A New QEM for Parameterization of Raster Images

We present an image processing method that converts a raster image to a simplical 2-complex which has only a small number of vertices (base mesh) plus a parameterization 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 parameterization 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 parameterization that is globally continuous visually and numerically. Inspired by multi-resolution adaptive parameterization of surfaces (MAPS) and quadric error metric (QEM), 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.