A skeletonization algorithm for gradient-based optimization

The skeleton of a digital image is a compact representation of its topology, geometry, and scale. It has utility in many computer vision applications, such as image description, segmentation, and registration. However, skeletonization has only seen limited use in contemporary deep learning solutions. Most existing skeletonization algorithms are not differentiable, making it impossible to integrate them with gradient-based optimization. Compatible algorithms based on morphological operations and neural networks have been proposed, but their results often deviate from the geometry and topology of the true medial axis. This work introduces the first three-dimensional skeletonization algorithm that is both compatible with gradient-based optimization and preserves an object's topology. Our method is exclusively based on matrix additions and multiplications, convolutional operations, basic non-linear functions, and sampling from a uniform probability distribution, allowing it to be easily implemented in any major deep learning library. In benchmarking experiments, we prove the advantages of our skeletonization algorithm compared to non-differentiable, morphological, and neural-network-based baselines. Finally, we demonstrate the utility of our algorithm by integrating it with two medical image processing applications that use gradient-based optimization: deep-learning-based blood vessel segmentation, and multimodal registration of the mandible in computed tomography and magnetic resonance images.Comment: Accepted at ICCV 202

Automatic adjustment of rigs to extracted skeletons

In the animation, the process of rigging a character is an elaborated and time consuming task. The rig is developed for a specific character, and it can not be reused in other meshes. In this paper we present a method to automatically adjust a human-like character rig to an arbitrary human-like 3D mesh, using a extracted skeleton obtained from the input mesh. Our method is based on the selection and extraction of feature points, to find an equivalence between an extracted skeleton and the animation rig.Peer ReviewedPostprint (published version

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

Machine learning of image analysis with convolutional networks and topological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 130-140).We present an approach to solving computer vision problems in which the goal is to produce a high-dimensional, pixel-based interpretation of some aspect of the underlying structure of an image. Such tasks have traditionally been categorized as ''low-level vision'' problems, and examples include image denoising, boundary detection, and motion estimation. Our approach is characterized by two main elements, both of which represent a departure from previous work. The first is a focus on convolutional networks, a machine learning strategy that operates directly on an input image with no use of hand-designed features and employs many thousands of free parameters that are learned from data. Previous work in low-level vision has been largely focused on completely hand-designed algorithms or learning methods with a hand-designed feature space. We demonstrate that a learning approach with high model complexity, but zero prior knowledge about any specific image domain, can outperform existing techniques even in the challenging area of natural image processing. We also present results that establish how convolutional networks are closely related to Markov random fields (MRFs), a popular probabilistic approach to image analysis, but can in practice can achieve significantly greater model complexity. The second aspect of our approach is the use of domain specific cost functions and learning algorithms that reflect the structured nature of certain prediction problems in image analysis.(cont.) In particular, we show how concepts from digital topology can be used in the context of boundary detection to both evaluate and optimize the high-order property of topological accuracy. We demonstrate that these techniques can significantly improve the machine learning approach and outperform state of the art boundary detection and segmentation methods. Throughout our work we maintain a special interest and focus on application of our methods to connectomics, an emerging scientific discipline that seeks high-throughput methods for recovering neural connectivity data from brains. This application requires solving low-level image analysis problems on a tera-voxel or peta-voxel scale, and therefore represents an extremely challenging and exciting arena for the development of computer vision methods.by Viren Jain.Ph.D

Pore-scale Modeling and Multi-scale Characterization of Liquid Transport in Shales

Distinct from conventional reservoirs, shale formations have limited pore connectivity and unique pore spatial-distribution. Consequently, theoretical pore-network models developed for conventional formations are not representative of the porous media in unconventional rocks. This work presents a novel theoretical pore-network model, the dendroidal model, based on the analysis of pore-scale model reconstruction extracted from Scanning Electron Microscope images. The dendroidal model is a “semi-acyclic” model, which characterizes the limited connectivity of void space without sacrificing the interaction among main flow paths. The dendroidal model infers pore-body distribution based on the hysteresis effect of isothermal adsorption/desorption measurements and characterizes pore-throat distribution using mercury drainage capillary pressure experiments. The use of dual-compressibility model in the pore-network model construction eliminates the compressibility effect of void space, including connected pores and dead-end pores, in mercury drainage experiments. The total organic carbon (TOC) content and minerology are measured by experiments to determine the composition of pore bodies and pore throats in the dendroidal model. The difference in mercury intrusion and extraction caused by the trapping hysteresis and contact-angle hysteresis affects the stochastically distributed parameters, including pore-throat length, pore-throat cross-sectional geometry, coordination number and pore-body spatial distribution. I validate the dendroidal model by predicting the absolute permeability of the core samples from Marcellus and Wolfcamp shales. This newly developed pore-network model integrates the aforementioned seven distinct types of experiments to capture the realistic pore structures of shales. Extracted pore-network modeling is an efficient and reliable way to provide a platform for mathematical simulation of fluid flow in porous media and for predicting the transport properties. However, the existing algorithms for pore-network extraction have deficiencies in characterizing the porous media of shale core samples in as much as they cannot capture the unique features of unconventional reservoirs. In nano-scale pores, the accurate characterization of the porous geometry is important, since the relative error will be significant without considering trivial information. The newly developed approach, based on the maximal-ball method, proposes a novel and enhanced algorithm for the classification of pore throats and pore bodies. It also has a better performance in characterizing the corresponding properties that include pore-throat length, pore size and geometric factors. The Marcellus shale core samples are scanned using scanning electron microscope imaging with the resolution of 4 nm. The pore-network models based on the tomographic images are constructed, and the aforementioned parameters are compared and analyzed. The quantification of liquid transport in liquid-rich shales is crucial for an economical exploitation of hydrocarbon. The laboratory measurement of permeability is challenging as it is time-consuming and includes large uncertainties. Direct pore-scale modeling and extracted pore-network modeling are alternatives for the prediction of transport properties. But due to its prohibitively high computational cost, its applications are limited to micro-scale. The emphasis of this work is to understand the mechanisms of nano-confined liquid transportation (nano-scale) and to quantify the liquid transport capacity in the scales of core samples (centi-scale). A modified Navier-Stokes equation is developed to integrate the variation of fluid properties with respect to the strength of liquid-wall interaction. To predict the apparent permeability in large scale, the dendroidal theoretical pore-network model is constructed by integrating mercury drainage/imbibition and isothermal adsorption/desorption experiments. The dendroidal model also integrates the data of Fourier Transform infra-red spectroscopy experiments to characterize the mineralogy distribution and total organic carbon to distinguish organic pores and inorganic pores. Results from molecular dynamics simulation indicate that the flow capacity of nano-confined liquid can be 1-3 orders different from that calculated by Navier-Stokes equation without considering the boundary-slippage effect. The geometry and composition also have considerable effect on the surface friction factor and viscosity in the near-wall fluid film, which in turn significantly influence the flow capacity in nano-pores. This work investigates the mechanisms of liquid flow in nano-confined pores with various composition and geometries. Accurate characterizations of liquid transport in shales will provide significant advantage in the field development planning of unconventional resources

Segmentation of medical images under topological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 135-142).Major advances in the field of medical imaging over the past two decades have provided physicians with powerful, non-invasive techniques to probe the structure, function, and pathology of the human body. This increasingly vast and detailed amount of information constitutes a great challenge for the medical imaging community, and requires significant innovations in all aspect of image processing. To achieve accurate and topologically-correct delineations of anatomical structures from medical images is a critical step for many clinical and research applications. In this thesis, we extend the theoretical tools applicable to the segmentation of images under topological control, apply these new concepts to broaden the class of segmentation methodologies, and develop generally applicable and well-founded algorithms to achieve accurate segmentations of medical images under topological constraints. First, we introduce a digital concept that offers more flexibility in controlling the topology of digital segmentations. Second, we design a level set framework that offers a subtle control over the topology of the level set components. Our method constitutes a trade-off between traditional level sets and topology-preserving level sets.(cont.) Third, we develop an algorithm for the retrospective topology correction of 3D digital segmentations. Our method is nested in the theory of Bayesian parameter estimation, and integrates statistical information into the topology correction process. In addition, no assumption is made on the topology of the initial input images. Finally, we propose a genetic algorithm to accurately correct the spherical topology of cortical surfaces. Unlike existing approaches, our method is able to generate several potential topological corrections and to select the maximum-a-posteriori retessellation in a Bayesian framework. Our approach integrates statistical, geometrical, and shape information into the correction process, providing optimal solutions relatively to the MRI intensity profile and the expected curvature.by Florent Ségonne.Ph.D

A Boolean characterization of three-dimensional simple points

International audienc

A Boolean characterization of three-dimensional simple points

International audienc