Publications

Equivalence between digital well-composedness and well-composedness in the sense of Alexandrov on $n$-D cubical grids

Abstract

Among the different flavors of well-composednesses on cubical grids, two of them, called respectively Digital Well-Composedness (DWCness) and Well-Composedness in the sens of Alexandrov (AWCness), are known to be equivalent in 2D and in 3D. The former means that a cubical set does not contain critical configurations when the latter means that the boundary of a cubical set is made of a disjoint union of discrete surfaces. In this paper, we prove that this equivalence holds in $n$-D, which is of interest because today images are not only 2D or 3D but also 4D and beyond. The main benefit of this proof is that the topological properties available for AWC sets, mainly their separation properties, are also true for DWC sets, and the properties of DWC sets are also true for AWC sets: an Euler number locally computable, equivalent connectivities from a local or global point of view… This result is also true for gray-level images thanks to cross-section topology, which means that the sets of shapes of DWC gray-level images make a tree like the ones of AWC gray-level images.

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Topological properties of the first non-local digitally well-composed interpolation on $n$-D cubical grids

Abstract

In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in $n$-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an $n$-D interpolation which is at the same time local, self-dual, and well-composed. By removing the locality constraint, we have obtained an $n$-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given.

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Two stages CNN-based segmentation of gliomas, uncertainty quantification and prediction of overall patient survival

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3BI-ECC: A decentralized identity framework based on blockchain technology and elliptic curve cryptography

Abstract

Most of the authentication protocols assume the existence of a Trusted Third Party (TTP) in the form of a Certificate Authority or as an authentication server. The main objective of this research is to present an autonomous solution where users could store their credentials, without depending on TTPs. For this, the use of an autonomous network is imperative, where users could use their uniqueness in order to identify themselves. We propose the framework “Three Blockchains Identity Management with Elliptic Curve Cryptography (3BI-ECC)”. Our proposed framework is a decentralize identity management system where users’ identities are self-generated.

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On the usefulness of clause strengthening in parallel SAT solving

Abstract

In the context of parallel SATisfiability solving, this paper presents an implementation and evaluation of a clause strengthening algorithm. The developed component can be easily combined with (virtually) any CDCL-like SAT solver. Our implementation is integrated as a part of Painless, a generic and modular framework for building parallel SAT solvers.

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A 4D counter-example showing that DWCness does not imply CWCness in $n$-D

Abstract

In this paper, we prove that the two flavours of well-composedness called Continuous Well-Composedness (shortly CWCness), stating that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical configuration, are not equivalent in dimension 4. To prove this, we exhibit the example of a configuration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know that CWCness and DWCness are equivalent in 2D and 3D. To reach our goal, we use local homology.

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Euler well-composedness

Abstract

In this paper, we define a new flavour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is $1$. A cell decomposition of a picture $I$ is a pair of regular cell complexes $\big(K(I),K(\bar{I})\big)$ such that $K(I)$ (resp. $K(\bar{I})$) is a topological and geometrical model representing $I$ (resp. its complementary, $\bar{I}$). Then, a cell decomposition of a picture $I$ is self-dual Euler well-composed if both $K(I)$ and $K(\bar{I})$ are Euler well-composed. We prove in this paper that, first, self-dual Euler well-composedness is equivalent to digital well-composedness in dimension 2 and 3, and second, in dimension 4, self-dual Euler well-composedness implies digital well-composedness, though the converse is not true.

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Non-iterative methods for image improvement in digital holography of the retina

Abstract

With the increase of the number of people with moderate to severe visual impairment, monitoring and treatment of vision disorders have become major issues in medicine today. At the Quinze-Vingts national ophthalmology hospital in Paris, two optical benches have been settled in recent years to develop two real-time digital holography techniques for the retina: holographic optical coherence tomography (OCT) and laser Doppler holography. The first reconstructs three-dimensional images, while the second allows visualization of blood flow in vessels. Besides problems inherent to the imaging system itself, optical devices are subject to external disturbance, bringing also difficulties in imaging and loss of accuracy. The main obstacles these technologies face are eye motion and eye aberrations. In this thesis, we have introduced several methods for image quality improvement in digital holography, and validated them experimentally. The resolution of holographic images has been improved by robust non-iterative methods: lateral and axial tracking and compensation of translation movements, and measurement and compensation of optical aberrations. This allows us to be optimistic that structures on holographic images of the retina will be more visible and sharper, which could ultimately provide very valuable information to clinicians.

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(Dynamic (programming paradigms)) ;; performance and expressivity

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Practical “paritizing” of Emerson–Lei automata

Abstract

We introduce a new algorithm that takes a Transition-based Emerson-Lei Automaton (TELA), that is, an $\omega$-automaton whose acceptance condition is an arbitrary Boolean formula on sets of transitions to be seen infinitely or finitely often, and converts it into a Transition-based Parity Automaton (TPA). To reduce the size of the output TPA, the algorithm combines and optimizes two procedures based on a latest appearance record principle, and introduces a partial degeneralization. Our motivation is to use this algorithm to improve our LTL synthesis tool, where producing deterministic parity automata is an intermediate step.

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