Volume intersection algorithms are used to reconstruct incomplete objects from their silhouettes. An imagined light source is moved about the data and the cumulative amount of "light" seen at each point an space is interpreted as indicating the likelihood that the point is inside the object. The object data need not be uniformly distributed nor exclusively surface data. Explicit distinction between noise, surface and interior data is avoided. The novel concept of a localised viewing region is introduced to overcome the inherent inability of volume intersection algorithms to reconstruct concave surfaces. Algorithms for 2D pixel and 3D voxel data are described and applied to 3D ultrasound data.