Variational approach to reconstruct surface from sparse and nonparallel contours in freehand 3D ultrasound imaging

The 3D reconstruction for freehand 3D ultrasound is a challenging issue because 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 contours that are arbitrarily oriented in 3D space. We developed 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. In the new method, we first constructed on- & off-surface constraints from the segmented contours of all recorded B-scans, then used a variational interpolation technique to get a single implicit function in 3D. Finally, the implicit function was evaluated to extract the zero-valued surface as reconstruction result. Two experiment was conducted to assess our variational surface reconstruction method, and the experiment results have shown that the new method is capable of reconstructing surface smoothly from sparse contours which can be arbitrarily oriented in 3D space.