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We present a new and much simpler formulation for the problem of reconstructing an implicit surface from an oriented point cloud acquired by a range scanner or a stereo vision system. Data vectors are first extended to a continuous vector field on a bounding volume, which is then integrated in the least squares sense yielding an implicit function whose zero level set approximates the data points. Function discretizations associated with regular grids automatically produce Iso-surface polygon meshes. Extrapolating missing and noisy data, integrating multiple scans, developing data structures and algorithms optimized for fast visualization and geometry processing, are challenging problems and active areas of research addressed by this work. We plan to use multi-resolution data structures to integrate streams of point clouds in real time.Implicit representations have the advantage of dealing with arbitrary topology. [Ohtake et al. 2003] introduces an adaptive hierarchal implicit representation composed of local quadric patches and weights associated with nodes in a oct-tree. Given that for rendering or post-processing we extract an isosurface over a regular grid (e.g., via Marching Cubes), it is worth exploring reconstruction algorithms that use implicit functions defined as a regular scalar field.In the area of geometry processing, the notion of decoupling the filtering of normal fields and geometry has emerged as a powerful method for denoising [Tasdizen et al. 2003]. We argue that a similar decoupling for the surface reconstruction problem is worth exploring. This preliminary work presents a volumetric method for surface reconstruction that directly incorporates both point and normal information. Instead of imposing constraints and regularization directly on the values of the potential (scalar) field, we impose constraints and regularization on the gradient field. We implement this using a combination of least-squares fitting and solving a Poisson problem over a uniform grid.The general problem of implicit surface reconstruction is as follows. Given an oriented point cloud i.e., m points and their normals,The least squares solution f using interpolatory constraints (1) will not, in general, produce satisfactory results without some regularization.We represent the scalar field f as a linear combination of basis functions(e.g.,trilinear) defined on a uniform Cartesian grid,

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We describe a data structure for improved quality of real-time rendering for large and dynamic heightfields on programmable graphics hardware. The new isometric heightfield has a more accurate surface and smoother shading, normals, and curvature.