Thierry Géraud

An equivalence relation between morphological dynamics and persistent homology in $n$-D

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2021-03-02

In Proceedings of the IAPR international conference on discrete geometry and mathematical morphology (DGMM)

Abstract

In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to $n$-D, $n \geq 2$, showing that this equality can be applied to $n$-D images and not only to 1D functions. This is a step further to show how much MM and MT are related.

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A global benchmark of algorithms for segmenting the left atrium from late gadolinium-enhanced cardiac magnetic resonance imaging

By Zhaohan Xiong, Qing Xia, Zhiqiang Hu, Ning Huang, Cheng Bian, Yefeng Zheng, Sulaiman Vesal, Nishant Ravikumar, Andreas Maier, Xin Yang, Pheng-Ann Heng, Dong Ni, Caizi Li, Qianqian Tong, Weixin Si, Élodie Puybareau, Younes Khoudli, Thierry Géraud, Chen Chen, Wenjia Bai, Daniel Rueckert, Lingchao Xu, Xiahai Zhuang, Xinzhe Luo, Shuman Jia, Maxime Sermesant, Yashu Liu, Kuanquan Wang, Davide Borra, Alessandro Masci, Cristiana Corsi, Coen Vente, Mitko Veta, Rashed Karim, Chandrakanth Jayachandran Preetha, Sandy Engelhardt, Menyun Qiao, Yuanyuan Wang, Qian Tao, Marta Nunez-Garcia, Oscar Camara, Nicolo Savioli, Pablo Lamata, Jichao Zhao

2020-11-10

In Medical Image Analysis

Abstract

Segmentation of medical images, particularly late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) used for visualizing diseased atrial structures, is a crucial first step for ablation treatment of atrial fibrillation. However, direct segmentation of LGE-MRIs is challenging due to the varying intensities caused by contrast agents. Since most clinical studies have relied on manual, labor-intensive approaches, automatic methods are of high interest, particularly optimized machine learning approaches. To address this, we organized the 2018 Left Atrium Segmentation Challenge using 154 3D LGE-MRIs, currently the world’s largest atrial LGE-MRI dataset, and associated labels of the left atrium segmented by three medical experts, ultimately attracting the participation of 27 international teams. In this paper, extensive analysis of the submitted algorithms using technical and biological metrics was performed by undergoing subgroup analysis and conducting hyper-parameter analysis, offering an overall picture of the major design choices of convolutional neural networks (CNNs) and practical considerations for achieving state-of-the-art left atrium segmentation. Results show that the top method achieved a Dice score of 93.2% and a mean surface to surface distance of 0.7 mm, significantly outperforming prior state-of-the-art. Particularly, our analysis demonstrated that double sequentially used CNNs, in which a first CNN is used for automatic region-of-interest localization and a subsequent CNN is used for refined regional segmentation, achieved superior results than traditional methods and machine learning approaches containing single CNNs. This large-scale benchmarking study makes a significant step towards much-improved segmentation methods for atrial LGE-MRIs, and will serve as an important benchmark for evaluating and comparing the future works in the field. Furthermore, the findings from this study can potentially be extended to other imaging datasets and modalities, having an impact on the wider medical imaging community.

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Do not treat boundaries and regions differently: An example on heart left atrial segmentation

By Zhou Zhao, Nicolas Boutry, Élodie Puybareau, Thierry Géraud

2020-11-02

In Proceedings of the 25th international conference on pattern recognition (ICPR)

Abstract

Atrial fibrillation is the most common heart rhythm disease. Due to a lack of understanding in matter of underlying atrial structures, current treatments are still not satisfying. Recently, with the popularity of deep learning, many segmentation methods based on fully convolutional networks have been proposed to analyze atrial structures, especially from late gadolinium-enhanced magnetic resonance imaging. However, two problems still occur: 1) segmentation results include the atrial- like background; 2) boundaries are very hard to segment. Most segmentation approaches design a specific network that mainly focuses on the regions, to the detriment of the boundaries. Therefore, this paper proposes an attention full convolutional network framework based on the ResNet-101 architecture, which focuses on boundaries as much as on regions. The additional attention module is added to have the network pay more attention on regions and then to reduce the impact of the misleading similarity of neighboring tissues. We also use a hybrid loss composed of a region loss and a boundary loss to treat boundaries and regions at the same time. We demonstrate the efficiency of the proposed approach on the MICCAI 2018 Atrial Segmentation Challenge public dataset.

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FOANet: A focus of attention network with application to myocardium segmentation

By Zhou Zhao, Nicolas Boutry, Élodie Puybareau, Thierry Géraud

2020-11-02

In Proceedings of the 25th international conference on pattern recognition (ICPR)

Abstract

In myocardium segmentation of cardiac magnetic resonance images, ambiguities often appear near the boundaries of the target domains due to tissue similarities. To address this issue, we propose a new architecture, called FOANet, which can be decomposed in three main steps: a localization step, a Gaussian-based contrast enhancement step, and a segmentation step. This architecture is supplied with a hybrid loss function that guides the FOANet to study the transformation relationship between the input image and the corresponding label in a three-level hierarchy (pixel-, patch- and map-level), which is helpful to improve segmentation and recovery of the boundaries. We demonstrate the efficiency of our approach on two public datasets in terms of regional and boundary segmentations.

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

By Nicolas Boutry, Laurent Najman, Thierry Géraud

2020-09-03

In Journal of Mathematical Imaging and Vision

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

By Nicolas Boutry, Laurent Najman, Thierry Géraud

2020-09-03

In Journal of Mathematical Imaging and Vision

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

By Nicolas Boutry, Rocio Gonzalez-Diaz, Laurent Najman, Thierry Géraud

2020-07-21

In Combinatorial image analysis: Proceedings of the 20th international workshop (IWCIA 2020)

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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A new minimum barrier distance for multivariate images with applications to salient object detection, shortest path finding, and segmentation

By Minh Ôn Vũ Ngọc, Nicolas Boutry, Jonathan Fabrizio, Thierry Géraud

2020-06-02

In Computer Vision and Image Understanding

Abstract

Distance transforms and the saliency maps they induce are widely used in image processing, computer vision, and pattern recognition. One of the most commonly used distance transform is the geodesic one. Unfortunately, this distance does not always achieve satisfying results on noisy or blurred images. Recently, a new (pseudo-)distance, called the minimum barrier distance (MBD), more robust to pixel variations, has been introduced. Some years after, Géraud et al. have proposed a good and fast-to compute approximation of this distance: the Dahu pseudo-distance. Since this distance was initially developped for grayscale images, we propose here an extension of this transform to multivariate images; we call it vectorial Dahu pseudo-distance. An efficient way to compute it is provided in this paper. Besides, we provide benchmarks demonstrating how much the vectorial Dahu pseudo-distance is more robust and competitive compared to other MB-based distances, which shows how much this distance is promising for salient object detection, shortest path finding, and object segmentation.

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Using separated inputs for multimodal brain tumor segmentation with 3D U-Net-like architectures

By Nicolas Boutry, Joseph Chazalon, Élodie Puybareau, Guillaume Tochon, Hugues Talbot, Thierry Géraud

2020-06-01

In Proceedings of the 5th international workshop, BrainLes 2019, held in conjunction with MICCAI 2019

Abstract

The work presented in this paper addresses the MICCAI BraTS 2019 challenge devoted to brain tumor segmentation using mag- netic resonance images. For each task of the challenge, we proposed and submitted for evaluation an original method. For the tumor segmentation task (Task 1), our convolutional neural network is based on a variant of the U-Net architecture of Ronneberger et al. with two modifications: first, we separate the four convolution parts to decorrelate the weights corresponding to each modality, and second, we provide volumes of size 240 * 240 * 3 as inputs in these convolution parts. This way, we profit of the 3D aspect of the input signal, and we do not use the same weights for separate inputs. For the overall survival task (Task 2), we compute explainable features and use a kernel PCA embedding followed by a Random Forest classifier to build a predictor with very few training samples. For the uncertainty estimation task (Task 3), we introduce and compare lightweight methods based on simple principles which can be applied to any segmentation approach. The overall performance of each of our contribution is honorable given the low computational requirements they have both for training and testing.

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A two-stage temporal-like fully convolutional network framework for left ventricle segmentation and quantification on MR images

By Zhou Zhao, Nicolas Boutry, Élodie Puybareau, Thierry Géraud

2020-02-07

In Statistical atlases and computational models of the heart. Multi-sequence CMR segmentation, CRT-EPiggy and LV full quantification challenges—10th international workshop, STACOM 2019, held in conjunction with MICCAI 2019, shenzhen, china, october 13, 2019, revised selected papers

Abstract

Automatic segmentation of the left ventricle (LV) of a living human heart in a magnetic resonance (MR) image (2D+t) allows to measure some clinical significant indices like the regional wall thicknesses (RWT), cavity dimensions, cavity and myocardium areas, and cardiac phase. Here, we propose a novel framework made of a sequence of two fully convolutional networks (FCN). The first is a modified temporal-like VGG16 (the “localization network”) and is used to localize roughly the LV (filled-in) epicardium position in each MR volume. The second FCN is a modified temporal-like VGG16 too, but devoted to segment the LV myocardium and cavity (the “segmentation network”). We evaluate the proposed method with 5-fold-cross-validation on the MICCAI 2019 LV Full Quantification Challenge dataset. For the network used to localize the epicardium, we obtain an average dice index of 0.8953 on validation set. For the segmentation network, we obtain an average dice index of 0.8664 on validation set (there, data augmentation is used). The mean absolute error (MAE) of average cavity and myocardium areas, dimensions, RWT are 114.77 mm^2; 0.9220 mm; 0.9185 mm respectively. The computation time of the pipeline is less than 2 s for an entire 3D volume. The error rate of phase classification is 7.6364%, which indicates that the proposed approach has a promising performance to estimate all these parameters.

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