Smooth Signed Distance Surface Reconstruction and Applications Gabriel Taubin Brown University, Providence RI 02912, USA taubin@brown.edu http://mesh.brown.edu/taubin Abstract. We describe a new and simple variational formulation to re- construct the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. Point clouds are nowadays obtained using a variety of techniques, including structured lighting sys- tems, pasive multi-view stereo algorithms, and 3D laser scanning. In our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. The formulation allows for a number of different efficient discretizations, reduces to a finite dimen- sional least squares problem for all linearly parameterized families of functions, does not require the specification of boundary conditions, and it is particularly good at extrapolating missing and/or irregularly sam- pled data. The resulting algorithms are significantly simpler and easier to implement than alternative methods. In particular, our implementation based on a primal-graph octree-based hybrid finite element-finite differ- ence discretization, and the Dual Marching Cubes isosurface extraction algorithm is very efficient, and produces high quality crack-free adaptive manifold polygon meshes. After the geometry and topology are recon- structed, the color information from the points is smoothly extrapolated to the surface by solving a second variational problem which also reduces to a finite dimensional least squares problem. The resulting method pro- duces high quality polygon meshes with smooth color maps, which accu- rately approximate the source colored oriented points. An open source implementation of this method is available for download. We describe applications to digital archaeology, 3D forensics, and 3D broadcasting. Keywords: surface reconstruction, multi-view stereo, geometry processing, digital archaeology, digital forensics. 1 Introduction A new variational formulation was recently introduced [7,8] for the problem of reconstructing a watertight surface defined by an implicit equation f (p)=0 from a finite set of oriented points {(p 1 n 1 ),..., (p N ,n N )}. Oriented point clouds are obtained from laser scanners, structured lighting systems, and multi-view L. Alvarez et al. (Eds.): CIARP 2012, LNCS 7441, pp. 38–45, 2012. c  Springer-Verlag Berlin Heidelberg 2012