Implicit functions: applications in medicine and biology
Jean‐Marie C. Bouteiller, Benjamin M. Wu, Michel Baudry · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
3D reconstructions constitute a valuable tool in medicine and biology. They allow researchers to further analyze, compare and register anatomical data. In medical cases, they allow a better understanding of the condition to treat and may increase the changes of an accurate diagnostic, surgery and treatment. In these fields, the initial dataset mostly consists of parallel sections. The accuracy of this dataset usually suffers from technological limitations of the acquisition system. These limitations can result in a possible low accuracy in the plane of sections, but can also consist of a limitation in the number of sections. This induces undersampling which constitutes a major problem for the subsequent 3D reconstruction. Many reconstruction methods exist. This paper provides a qualitative and quantitative comparison of several of these methods. We present the perspectives introduced by the utilization of implicit functions in terms of accuracy but also in their application to higher dimensional problems. The main dataset consists of neuroanatomical data, but other examples are also provided. Emphasis is made on undersampled initial data and the reconstruction of structures with complex geometry.