The task of assigning geographic coordinates to textual resources plays an increasingly central role in geographic information retrieval. The ability to select those terms from a given collection that are most indicative of geographic location is of key importance in successfully addressing this task. However, this process of selecting spatially relevant terms is at present not well understood, and the majority of current systems are based on standard term selection techniques, such as $(\chi^2)$ or information gain, and thus fail to exploit the spatial nature of the domain. In this paper, we propose two classes of term selection techniques based on standard geostatistical methods. First, to implement the idea of spatial smoothing of term occurrences, we investigate the use of kernel density estimation (KDE) to model each term as a two-dimensional probability distribution over the surface of the Earth. The second class of term selection methods we consider is based on Ripley's K statistic, which measures the deviation of a point set from spatial homogeneity. We provide experimental results which compare these classes of methods against existing baseline techniques on the tasks of assigning coordinates to Flickr photos and to Wikipedia articles, revealing marked improvements in cases where only a relatively small number of terms can be selected.

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.