We describe a novel approach for image matching based on deformable intensity surfaces. In this approach, the intensity surface of the image is modeled as a deformable 3D mesh in the (x,y,I(x,y)) space. Each surface point has 3 degrees of freedom, thus capturing fine surface changes. A set of representative deformations within a class of objects (e.g. faces) are statistically learned through a Principal Components Analysis, thus providing a priori knowledge about object-specific deformations. We demonstrate the power of the approach by examples such as image matching and interpolation of missing data. Moreover this approach dramatically reduces the computational cost of solving the governing equation for the physically based system by approximately three orders of magnitude.