The MLS surface, used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. This definition reveals connections to research in computer vision and computational topology. Variants of the MLS surface can be created by varying the vector field and the energy function. As an example of such a generalization, we define a point-set surface for surfels (points equipped with normals). We also make an important technical observation: the procedures described in the literature to take points in space onto the MLS surface do not, in fact, produce points of the MLS surface. We describe a simple iterative procedure which does, for any of the variants.

We give a method for improving the resolution of surfaces captured with a laser range scanner by combining many very similar scans. This idea is an application of the 2D image processing technique known as super-resolution. The input lower-resolution scans are each randomly shifted, so that each one contributes slightly different information to the final model. Noise is reduced by averaging the input scans.

Optical triangulation laser scanners produce errors at surface discontinuities and sharp features. These systematic errors are anisotropic. We examine the causes of these errors theoretically, and we study the correlation of systematic error with edge size and orientation experimentally. We then present a novel processing method for removing systematic errors, by combining scans taken at several different orientations. We apply an anisotropic filter to the separate scans, and use it to weight the data in a final combination step. Unlike previous approaches, our method does not require access to the scanner's internal data or firmware. We demonstrate the technique on data from laser range scanners by two different manufacturers.

It is useful to be able to define a two-dimensional point-set surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a three-dimensional, a narrow region around the input point cloud. If we were to extend the definition outside the domain, we would produce components of the surface which are far from the point cloud. This is important in practice, since when moving points onto the MLS surface, we need to begin with an initial guess which is within the domain. We visualize the domain in two dimensions, and explain why it is so narrow. We also consider two MLS variants which can be defined on a wider domain without producing spurious surface components. One is efficient and works well except near sharp corners. The other is computationally expensive but seems to work well everywhere.

We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some collection of specimens - here the skulls of the some of the extant members of a family of monkeys - an evolutionary tree for the group implies a hypothesis about the way in which the shape changed through time. We use a statistical method which expresses the value of some variable - in this case the shape - at an internal point in the tree as a weighted average of the values at the leaves. The framework of geometric morphometrics can then be used to define a shape-space, based on the correspondences of landmark points on the surfaces, within which these weighted averages can be realized as actual surfaces. Our software provides tools for performing and visualizing such an analysis in three dimensions. Beginning with laser range surfaces scans of skulls, we use our landmark editor to interactively place landmark points on the surface. We use these to compute a treemorph which smoothly interpolates the shapes across the tree. Each intermediate shape in the morph is a linear combination of all of the input surfaces. We create a surface model for an intermediate shape by warping all the input meshes towards the correct shape and then merging them together. Our merging procedure is novel. Given several similar surface meshes, we compute a weighted average between them by averaging their associated trivariate squared distance functions, and then extract the extremal surface which traces out the ''valleys'' along which the averaged function is nearly zero.