Most three-dimensional acquisition systems generate several partial reconstructions that have to be registered and integrated for building a complete 3D model. In this paper, we propose a volumetric shape integration method, consisting of weighted signed distance functions represented as variational implicit functions (VIF) or surfaces (VIS). Texture integration is solved similarly by using three weighted color functions also based on VIFs. Using these continuous (not grid-based) representations solves current limitations of volumetric methods: no memory inefficient and resolution limiting grid representation is required. The built-in smoothing properties of the VIS representations also improve the robustness of the final integration against noise in the input data. Experimental results are performed on real-live, noiseless and noisy synthetic data of human faces in order to show the robustness and accuracy of the integration algorithm.