The use of transformations in ultrasound systems is disclosed. A first set of points in a first data set or a subset of a first data set is known to correspond to a second set of points in a second data set or a subset of a second data set. The point correspondence can be established using any number of techniques including speckle and/or feature correlation, speckle decorrelation time delays. Spectral broadening, power and spectral peak. A method for estimating the best fitting rigid body transformation that maps the first data set or a subset of the first data set to the second data set or a subset of the second data set is disclosed. This yields three dimensional ultrasonic data sets which preserves the shapes of object they represent.