pairs of centered and coaxial bodies of revolution in Ed, d > 3, whose projections onto each two-dimensional subspace are similar, but which are not themselves even affinely equivalent.
متن کاملReconstructing Convex Polyominoes from Horizontal and Vertical Projections
Reconstructing discrete bidimensional sets from their projections is involved in many different problems of computer-aided tomography, pattern recognition, image processing and data compression. In this paper, we examine the problem of reconstructing a discrete bidimensional set S satisfying some convexity conditions from its two orthogonal projections (H, v). We develop an algorithm that start...
متن کاملAn algorithm reconstructing convex lattice sets
In this paper, we study the problem of reconstructing special lattice sets from X-rays in a finite set of prescribed directions. We present the class of “Q-convex” sets which is a new class of subsets of Z2 having a certain kind of weak connectedness. The main result of this paper is a polynomial-time algorithm solving the reconstruction problem for the “Q-convex” sets. These sets are uniquely ...
متن کاملEstimating the Sizes of Convex Bodies from Projections
Let 1 ^ r ^ s ^ d— 1, and let i ? s = (L,, <xt;...; Ln, an) be a finite family of s-dimensional linear subspaces L; of E , with associated positive weights a,-, for i = 1,...,«. Denote by Kr(K, L) the intrinsic r-volume of the image of the at least r-dimensional compact convex set K under orthogonal projection on to L, write Vr{K,£P ) = £ ajK^K.L;), and let Vr(K) be the intrinsic r-volume of K....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1989
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187723