Holographic representations of images

Bruckstein, Alfred M.; Holt, Robert J.; Netravali, Arun N.

doi:10.1109/83.725365

Cited by 41 publications

(19 citation statements)

References 11 publications

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“…The holographic image representation presented in [4] maps the image into a sequence of sample pixels, such that any partition of this sequence allows for a reconstruction of the whole image with similar quality. This requires the samples in each portion to be equally optimal.…”

Section: Introductionmentioning

confidence: 99%

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Mainberger

Hoffmann

Weickert

et al. 2012

Lecture Notes in Computer Science

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Abstract. Finding optimal inpainting data plays a key role in the field of image compression with partial differential equations (PDEs). In this paper, we optimise the spatial as well as the tonal data such that an image can be reconstructed with minimised error by means of discrete homogeneous diffusion inpainting. To optimise the spatial distribution of the inpainting data, we apply a probabilistic data sparsification followed by a nonlocal pixel exchange. Afterwards we optimise the grey values in these inpainting points in an exact way using a least squares approach. The resulting method allows almost perfect reconstructions with only 5% of all pixels. This demonstrates that a thorough data optimisation can compensate for most deficiencies of a suboptimal PDE interpolant.

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Section: Introductionmentioning

confidence: 99%

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Mainberger

Hoffmann

Weickert

et al. 2012

Lecture Notes in Computer Science

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“…Such a data hierarchy can be constructed using the holographic sampling [20] or the farthest point sampling (FPS) strategies [30]. For passing from one resolution level to another we use the geodesic interpolation technique, detailed in [15].…”

Section: Multiresolution Optimizationmentioning

confidence: 99%

Analysis of Two-Dimensional Non-Rigid Shapes

Bronstein

Bruckstein

et al. 2007

Int J Comput Vis

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Abstract. Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.

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“…In this context, holographic means whole picture, and such representations enable the reconstruction of a complete image from portions of its representation with quality dependent on the size of the portion available. If we break the representation into several packets, the holographic property of the representation discussed in Bruckstein et al (1998) enables progressive image recovery with the packets received in random orderings. This is in contrast to the traditional approaches for progressive coding of images for which the most important low frequency information is transmitted (and has to be received) first and subsequent data provide refinements on the information encoded previously.…”

Section: Introductionmentioning

confidence: 99%

On holographic transform compression of images

Bruckstein¹,

Holt²,

Netravali³

2000

Int J Imaging Syst Tech

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Lossy transform compression of images is successful and widespread. The JPEG standard uses the discrete cosine transform on blocks of the image and a bit allocation process that takes advantage of the uneven energy distribution in the transform domain. For most images, 10:1 compression ratios can be achieved with no visible degradations. However, suppose that multiple versions of the compressed image exist in a distributed environment such as the internet, and several of them could be made available upon request. The classical approach would provide no improvement in the image quality if more than one version of the compressed image became available. In this paper, we propose a method, based on multiple description scalar quantization, that yields decompressed image quality that improves with the number of compressed versions available.

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Holographic representations of images

Cited by 41 publications

References 11 publications

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Analysis of Two-Dimensional Non-Rigid Shapes

On holographic transform compression of images

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