TY - GEN

T1 - Displacement interpolation using Lagrangian mass transport

AU - Bonneel, Nicolas

AU - Van De Panne, Michiel

AU - Paris, Sylvain

AU - Heidrich, Wolfgang

PY - 2011

Y1 - 2011

N2 - Interpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e.g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.

AB - Interpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e.g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.

KW - Displacement interpolation

KW - Mass transport

UR - http://www.scopus.com/inward/record.url?scp=84855461410&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84855461410

SN - 9781450308076

T3 - Proceedings of the 2011 SIGGRAPH Asia Conference, SA'11

BT - Proceedings of the 2011 SIGGRAPH Asia Conference, SA'11

T2 - 2011 SIGGRAPH Asia Conference, SA'11

Y2 - 12 December 2011 through 15 December 2011

ER -