Automatic generation of synthetic datasets for digital pathology image analysis

The project is inspired by an actual problem of timing and accessibility in the analysis of histological samples in the health-care system. In this project, I address the problem of synthetic histological image generation for the purpose of training Neural Networks for the segmentation of real histological images. The collection of real histological human-labeled samples is a very time consuming and expensive process and often is not representative of healthy samples, for the intrinsic nature of the medical analysis. The method I propose is based on the replication of the traditional specimen preparation technique in a virtual environment. The first step is the creation of a 3D virtual model of a region of the target human tissue. The model should represent all the key features of the tissue, and the richer it is the better will be the yielded result. The second step is to perform a sampling of the model through a virtual tomography process, which produces a first completely labeled image of the section. This image is then processed with different tools to achieve a histological-like aspect. The most significant aesthetical post-processing is given by the action of a style transfer neural network that transfers the typical histological visual texture on the synthetic image. This procedure is presented in detail for two specific models: one of pancreatic tissue and one of dermal tissue. The two resulting images compose a pair of images suitable for a supervised learning technique. The generation process is completely automatized and does not require the intervention of any human operator, hence it can be used to produce arbitrary large datasets. The synthetic images are inevitably less complex than the real samples and they offer an easier segmentation task to solve for the NN. However, the synthetic images are very abundant, and the training of a NN can take advantage of this feature, following the so-called curriculum learning strategy

Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibliography update

The discretized polyhedra simplification (DPS): a framework for polyhedra simplification based on decomposition schemes

This work discusses simplification algorithms for the generation of a multiresolution family of solid representations from an initial polyhedral solid. We introduce the Discretized Polyhedra Simplification (DPS), a framework for polyhedra simplification using space decomposition models. The DPS is based on a new error measurement and provides a sound scheme for error-bounded, geometry and topology simplification while preserving the validity of the model. A method following this framework, Direct DPS, is presented and discussed. Direct DPS uses an octree for topology simplification and error control, and generates valid solid representations. Our method is also able to generate approximations which do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Unlike most of the current methods, our algorithm can deal and also produces faces with arbitrary complexity. An extension of the Direct method for appearance preservation, called Hybrid DPS, is also discussed

Stereo Imaging Camera Model for 3D Shape Reconstruction of Complex Crystals and Estimation of Facet Growth Kinetics

The principle that the 3D shape of crystals that grow from a solution can be characterised in real-time using stereo imaging has been demonstrated previously. It uses the 2D images of a crystal that are obtained from two or more cameras arranged in defined angles as well as a mathematical reconstruction algorithm. Here attention is given to the development of a new and more robust 3D shape reconstruction method for complicated crystal structures. The proposed stereo imaging camera model for 3D crystal shape reconstruction firstly rotates a digitised crystal in the three-dimensional space and varies the size dimensions in all face directions. At each size and orientation, 2D projections of the crystal, according to the angles between the 2D cameras, are recorded. The contour information of the 2D images is processed to calculate Fourier descriptors and radius-based signature that are stored in a database. When the stereo imaging instrument mounted on a crystalliser captures 2D images, the images are segmented to obtain the contour information and processed to obtain Fourier descriptors and radius-based information. The calculated Fourier descriptors and radius-based signature are used to find the best matching in the database. The corresponding 3D crystal shape is thus found. Potash alum crystals that each has 26 habit faces were used as a case study. The result shows that the new approach for 3D shape reconstruction is more accurate and significantly robust than previous methods. In addition, the growth rates of {111}, {110} and {100} faces were correlated with relative supersaturation to derive models of facet growth kinetics

Nanoinformatics

Machine learning; Big data; Atomic resolution characterization; First-principles calculations; Nanomaterials synthesi

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Voids and the large-scale structure of the Universe

The Cosmic Web describes the distribution of matter on the largest scales of the Universe. It is composed of dense regions full of galaxies, long filamentary structures and low density voids. In this thesis we introduce the Cosmic Web and we focus on the description of voids, large underdense regions pratically devoid of galaxies occupying the major volume of the Universe. Voids are a key component of the Cosmic Web, since their pristine environment is an important testing ground for our understanding of the importance of environmental influences on the evolution of galaxies. Then we introduce Voronoi and Delaunay tessellations, two random tessellation methods. Tessellation methods are used to divide a d-dimensional space into polytopes covering the whole space without overlapping. Voronoi and Delaunay tessellations are the basis of the DTFE method, useful when we want to compute a continuous field from a large point sample. Finally, we briefly discuss and compare two void finders: ZOBOV and WVF, whose aim is to find density depressions in a set of points, without introducing any free parameters

Nanoinformatics

Machine learning; Big data; Atomic resolution characterization; First-principles calculations; Nanomaterials synthesi