Analysis of projection geometry for few-view reconstruction of sparse objects

In this paper certain projections are examined as to why they are better than others when used to reconstruct sparse objects from a small number 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 that after two or more projections have been obtained, it is possible to predict how well as subsequent view will perform in terms of resolving ambiguities in the object reconstructed from only the first few views. The prediction is based on a step where views of the partial reconstruction are simulated and the use of consistency to estimate the effectiveness of a given projection is exploited. Here some freedom is presumed to acquire arbitrary as opposed to predetermined views of the object. The principles underlying this approach are outlined, and experiments are performed to illustrate its use in reconstructing a realistic 3-D model. Reflecting an interest in reconstructing cerebral vasculature from angiographic projections, the experiments employ simulations based on a 3-D wireframe model derived from an internal carotid arteriogram. It is found that for such an object, the predictions can be improved significantly by introducing a correction to account for the degree to which the object possesses some symmetry in shape. For objects sufficiently sparse, this correction is less important. It is concluded that when the number of projections is limited, it may be possible to favorably affect the reconstruction process in this manner.