We present a variational approach to jointly estimate a displacement map and a superresolution texture for a 3D model from multiple calibrated views. The superresolution image formation model leads to an energy functional defined in terms of an integral over the object surface. This functional can be minimized by alternately solving a deblurring PDE and a total variation minimization on the surface, leading to increasingly accurate estimates of photometry and geometry, respectively. The resulting equations can be discretized and solved on texture space with the help of a conformal atlas. The superresolution approach to texture reconstruction allows to obtain fine details in the texture map which surpass individual input image resolution.