International audienceIn this paper we introduce a new family of partial difference operators on graphs and study equations involving these operators. This family covers local variational $p$-Laplacian, $\infty$-Laplacian, nonlocal $p$-Laplacian and $\infty$-Laplacian, $p$-Laplacian with gradient terms, and gradient operators used in morphology based on the partial differential equation. We analyze a corresponding parabolic equation involving these operators which enables us to interpolate adaptively between $p$-Laplacian diffusion-based filtering and morphological filtering, i.e., erosion and dilation. Then, we consider the elliptic partial difference equation with its corresponding Dirichlet problem and we prove the existence and uniqueness of respective solutions. For $p=\infty$, we investigate the connection with Tug-of-War games. Finally, we demonstrate the adaptability of this new formulation for different tasks in image and point cloud processing, such as filtering, segmentation, clustering, and inpainting

In this paper we propose to use the Eikonal equation on graphs for generalized data clustering. We introduce a new potential function that favors the creation of homogeneous clusters together with an iterative algorithm that place seeds vertices at smart locations. Oversegmentation application shows the effectiveness of our approach and gives results comparable to the state-of-the-art methods.

Background Current automated cervical cytology screening systems require purchase of a dedicated preparation machine and use of a specific staining protocol. CytoProcessor (DATEXIM, Caen, France) is a new automated system, designed to integrate seamlessly into the laboratory's existing workflow. We previously demonstrated the superior performance of CytoProcessor for diagnosis of ThinPrep slides compared to the ThinPrep Imaging System (HOLOGIC, Marlborough, MA). Next, we analyzed whether CytoProcessor technology can be adapted for use on Novaprep slides. Methods Using artificial intelligence, we developed a new algorithm in CytoProcessor for the analysis of slides prepared using the NOVAPREP Processor System NPS50 (Novacyt, Vélizy‐Villacoublay, France). A representative population of 309 cases was selected from the routine workflow in a public hospital. We compared the diagnoses made using CytoProcessor or conventional screening with a microscope. All discordances were resolved by a consensus committee. Results The performance of CytoProcessor in terms of diagnostic accuracy on Novaprep slides was very similar to that observed previously on ThinPrep slides. Compared to conventional screening, CytoProcessor slightly improves diagnostic sensitivity while maintaining a statistically equivalent specificity. Diagnosis was reached 1.6 times faster with CytoProcessor compared to using a microscope. Conclusion CytoProcessor is a robust automated cervical cytology screening system that can be used successfully with samples having very different characteristics. As previously shown, CytoProcessor confers significant gains in processing time and diagnostic precision. CytoProcessor is accessible through a secured internet connection, making remote diagnosis of Papanicolaou tests possible.

Background: Current automated cervical cytology screening systems still heavily depend on manipulation of glass slides. We developed a new system called CytoProcessor^TM (DATEXIM, Caen, France), which increases sensitivity and takes advantage of virtual slide technology to simplify the workflow and save worker time. We used an approach based on artificial intelligence to identify abnormal cells among the tens of thousands in a cervical preparation. Objectives: We set out to compare the diagnostic sensitivity and specificity of CytoProcessor^TM and the ThinPrep Imaging System (HOLOGIC, Marlborough, MA, USA). Methods: A representative population of 1,352 cases was selected from the routine workflow in a private laboratory. Diagnoses were established using the ThinPrep Imaging System and CytoProcessor^TM. All discordances were resolved by a consensus committee. Results: Compared to the ThinPrep Imaging System, CytoProcessor^TM significantly improves diagnostic sensitivity without compromising specificity. The sensitivity of detection of “atypical squamous cells of undetermined significance (ASC-US) and more severe” and “low-grade squamous intraepithelial lesion and more severe” was significantly higher using CytoProcessor^TM. Considering that cases with a truth diagnosis of ASC-US or more severe required clinical follow-up, 1.5% of the cases (21/1,360) would have been missed if the CytoProcessor^TM diagnosis had been used for clinical decision-making. In contrast, 4% of the cases (54/1,360) were missed when the ThinPrep Imaging System diagnosis was used for clinical decision-making. There were 2.6 times fewer false negatives using CytoProcessor^TM. The CytoProcessor^TM workflow was 1.5 times faster in terms of worker time. Conclusions: CytoProcessor^TM is the first of a new generation of automated screening systems, demonstrating improved sensitivity and yielding significant gains in processing time. In addition, the fully digital nature of slide presentation in CytoProcessor^TM allows the remote diagnosis of Papanicolaou tests for the first time.

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Game-theoretic p-Laplacian or normalized p-Laplacian operator is a version of classical variational p-Laplacian which was introduced recently in connection with stochastic games called Tug-of-War with noise (Peres et al. 2008, Tug-of-war with noise: A game-theoretic view of the p-laplacian. Duke Mathematical Journal145(1), 91–120). In this paper, we propose an adaptation and generalization of this operator on weighted graphs for 1 ≤ p ≤ ∞. This adaptation leads to a partial difference operator which is a combination between 1-Laplace, infinity-Laplace and 2-Laplace operators on graphs. Then we consider the Dirichlet problem associated to this operator and we prove the uniqueness and existence of the solution. We show that the solution leads to an iterative non-local average operator on graphs. Finally, we propose to use this operator as a unified framework for interpolation problems in signal processing on graphs, such as image processing and machine learning.

In this paper we propose an adaptation of the ∞-Poisson equation on weighted graphs, and propose a finer expression of the ∞-Laplace operator with gradient terms on weighted graphs, by making the link with the biased version of the tug-of-war game. By using this formulation, we propose a hybrid ∞-Poisson Hamilton-Jacobi equation, and we show the link between this version of the ∞-Poisson equation and the adaptation of the eikonal equation on weighted graphs. Our motivation is to use this extension to compute distances on any discrete data that can be represented as a weighted graph. Through experiments and illustrations, we show that this formulation can be used in the resolution of many applications in image, 3D point clouds, and high dimensional data processing using a single framework.

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