Publications

An equivalence relation between morphological dynamics and persistent homology in 1D

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topological information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. Furthermore, self-duality and injectivity of these pairings are proved.

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Constructing a braid of partitions from hierarchies of partitions

By Guillaume Tochon, Mauro Dalla Mura, Jocelyn Chanussot

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

Braids of partitions have been introduced in a theoretical framework as a generalization of hierarchies of partitions, but practical guidelines to derive such structures remained an open question. In a previous work, we proposed a methodology to build a braid of partitions by experimentally composing cuts extracted from two hierarchies of partitions, notably paving the way for the hierarchical representation of multimodal images. However, we did not provide the formal proof that our proposed methodology was yielding a braid structure. We remedy to this point in the present paper and give a brief insight on the structural properties of the resulting braid of partitions.

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Introducing multivariate connected openings and closings

By Edwin Carlinet, Thierry Géraud

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

The component trees provide a high-level, hierarchical, and contrast invariant representations of images, suitable for many image processing tasks. Yet their definition is ill-formed on multivariate data, e.g., color images, multi-modality images, multi-band images, and so on. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems, such as artifacts, loss of invariances, etc. In this paper, inspired by the way the Multivariate Tree of Shapes (MToS) has been defined, we propose a definition for a Multivariate min-tree or max-tree. We do not impose an arbitrary total ordering on values; we use only the inclusion relationship between components. As a straightforward consequence, we thus have a new class of multivariate connected openings and closings.

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Spherical fluorescent particle segmentation and tracking in 3D confocal microscopy

By Élodie Puybareau, Edwin Carlinet, Alessandro Benfenati, Hugues Talbot

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

Spherical fluorescent particle are micrometer-scale spherical beads used in various areas of physics, chemistry or biology as markers associated with local physical media. They are useful for example in fluid dynamics to characterize flows, diffusion coefficients, viscosity or temperature; they are used in cells dynamics to estimate mechanical strain and stress at the micrometer scale. In order to estimate these physical measurements, tracking these particles is necessary. Numerous approaches and existing packages, both open-source and proprietary are available to achieve tracking with a high degree of precision in 2D. However, little such software is available to achieve tracking in 3D. One major difficulty is that 3D confocal microscopy acquisition is not typically fast enough to assume that the beads are stationary during the whole 3D scan. As a result, beads may move between planar scans. Classical approaches to 3D segmentation may yield objects are not spherical. In this article, we propose a 3D bead segmentation that deals with this situation.

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Modular and efficient divide-and-conquer SAT solver on top of the Painless framework

By Ludovic Le Frioux, Souheib Baarir, Julien Sopena, Fabrice Kordon

2019-02-13

In Proceedings of the 25th international conference on tools and algorithms for the construction and analysis of systems (TACAS’19)

Abstract

Over the last decade, parallel SATisfiability solving has been widely studied from both theoretical and practical aspects. There are two main approaches. First, divide-and-conquer (D&C) splits the search space, each solver being in charge of a particular subspace. The second one, portfolio launches multiple solvers in parallel, and the first to find a solution ends the computation. However although D&C based approaches seem to be the natural way to work in parallel, portfolio ones experimentally provide better performances. An explanation resides on the difficulties to use the native formulation of the SAT problem (i.e., the CNF form) to compute an a priori good search space partitioning (i.e., all parallel solvers process their subspaces in comparable computational time). To avoid this, dynamic load balancing of the search subspaces is implemented. Unfortunately, this is difficult to compare load balancing strategies since state-of-the-art SAT solvers appropriately dealing with these aspects are hardly adaptable to various strategies than the ones they have been designed for. This paper aims at providing a way to overcome this problem by proposing an implementation and evaluation of different types of divide-and- conquer inspired from the literature. These are relying on the Painless framework, which provides concurrent facilities to elaborate such parallel SAT solvers. Comparison of the various strategies are then discussed.

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How to make $n$-D plain maps Alexandrov-well-composed in a self-dual way

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2019-02-04

In Journal of Mathematical Imaging and Vision

Abstract

In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.

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High throughput automated detection of axial malformations in Medaka embryo

By Diane Genest, Élodie Puybareau, Marc Léonard, Jean Cousty, Noémie De Crozé, Hugues Talbot

2019-01-22

In Computers in Biology and Medicine

Abstract

Fish embryo models are widely used as screening tools to assess the efficacy and/or toxicity of chemicals. This assessment involves the analysis of embryo morphological abnormalities. In this article, we propose a multi-scale pipeline to allow automated classification of fish embryos (Medaka: Oryzias latipes) based on the presence or absence of spine malformations. The proposed pipeline relies on the acquisition of fish embryo 2D images, on feature extraction based on mathematical morphology operators and on machine learning classification. After image acquisition, segmentation tools are used to detect the embryo before analysing several morphological features. An approach based on machine learning is then applied to these features to automatically classify embryos according to the presence of axial malformations. We built and validated our learning model on 1459 images with a 10-fold cross-validation by comparison with the gold standard of 3D observations performed under a microscope by a trained operator. Our pipeline results in correct classification in 85% of the cases included in the database. This percentage is similar to the percentage of success of a trained human operator working on 2D images. The key benefit of our approach is the low computational cost of our image analysis pipeline, which guarantees optimal throughput analysis..

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Finite automata theory based optimization of conditional variable binding

By Jim Newton, Didier Verna

2019-01-14

In ELS 2019, the 12th european lisp symposium

Abstract

We present an efficient and highly optimized implementation of destructuring-case in Common Lisp. This macro allows the selection of the most appropriate destructuring lambda list of several given based on structure and types of data at run-time and thereafter dispatches to the corresponding code branch. We examine an optimization technique, based on finite automata theory applied to conditional variable binding and execution, and type-based pattern matching on Common Lisp sequences. A risk of inefficiency associated with a naive implementation of destructuring-case is that the candidate expression being examined may be traversed multiple times, once for each clause whose format fails to match, and finally once for the successful match. We have implemented destructuring-case in such a way to avoid multiple traversals of the candidate expression. This article explains how this optimization has been implemented.

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Motion compensation in digital holography for retinal imaging

By Julie Rivet, Guillaume Tochon, Serge Meimon, Michel Paques, Michael Atlan, Thierry Géraud

2018-12-19

In Proceedings of the IEEE international symposium on biomedical imaging (ISBI)

Abstract

The measurement of medical images can be hindered by blur and distortions caused by the physiological motion. Specially for retinal imaging, images are greatly affected by sharp movements of the eye. Stabilization methods have been developed and applied to state-of-the-art retinal imaging modalities; here we intend to adapt them for coherent light detection schemes. In this paper, we demonstrate experimentally cross-correlation-based lateral and axial motion compensation in laser Doppler imaging and optical coherence tomography by digital holography. Our methods improve lateral and axial image resolution in those innovative instruments and allow a better visualization during motion.

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Taking into account inclusion and adjacency information in morphological hierarchical representations, with application to the extraction of text in natural images and videos.

By Lê Duy Huỳnh

2018-12-01

In

Abstract

The inclusion and adjacency relationship between image regions usually carry contextual information. The later is widely used since it tells how regions are arranged in images. The former is usually not taken into account although it parallels the object-background relationship. The mathematical morphology framework provides several hierarchical image representations. They include the Tree of Shapes (ToS), which encodes the inclusion of level-line, and the hierarchies of segmentation (e.g., alpha-tree, BPT), which is useful in the analysis of the adjacency relationship. In this work, we take advantage of both inclusion and adjacency information in these representations for computer vision applications. We introduce the spatial alignment graph w.r.t inclusion that is constructed by adding a new adjacency relationship to nodes of the ToS. In a simple ToS such as our Tree of Shapes of Laplacian sign, which encodes the inclusion of Morphological Laplacian 0-crossings, the graph is reduced to a disconnected graph where each connected component is a semantic group. In other cases, e.g., classic ToS, the spatial alignment graph is more complex. To address this issue, we expand the shape-spaces morphology. Our expansion has two primary results: 1)It allows the manipulation of any graph of shapes. 2)It allows any tree filtering strategy proposed by the connected operators frameworks. With this expansion, the spatial graph could be analyzed with the help of an alpha-tree. We demonstrated the application aspect of our method in the application of text detection. The experiment results show the efficiency and effectiveness of our methods, which is appealing to mobile applications.

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