Image representation with explicit discontinuities using triangle meshes

Date

2012-09-11

Authors

Tu, Xi

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Abstract

Triangle meshes can provide an effective geometric representation of images. Although many mesh generation methods have been proposed to date, many of them do not explicitly take image discontinuities into consideration. In this thesis, a new mesh model for images, which explicitly represents discontinuities (i.e., image edges), is proposed along with two corresponding mesh-generation methods that determine the mesh-model parameters for a given input image. The mesh model is based on constrained Delaunay triangulations (DTs), where the constrained edges correspond to image edges. One of the proposed methods is named explicitly-represented discontinuities-with error diffusion (ERDED), and is fast and easy to implement. In the ERDED method, the error diffusion (ED) scheme is employed to select a subset of sample points that are not on the constrained edges. The other proposed method is called ERDGPI. In the ERDGPI method, a constrained DT is first constructed with a set of prespecified constrained edges. Then, the greedy point insertion (GPI) scheme is employed to insert one point into the constrained DT in each iteration until a certain number of points is reached. The ERDED and ERDGPI methods involve several parameters which must be provided as input. These parameters can affect the quality of the resulting image approximations, and are discussed in detail. We also evaluate the performance of our proposed ERDED and ERDGPI methods by comparing them with the highly effective ED and GPI schemes. Our proposed methods are demonstrated to be capable of producing image approximations of higher quality both in terms of PSNR and subjective quality than those generated by other schemes. For example, the reconstructed images produced by the proposed ERDED method are often about 3.77 dB higher in PSNR than those produced by the ED scheme, and our proposed ERDGPI scheme produces image approximations of about 1.08 dB higher PSNR than those generated by the GPI approach.

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Keywords

mesh generation, image representation, constrained Delaunay triangulation

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