It's well known that DEMs (Digital Elevation Models) obtained by stereo correletion techniques suffer from adhesion phenomenon, which is a distortion of the model that appears near strong discontinuties or borders of the image. This phenomenon is directly related to the correlation process, and the magnitudes of the artifacts cannot be neglected when trying to obtain sub-pixel accuracies. The work by Delon and Rougé [3] characterizes this phenomenon, giving a link between measured and true disparities, and allowing to detect uncorrelatable regions (or regions providing no useful information for correlation). Since this leads to a very ill posed system of equations, many simplifying assumptions have been adopted in order to easily solve it, leading to the so called barycentric correction of the adhesion phenomenon. Even though the result is highly improved with respect to the raw correlation disparities, one still observes a slightly blurred disparity map, which is specially annoying in urban areas. In this work we propose more precise and natural assumptions to solve this system, namely to regularize the solution by a minimal surface or total variation term. Such an approach is naturally expected to allow less blurred edges while still filling in empty areas (without meaningful correlation information) in a reasonable manner.