Adaptive thinning for bivariate scattered data

Dyn, Nira; Floater, Michael S.; Iske, Armin

doi:10.1016/s0377-0427(02)00352-7

Cited by 37 publications

(42 citation statements)

References 7 publications

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“…The second mesh-generation method of interest herein is the greedy point-removal (GPR) scheme of Demaret and Iske [4] (called "adaptive thinning" in [4]), which is closely related to the adaptive thinning technique of Dyn et al [8]. The GPR method first constructs a mesh that employs all of the sample points of an image, and then repeatedly removes the sample point that yields the smallest increase in the squared error of the mesh approximation, until the desired number of sample points is obtained.…”

Section: Greedy Point-removal (Gpr) Methodsmentioning

confidence: 99%

A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation

Adams

2011

IEEE Trans. on Image Process.

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Based on the greedy-point removal (GPR) scheme of Demaret and Iske, a simple yet highly-effective framework for constructing triangle-mesh representations of images, called GPRFS, is proposed. By using this framework and ideas from the error diffusion (ED) scheme (for mesh-generation) of Yang et al., a highly effective mesh-generation method, called GPRFS-ED, is derived and presented. Since the ED scheme plays a crucial role in our work, factors affecting the performance of this scheme are also studied in detail. Through experimental results, our GPRFS-ED method is shown to be capable of generating meshes of quality comparable to, and in many cases better than, the state-of-the-art GPR scheme, while requiring very substantially less computation and memory. Furthermore, with our GPRFS-ED method, one can easily tradeoff between mesh quality and computational/memory complexity. A reduced complexity version of the GPRFS-ED method (called GPRFS-MED) is also introduced to further demonstrate the computational/memory-complexity scalability of our GPRFS-ED method.

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Section: Greedy Point-removal (Gpr) Methodsmentioning

confidence: 99%

A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation

Adams

2011

IEEE Trans. on Image Process.

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“…Adaptive thinning algorithms [12] are a class of greedy point removal schemes for bivariate scattered data. In our recent work [8,9,10], adaptive thinning algorithms were applied to image data, and more recently, also to video data [11] to obtain an adaptive approximation scheme for images and videos.…”

Section: Adaptive Thinning Algorithmsmentioning

confidence: 99%

“…To this end, several different significance measures were proposed in [7,8,9,10,12]. Each of the utilized significance measures are relying on (an estimate) of the anticipated error that is incurred by the removal of the pixel point.…”

Section: Adaptive Thinning Algorithmsmentioning

confidence: 99%

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Anisotropic Triangulation Methods in Adaptive Image Approximation

Demaret

Iske

2010

Approximation Algorithms for Complex Systems

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Summary. Anisotropic triangulations are utilized in recent methods for sparse representation and adaptive approximation of image data. This article first addresses selected computational aspects concerning image approximation on triangular meshes, before four recent image approximation algorithms, each relying on anisotropic triangulations, are discussed. The discussion includes generic triangulations obtained by simulated annealing, adaptive thinning on Delaunay triangulations, anisotropic geodesic triangulations, and greedy triangle bisections. Numerical examples are presented for illustration.

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“…In recent years, there has been a growing interest in image representations that employ adaptive (i.e., nonuniform) sampling [1][2][3][4][5][6][7] as such representations can, in many applications, have numerous advantages over traditional lattice-based sampling, including greater compactness and the ability to facilitate methods that yield higher quality results or have lower overall complexity. Some of the many applications that can benefit from adaptive sampling include: feature detection [8], pattern recognition [9], computer vision [10], restoration [11], tomographic reconstruction [12], filtering [13], and image/video coding [7,[14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A highly-effective incremental/decremental Delaunay mesh-generation strategy for image representation

Adams

2013

Signal Processing

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A flexible mesh-generation framework for image representation based on Delaunay triangulations is proposed. By fixing the various degrees of freedom available within this framework, two mesh-generation methods, known as ID1 and ID2, are derived. These two methods are shown to perform extremely well, producing meshes of significantly higher quality than state-of-the-art schemes at relatively low computational cost. Furthermore, the ID1 and ID2 methods each provide a mechanism whereby mesh quality can be increased (or decreased) in return for a corresponding increase (or decrease) in computational cost.Lastly, we demonstrate that one component of our proposed methods, called bad-point replacement, can be used as a postprocessing optimization step that, when added to other previously-proposed mesh-generation methods, yields meshes of much greater quality.

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Adaptive thinning for bivariate scattered data

Cited by 37 publications

References 7 publications

A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation

A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation

Anisotropic Triangulation Methods in Adaptive Image Approximation

A highly-effective incremental/decremental Delaunay mesh-generation strategy for image representation

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