GP-MPU Method for Implicit Surface Reconstruction Manuel Guillermo L´ opez 1 , Boris Mederos 2 and Oscar Dalmau 1 1 Centro de Investigaci´ on en Matem´aticas, CIMAT 2 Universidad Aut´ onoma de Ciudad Ju´ arez, UACJ, Departamento de F´ ısica y Matem´ aticas manuel.lopez@cimat.mx, boris.mederos@uacj.mx, dalmau@cimat.mx Abstract. This work addresses the problem of surface reconstruction from unorganized points and normals that are acquired from laser scan- ning of 3D objects. We propose a novel technique for implicit surface reconstruction that effectively combines the trend setting method known as Multi-level Partition of the Unity (MPU) with the Gaussian Process Regression. The reconstructed implicit surface is obtained by subdividing the domain into a set of smaller sub-domains using the MPU algorithm, in each sub-domain a Gaussian Process Regression is carried out that pro- vides accurate local approximations which are blended to obtain a global representation corresponding to the reconstructed implicit surface. The proposed algorithm is able to deal efficiently with point clouds presenting several features such as complex topology and geometry, missing regions and very low sampling rate. Moreover, we conduct some experiments with several acquired data and perform some comparisons with state of the art techniques showing competitive results. 1 Introduction The development of 3D scanning technology has made possible the application of 3D object modeling to a wide range of practical applications in multimedia, entertainment, medicine, biomechanic, and cultural heritage, just to mention a few. This has trigger several computational challenges problems such as acqui- sition, reconstruction, and simulation, etc. In this work we will focus on the problem of surface reconstruction from unorganized point clouds which is stated formally as: Given a finite set of point P ⊂ R 3 with normal N ⊂ R 3 sampled from a smooth surface S find a smooth surface F close to S. The surface reconstruction problem has received in the last two decades a lot of attention entailing several approaches to deal with it. The main techniques used can be generally categorized in two types: Delaunay Triangulation/Voronoi Diagram: These algorithms yield a polyg- onal mesh filtering the Delaunay/Voronoi diagram and the resulting mesh inter- polates the point clouds, some examples of this kind of methods are Ameta et