Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Deformable meshes for shape recovery: models and applications

With the advance of scanning and imaging technology, more and more 3D objects become available. Among them, deformable objects have gained increasing interests. They include medical instances such as organs, a sequence of objects in motion, and objects of similar shapes where a meaningful correspondence can be established between each other. Thus, it requires tools to store, compare, and retrieve them. Many of these operations depend on successful shape recovery. Shape recovery is the task to retrieve an object from the environment where its geometry is hidden or implicitly known. As a simple and versatile tool, mesh is widely used in computer graphics for modelling and visualization. In particular, deformable meshes are meshes which can take the deformation of deformable objects. They extend the modelling ability of meshes. This dissertation focuses on using deformable meshes to approach the 3D shape recovery problem. Several models are presented to solve the challenges for shape recovery under different circumstances. When the object is hidden in an image, a PDE deformable model is designed to extract its surface shape. The algorithm uses a mesh representation so that it can model any non-smooth surface with an arbitrary precision compared to a parametric model. It is more computational efficient than a level-set approach. When the explicit geometry of the object is known but is hidden in a bank of shapes, we simplify the deformation of the model to a graph matching procedure through a hierarchical surface abstraction approach. The framework is used for shape matching and retrieval. This idea is further extended to retain the explicit geometry during the abstraction. A novel motion abstraction framework for deformable meshes is devised based on clustering of local transformations and is successfully applied to 3D motion compression

Statistical Shape Modelling and Segmentation of the Respiratory Airway

The human respiratory airway consists of the upper (nasal cavity, pharynx) and the lower (trachea, bronchi) respiratory tracts. Accurate segmentation of these two airway tracts can lead to better diagnosis and interpretation of airway-specific diseases, and lead to improvement in the localization of abnormal metabolic or pathological sites found within and/or surrounding the respiratory regions. Due to the complexity and the variability displayed in the anatomical structure of the upper respiratory airway along with the challenges in distinguishing the nasal cavity from non-respiratory regions such as the paranasal sinuses, it is difficult for existing algorithms to accurately segment the upper airway without manual intervention. This thesis presents an implicit non-parametric framework for constructing a statistical shape model (SSM) of the upper and lower respiratory tract, capable of distinct shape generation and be adapted for segmentation. An SSM of the nasal cavity was successfully constructed using 50 nasal CT scans. The performance of the SSM was evaluated for compactness, specificity and generality. An averaged distance error of 1.47 mm was measured for the generality assessment. The constructed SSM was further adapted with a modified locally constrained random walk algorithm to segment the nasal cavity. The proposed algorithm was evaluated on 30 CT images and outperformed comparative state-of-the-art and conventional algorithms. For the lower airway, a separate algorithm was proposed to automatically segment the trachea and bronchi, and was designed to tolerate the image characteristics inherent in low-contrast CT images. The algorithm was evaluated on 20 clinical low-contrast CT from PET-CT patient studies and demonstrated better performance (87.1±2.8 DSC and distance error of 0.37±0.08 mm) in segmentation results against comparative state-of-the-art algorithms

Deformable Multisurface Segmentation of the Spine for Orthopedic Surgery Planning and Simulation

Purpose: We describe a shape-aware multisurface simplex deformable model for the segmentation of healthy as well as pathological lumbar spine in medical image data. Approach: This model provides an accurate and robust segmentation scheme for the identification of intervertebral disc pathologies to enable the minimally supervised planning and patient-specific simulation of spine surgery, in a manner that combines multisurface and shape statistics-based variants of the deformable simplex model. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user assistance is allowed to disable the prior shape influence during deformation. Results: Results demonstrate validation against user-assisted expert segmentation, showing excellent boundary agreement and prevention of spatial overlap between neighboring surfaces. This section also plots the characteristics of the statistical shape model, such as compactness, generalizability and specificity, as a function of the number of modes used to represent the family of shapes. Final results demonstrate a proof-of-concept deformation application based on the open-source surgery simulation Simulation Open Framework Architecture toolkit. Conclusions: To summarize, we present a deformable multisurface model that embeds a shape statistics force, with applications to surgery planning and simulation