Dual beam electronic speckle interferometers provide raw data in the form of maps of wrapped relative phase or fringe patterns. Interpretation of such fringe patterns is complicated by aliased and random speckle noise. This noise can result in misidentification of the phase at a given point in the image. Automated determination of the loci of fringe extrema, useful for quantitative evaluation, are particularly affected. A nonlinear image filtering technique referred to as mean curvature diffusion is applied to overcome this difficulty. This technique essentially smooths the image without a substantial reduction in the magnitude of the underlying trends that here represent the fringes. Mean curvature diffusion uses calculations analogous to those for the diffusion of heat with the difference that the diffusion coefficient, reminiscent of thermal diffusivity, varies spatially within the image with a value given by the reciprocal of the local surface gradient. At a given point in the image, the rate of surface diffusion depends only on the average value of the normal curvature in any two orthogonal directions and not on its magnitude; this allows the lower frequency underlying components of the image structure to be retained. The method is tested on both calculated and real speckle interferograms to highlight the effectiveness of this smoothing technique relative to more standard smoothing algorithms.