Anisotropic mesh adaptation for image representation

Xianping Li

doi:10.1186/s13640-016-0132-7

Abstract

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation and proposes a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme. Different than many other methods that triangulate sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provide flexibility for both image representation and image reconstruction. A mesh patching technique is developed for the implementation of the GPRAMA method, which leads to an improved version of the popular GPRFS-ED method. The GPRAMA method can achieve better quality than the GPRFS-ED method but with lower computational cost.

Highlights

Triangular meshes have recently received considerable interest in adaptive sampling for image representation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
According to the different triangulation methods for the mesh patching technique in step 3, the final mesh and the corresponding representation are denoted as GPRAMA(γ )-CDT if constrained Delaunay triangulation is used and GPRAMA(γ )-EC if ear clipping method is used, where γ specifies the number of initial points
For GPRAMA, using constrained Delaunay triangulation for mesh patching does not preserve the anisotropy of the initial mesh, especially when significant amount of points are removed

Summary

Introduction

Triangular meshes have recently received considerable interest in adaptive sampling for image representation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. A metric tensor Maniso is developed in [24] that is based on minimization of a bound on the H1 semi-norm of linear interpolation error and is defined for any triangular element K as follows Step 2: Assign function values to mesh vertices (and interpolation nodes) from original image using linear finite element interpolation and compute the user-defined metric tensor M on the mesh.

Results

Conclusion