Surface Reconstruction from Sparse Non-parallel Cross-sections for Freehand 3D Ultrasound Using Variational Implicit Functions

The 3D reconstruction for freehand 3D ultrasound remains a hard problem because that the recorded B-scans are not only sparse, but also non-parallel (actually they may intersect each other). Conventional volume reconstruction methods can't reconstruct sparse data efficiently while not introducing geometrical artifacts, and conventional surface reconstruction methods can't reconstruct surfaces from cross-sections that are arbitrarily oriented in 3D space. We develop a new surface reconstruction method for freehand 3D ultrasound. It is based on variational implicit function, which is presented by Greg Turk for shape transformation, so we name this method as variational implicit function (VIF) method. In VIF method, we first create boundary and normal constraints from the segmented cross-sections of all recorded B-scans, then we invoke a variational interpolation technique to get a single implicit function in 3D. Last the implicit function is evaluated to extract the zero-valued surface, which is what we expected as the reconstruction result. Two experiments are conducted to assess our VIF surface reconstruction method. Experiment results have shown that VIF method is capable of reconstructing smooth surface from sparse cross-sections which can be arbitrarily oriented in 3D space. A very small number of cross-sections can lead to a close approximation of the original data.