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

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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

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