International Conference on 3D Vision Paper

Simon Fuhrmann, Misha Kazhdan and Michael Goesele – GCC – Graphics, Capture and Massively Parallel Computing, TU Darmstadt – “Accurate Isosurface Interpolation with Hermite Data” – In this work we study the interpolation problem in contouring methods such as Marching Cubes. Traditionally, linear interpolation is used to define the position of an isovertex along a zero-crossing edge, which is a suitable approach if the underlying implicit function is (approximately) piecewise linear along each edge.  Non-linear implicit functions, however, are frequently encountered and linear interpolation leads to inaccurate isosurfaces with visible reconstruction artifacts. We instead utilize the gradient of the implicit function to generate more accurate isosurfaces by means of Hermite interpolation techniques. We propose and compare several interpolation methods and demonstrate clear quality improvements by using higher  order interpolants. We further show the effectiveness of the approach even when Hermite data is not available and gradients are approximated using finite differences. (Paper)