Generalized Ricci curvature based sampling and reconstruction of images

Lin, Aijin; Bi, Luo; Zhang, C. Jielin; Saucan, D. Emil

doi:10.1109/eusipco.2015.7362454

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…The reader should note that, unlike Morgan [31], but following other authors, and, moreover, in concordance with Forman's work, we adopt here the "+" convention for the sign of the Hessian and Laplacian commonly, since this is more intuitive, at least in the context of Imaging and where weights, that is grayscale values are always positive. This simpler approach can be indeed applied the sampling of images, where grayscale value can be interpreted as a measure (distribution) over the pixels' grid [29]. This fact further encourages us to extend the Ricci curvature-based sampling to Complex Networks.…”

Section: Background: Ricci Curvature Based Sampling Of Manifoldsmentioning

confidence: 94%

Geometric Sampling of Networks

Barkanass¹,

Jost²,

Saucan³

2020

Preprint

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Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks.To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman-and Haantjes-Ricci curvatures for edgebased and node-based sampling. We present the results of experiments on real life networks, as well as for square grids arising in Image Processing. Moreover, we consider fitting Ricci flows and we employ them for the detection of networks' backbone. We also develop embedding kernels related to the Forman-Ricci curvatures and employ them for the detection of the coarse structure of networks, as well as for network visualization with applications to SVM. The relation between the Ricci curvature of the original manifold and that of a Ricci curvature driven discretization is also studied. J. Jost and E. Saucan were partly supported by the German-Israeli Foundation Grant I-1514-304.6/2019.

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Section: Background: Ricci Curvature Based Sampling Of Manifoldsmentioning

confidence: 94%

Geometric Sampling of Networks

Barkanass¹,

Jost²,

Saucan³

2020

Preprint

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“…Although powerful, this method employs simple formulae that represent straightforward generalizations of classical ones. Even so, only one attempt has been made so far (at least to best of or knowledge) to employ this approach in an applicative context -see [51].…”

Section: Introduction: Why Ricci Curvature?mentioning

confidence: 99%

Metric curvatures and their applications 2: metric Ricci curvature and flow

Saucan

2021

Mathematics, Computation and Geometry of Data

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In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies on the subject, based upon Wald's curvature. In addition to our previous metric approaches to the discretization of Ricci curvature, we consider yet another one, based on the Haantjes curvature, interpreted as a geodesic curvature. We also try to understand the mathematical reasons behind the recent proliferation of discretizations of Ricci curvature. Furthermore, we propose another approach to the metrization of Ricci curvature, based on Forman's discretization, and in particular we propose on that uses our graph version of Forman's Ricci curvature.

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“…Ramponi et al [8] developed an irregular sampling method based on a measure of the local sample skewness. Lin et al [9] viewed grey scale images as manifolds with density and sampled them according to the generalized Ricci curvature. Liu et al [10] proposed an adaptive progressive image acquisition algorithm based on kernel construction.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Image Sampling Using Deep Learning and Its Application on X-Ray Fluorescence Image Reconstruction

Dai

Chopp

Pouyet

et al. 2020

IEEE Trans. Multimedia

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This paper presents an adaptive image sampling algorithm based on Deep Learning (DL). It consists of an adaptive sampling mask generation network which is jointly trained with an image inpainting network. The sampling rate is controlled by the mask generation network, and a binarization strategy is investigated to make the sampling mask binary. In addition to the image sampling and reconstruction process, we show how it can be extended and used to speed up raster scanning such as the X-Ray fluorescence (XRF) image scanning process. Recently XRF laboratory-based systems have evolved into lightweight and portable instruments thanks to technological advancements in both X-Ray generation and detection. However, the scanning time of an XRF image is usually long due to the long exposure requirements (e.g., 100µs − 1ms per point). We propose an XRF image inpainting approach to address the long scanning times, thus speeding up the scanning process, while being able to reconstruct a high quality XRF image. The proposed adaptive image sampling algorithm is applied to the RGB image of the scanning target to generate the sampling mask. The XRF scanner is then driven according to the sampling mask to scan a subset of the total image pixels. Finally, we inpaint the scanned XRF image by fusing the RGB image to reconstruct the full scan XRF image. The experiments show that the proposed adaptive sampling algorithm is able to effectively sample the image and achieve a better reconstruction accuracy than that of existing methods.

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Generalized Ricci curvature based sampling and reconstruction of images

Cited by 6 publications

References 15 publications

Geometric Sampling of Networks

Geometric Sampling of Networks

Metric curvatures and their applications 2: metric Ricci curvature and flow

Adaptive Image Sampling Using Deep Learning and Its Application on X-Ray Fluorescence Image Reconstruction

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