A New QEM for Parametrization of Raster Images

Abstract

AbstractWe present an image processing method that converts a raster image to a simplical two‐complex which has only a small number of vertices (base mesh) plus a parametrization that maps each pixel in the original image to a combination of the barycentric coordinates of the triangle it is finally mapped into. Such a conversion of a raster image into a base mesh plus parametrization can be useful for many applications such as segmentation, image retargeting, multi‐resolution editing with arbitrary topologies, edge preserving smoothing, compression, etc. The goal of the algorithm is to produce a base mesh such that it has a small colour distortion as well as high shape fairness, and a parametrization that is globally continuous visually and numerically. Inspired by multi‐resolution adaptive parametrization of surfaces and quadric error metric, the algorithm converts pixels in the image to a dense triangle mesh and performs error‐bounded simplification jointly considering geometry and colour. The eliminated vertices are projected to an existing face. The implementation is iterative and stops when it reaches a prescribed error threshold. The algorithm is feature‐sensitive, i.e. salient feature edges in the images are preserved where possible and it takes colour into account thereby producing a better quality triangulation.