The Probabilistic Active Shape Model: From Model Construction to Flexible Medical Image Segmentation

Automatic processing of three-dimensional image data acquired with computed tomography or magnetic resonance imaging plays an increasingly important role in medicine. For example, the automatic segmentation of anatomical structures in tomographic images allows to generate three-dimensional visualizations of a patient’s anatomy and thereby supports surgeons during planning of various kinds of surgeries. Because organs in medical images often exhibit a low contrast to adjacent structures, and because the image quality may be hampered by noise or other image acquisition artifacts, the development of segmentation algorithms that are both robust and accurate is very challenging. In order to increase the robustness, the use of model-based algorithms is mandatory, as for example algorithms that incorporate prior knowledge about an organ’s shape into the segmentation process. Recent research has proven that Statistical Shape Models are especially appropriate for robust medical image segmentation. In these models, the typical shape of an organ is learned from a set of training examples. However, Statistical Shape Models have two major disadvantages: The construction of the models is relatively difficult, and the models are often used too restrictively, such that the resulting segmentation does not delineate the organ exactly. This thesis addresses both problems: The first part of the thesis introduces new methods for establishing correspondence between training shapes, which is a necessary prerequisite for shape model learning. The developed methods include consistent parameterization algorithms for organs with spherical and genus 1 topology, as well as a nonrigid mesh registration algorithm for shapes with arbitrary topology. The second part of the thesis presents a new shape model-based segmentation algorithm that allows for an accurate delineation of organs. In contrast to existing approaches, it is possible to integrate not only linear shape models into the algorithm, but also nonlinear shape models, which allow for a more specific description of an organ’s shape variation. The proposed segmentation algorithm is evaluated in three applications to medical image data: Liver and vertebra segmentation in contrast-enhanced computed tomography scans, and prostate segmentation in magnetic resonance images

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Groupwise shape correspondence with local features

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies. However, anatomical correspondence is rarely a direct result of spatial proximity of sample points but rather depends on many other features such as local curvature, position with respect to blood vessels, or connectivity to other parts of the anatomy. This dissertation presents a novel method for computing point-based correspondence among populations of surfaces by combining spatial location of the sample points with non-spatial local features. A framework for optimizing correspondence using arbitrary local features is developed. The performance of the correspondence algorithm is objectively assessed using a set of evaluation metrics. The main focus of this research is on correspondence across human cortical surfaces. Statistical analysis of cortical thickness, which is key to many neurological research problems, is the driving problem. I show that incorporating geometric (sulcal depth) and non-geometric (DTI connectivity) knowledge about the cortex significantly improves cortical correspondence compared to existing techniques. Furthermore, I present a framework that is the first to allow the white matter fiber connectivity to be used for improving cortical correspondence

Development of an Atlas-Based Segmentation of Cranial Nerves Using Shape-Aware Discrete Deformable Models for Neurosurgical Planning and Simulation

Twelve pairs of cranial nerves arise from the brain or brainstem and control our sensory functions such as vision, hearing, smell and taste as well as several motor functions to the head and neck including facial expressions and eye movement. Often, these cranial nerves are difficult to detect in MRI data, and thus represent problems in neurosurgery planning and simulation, due to their thin anatomical structure, in the face of low imaging resolution as well as image artifacts. As a result, they may be at risk in neurosurgical procedures around the skull base, which might have dire consequences such as the loss of eyesight or hearing and facial paralysis. Consequently, it is of great importance to clearly delineate cranial nerves in medical images for avoidance in the planning of neurosurgical procedures and for targeting in the treatment of cranial nerve disorders. In this research, we propose to develop a digital atlas methodology that will be used to segment the cranial nerves from patient image data. The atlas will be created from high-resolution MRI data based on a discrete deformable contour model called 1-Simplex mesh. Each of the cranial nerves will be modeled using its centerline and radius information where the centerline is estimated in a semi-automatic approach by finding a shortest path between two user-defined end points. The cranial nerve atlas is then made more robust by integrating a Statistical Shape Model so that the atlas can identify and segment nerves from images characterized by artifacts or low resolution. To the best of our knowledge, no such digital atlas methodology exists for segmenting nerves cranial nerves from MRI data. Therefore, our proposed system has important benefits to the neurosurgical community

Proceedings of the Fourth International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Biological Shape Variability Modeling (MFCA 2013), Nagoya, Japan

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the first edition of this workshop in 2006, second edition in New-York in 2008, the third edition in Toronto in 2011, the forth edition was held in Nagoya Japan on September 22 2013

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations.Following the first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions

Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review

The medical image analysis field has traditionally been focused on the development of organ-, and disease-specific methods. Recently, the interest in the development of more 20 comprehensive computational anatomical models has grown, leading to the creation of multi-organ models. Multi-organ approaches, unlike traditional organ-specific strategies, incorporate inter-organ relations into the model, thus leading to a more accurate representation of the complex human anatomy. Inter-organ relations are not only spatial, but also functional and physiological. Over the years, the strategies 25 proposed to efficiently model multi-organ structures have evolved from the simple global modeling, to more sophisticated approaches such as sequential, hierarchical, or machine learning-based models. In this paper, we present a review of the state of the art on multi-organ analysis and associated computation anatomy methodology. The manuscript follows a methodology-based classification of the different techniques 30 available for the analysis of multi-organs and multi-anatomical structures, from techniques using point distribution models to the most recent deep learning-based approaches. With more than 300 papers included in this review, we reflect on the trends and challenges of the field of computational anatomy, the particularities of each anatomical region, and the potential of multi-organ analysis to increase the impact of 35 medical imaging applications on the future of healthcare.Comment: Paper under revie

Synthesizing and Editing Photo-realistic Visual Objects

In this thesis we investigate novel methods of synthesizing new images of a deformable visual object using a collection of images of the object. We investigate both parametric and non-parametric methods as well as a combination of the two methods for the problem of image synthesis. Our main focus are complex visual objects, specifically deformable objects and objects with varying numbers of visible parts. We first introduce sketch-driven image synthesis system, which allows the user to draw ellipses and outlines in order to sketch a rough shape of animals as a constraint to the synthesized image. This system interactively provides feedback in the form of ellipse and contour suggestions to the partial sketch of the user. The user's sketch guides the non-parametric synthesis algorithm that blends patches from two exemplar images in a coarse-to-fine fashion to create a final image. We evaluate the method and synthesized images through two user studies. Instead of non-parametric blending of patches, a parametric model of the appearance is more desirable as its appearance representation is shared between all images of the dataset. Hence, we propose Context-Conditioned Component Analysis, a probabilistic generative parametric model, which described images with a linear combination of basis functions. The basis functions are evaluated for each pixel using a context vector computed from the local shape information. We evaluate C-CCA qualitatively and quantitatively on inpainting, appearance transfer and reconstruction tasks. Drawing samples of C-CCA generates novel, globally-coherent images, which, unfortunately, lack high-frequency details due to dimensionality reduction and misalignment. We develop a non-parametric model that enhances the samples of C-CCA with locally-coherent, high-frequency details. The non-parametric model efficiently finds patches from the dataset that match the C-CCA sample and blends the patches together. We analyze the results of the combined method on the datasets of horse and elephant images