Image-guided blended neighbor interpolation of scattered data

Uniformly sampled images are often used to interpolate other data acquired more sparsely with an entirely different mode of measurement. For example, downhole tools enable geophysical properties to be measured with high precision near boreholes that are scattered spatially, and less precise seismic images acquired at the earth’s surface are used to interpolate those properties at locations far away from the boreholes. Image-guided interpolation is designed specifically to enhance this process. Most existing methods for interpolation require distances from points where data will be interpolated to nearby points where data are known. Image-guided interpolation requires non-Euclidean distances in metric tensor fields that represent the coherence, orientations and shapes of features in images. This requirement leads to a new method for interpolating scattered data that I call blended neighbor interpolation. For simple Euclidean distances, blended neighbor interpolation resembles the classic natural neighbor interpolation.