Reconstruction of the shape and size of objects from two orthogonal projections

Abstract

Suppose that γ is a family of regular regions in R^d (d ≥ 2) with a common constructive profile (CP), i.e. the projection along the x^d-axis. In this paper, the authors establish, under certain restrictions on the equal divisor, the one-to-one correspondence between γand the family of the induced testing profiles (TP), i.e. the projections along the x₁-axis of the element in γ. This proves that, under certain restrictions, a regular region in R^d is a continuous function of its profiles (CP and TP), which theoretically guarantees the justification of the reconstruction of the left ventricle given in a previous paper.