The Application of Convex Hull in Industrial X-Ray Computerized Tomography

Abstract

In some x-ray CT situations, the x-ray data of the object are available only in a limited angular range. Limited-angle imaging occurs, for example, when scanning in an angular range is obstructed by other physical objects, or when the x-ray is attenuated too much in a particular angular range to serve any useful purpose. These situations are illustrated in Fig. 1. Under such circumstances limited-angle image reconstruction techniques could be employed to reconstruct the object from the x-ray data and other information about the object, such as (1) exterior boundary of the object; (2) upper bound of the object density; (3) lower bound of the object density. It has been shown that by using this information in addition to the limited-angle x-ray data, the object can be reconstructed uniquely [1]. The limited-angle reconstruction algorithm developed in the above reference is shown in Fig. 2; the image is transformed back and forth between the object space by filtered backprojection, and the projection space by projection, with corrections by the a priori information in the object space and the limited-angle known projections in the projection space.