This paper focuses on the correlation of two successive scalar images for the purpose of measuring imaged fluid motions. A method is presented for deforming, or transforming, one image to another. Taylor series expansions of the Lagrangian displacement field are used, in conjunction with an integral form of the equations of motion, to approximate this transformation. The proposed method locally correlates images for displacements, rotations, deformations, and higher-order displacement gradient fields, and applies a global minimization procedure to insure a global consistency in the results. An integral form of the equations of motion is employed. No explicit spatial or temporal differentiation of the image data is required in estimating the displacement field. As a consequence, this method is appropriate for both continuous-scalar as well as discrete-particle-image data. Successive two-dimensional digital CCD images of fluid motion marked with dye, are used to verify the capabilities of the method. The utility of the method is also illustrated using a pair of Voyager 2 images of Jupiter.