Tetrahedron based, least squares, progressive volume models with application to freehand ultrasound data

We present a new method for the modeling of freehand collected three-dimensional ultrasound data. The model is piecewise linear and based upon progressive tetrahedral domains created by a subdivision scheme which splits a tetrahedron on on its longest edge and guarantees a valid tetrahedrization. Least squares error is used to characterize the model and an effective iterative technique is used to compute the values of the model at the vertices of the tetrahedral grid. Since the subdivision strategy is adaptive, the complexity of the model conforms to the complexity of the data leading to an extremely efficient and highly compressed volume model. The model is evaluated in real time using piecewise linear interpolation, and gives a medical professional the chance to see images which would not be possible using conventional ultrasound techniques.