Surface interpolation for sparse cross-sections using region correspondence

The ability to estimate a surface from a set of cross-sections allows calculation of the enclosed volume and display of the surface in three-dimensions (3-D). However, extracting the cross-sections (segmenting) can be very difficult, and automatic segmentation methods are not sufficiently robust to deal with all situations. Hence, it is an advantage if the surface reconstruction algorithm can work effectively on a small number of cross-sections. An algorithm is presented which can interpolate a surface through sparse, complex crosssections. This is an extension of maximal disc guided interpolation [1], which is itself based on shape based interpolation [2]. The performance of this algorithm is demonstrated on various types of medical data (X-ray Computed Tomography, Magnetic Resonance Imaging and three-dimensional ultrasound). Although the correspondence problem in general remains unsolved, it is demonstrated that correct surfaces can be estimated from limited real data, through the use of region rather than object correspondence.