ANALYSIS OF PROJECTION GEOMETRY FOR FEW-VIEW RECONSTRUCTION OF SPARSEOBJECTS

In this paper certain projections are examined as to why they are bett er than others when used to reconstruct sparse objects from a small nu mber of projections. At the heart of this discussion is the notion of ''consistency,'' which is defined as the agreement between the object' s 3-D structure and its appearance in each image. It is hypothesized t hat after two or more projections have been obtained, it is possible t o predict how well a subsequent view will perform in terms of resolvin g ambiguities in the object reconstructed from only the first few view s. The prediction is based on a step where views of the partial recons truction are simulated and the use of consistency to estimate the effe ctiveness of a given projection is exploited. Here some freedom is pre sumed to acquire arbitrary as opposed to predetermined views of the ob ject. The principles underlying this approach are outlined, and experi ments are performed to illustrate its use in reconstructing a realisti c 3-D model. Reflecting an interest in reconstructing cerebral vascula ture from angiographic projections, the experiments employ simulations based on a 3-D wire-frame model derived from an internal carotid arte riogram. It is found that for such an object, the predictions can be i mproved significantly by introducing a correction to account for the d egree to which the object possesses some symmetry in shape. For object s sufficiently sparse, this correction is less important. It is conclu ded that when the number of projections is limited, it may be possible to favorably affect the reconstruction process in this manner.