On Interpolation for Triangulation-represented Digital Image

Triangulation is a good tool for vector representation of raster image data. To visualize the image represented by triangulation, one needs to fit a continuous surface of colour intensity in the triangulation, i.e. to interpolate data stored in its vertices. This paper presents some interpolation methods for the purpose of use on digital images and compares them. The commonly used piecewise linear interpolation lacks means to adapt to behaviour of intensity in the surroundings of currently interpolated triangle. This leads to disturbance of continuity of the mentioned intensity surface. In this paper, two possible solutions to this problem are given. One suggests making an approximation of the surface in a surrounding area by estimation of surface normals, the other is to interpolate directly on larger formations instead of on a single triangle. Zienkiewicz’s interpolation is presented as a method to use the normal information, interpolation on Bézier triangle patch and on Coons patch are presented as methods of interpolation on larger surfaces.