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By exploiting the correlation of ultrasound speckle patterns that result from scattering by underlying tissue elements, two-dimensional tissue motion theoretically can be recovered by tracking the apparent movement of the associated speckle patterns. Speckle tracking, however, is an ill-posed inverse problem because of temporal decorrelation of the speckle patterns and the inherent low signal-to-noise ratio of medical ultrasonic images. This paper investigates the use of an adaptive deformable mesh for nonrigid tissue motion recovery from ultrasound images. The nodes connecting the mesh elements are allocated adaptively to stable speckle patterns that are less susceptible to temporal decorrelation. The authors use the approach of finite clement analysis in manipulating the irregular mesh elements. A novel deformable block matching algorithm, making use of a Lagrange element for higher-order description of local motion, is proposed to estimate a nonrigid motion vector at each node. In order to ensure that the motion estimates are admissible to a physically plausible solution, the nodal displacements are regularized by minimizing the strain energy associated with the mesh deformations. Experiments based on ultrasound images of a tissue mimicking phantom and a muscle undergoing contraction, and on computer simulations, have shown that the proposed algorithm can successfully track nonrigid displacement fields.