Generalized anisotropic stratified surface sampling.

We introduce a novel stratified sampling technique for mesh surfaces that gives the user control over sampling density and anisotropy via a tensor field. Our approach is based on sampling space-filling curves mapped onto mesh segments via parametrizations aligned with the tensor field. After a short preprocessing step, samples can be generated in real time. Along with visual examples, we provide rigorous spectral analysis and differential domain analysis of our sampling. The sample distributions are of high quality: they fulfil the blue noise criterion, so have minimal artifacts due to regularity of sampling patterns, and they accurately represent isotropic and anisotropic densities on the plane and on mesh surfaces. They also have low discrepancy, ensuring that the surface is evenly covered.

Registration of 3D point clouds and meshes: a survey from rigid to nonrigid.

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends.

Bas-relief generation using adaptive histogram equalization.

An algorithm is presented to automatically generate bas-reliefs based on adaptive histogram equalization (AHE), starting from an input height field. A mesh model may alternatively be provided, in which case a height field is first created via orthogonal or perspective projection. The height field is regularly gridded and treated as an image, enabling a modified AHE method to be used to generate a bas-relief with a user-chosen height range. We modify the original image-contrast-enhancement AHE method to use gradient weights also to enhance the shape features of the bas-relief. To effectively compress the height field, we limit the height-dependent scaling factors used to compute relative height variations in the output from height variations in the input; this prevents any height differences from having too great effect. Results of AHE over different neighborhood sizes are averaged to preserve information at different scales in the resulting bas-relief. Compared to previous approaches, the proposed algorithm is simple and yet largely preserves original shape features. Experiments show that our results are, in general, comparable to and in some cases better than the best previously published methods.