1. An elasticity imaging machine comprising: an imaging system adapted to acquire first and second speckle fields in a region of interest of a material with the material in a respective first and second state of deformation; an electronic computer providing an output display and receiving the speckle fields from the imaging system and executing a stored program to: (a) determine a displacement vector for spatially separated first region pairs of corresponding regions in each of the first and second speckle fields, each displacement vector indicating tissue displacement in the region pairs between the first and second state of deformation; (b) qualify the displacement vectors for the first region pairs with respect to both similarity between the speckle fields in the region pairs and continuity of displacement in neighboring region pairs of each first region pair; and (c) use displacement vectors of particular first region pairs selected according to their qualification to guide the determination of second displacement vectors in second region pairs surrounding the particular first region pairs.