Scale-based surface understanding using diffusion smoothing

The research discussed in this thesis is concerned with surface understanding from the viewpoint of recognition-oriented, scale-related processing based on surface curvatures and diffusion smoothing. Four problems below high level visual processing are investigated: 1) 3-dimensional data smoothing using a diffusion process; 2) Behaviour of shape features across multiple scales, 3) Surface segmentation over multiple scales; and 4) Symbolic description of surface features at multiple scales. In this thesis, the noisy data smoothing problem is treated mathematically as a boundary value problem of the diffusion equation instead of the well-known Gaussian convolution, In such a way, it provides a theoretical basis to uniformly interpret the interrelationships amongst diffusion smoothing, Gaussian smoothing, repeated averaging and spline smoothing. It also leads to solving the problem with a numerical scheme of unconditional stability, which efficiently reduces the computational complexity and preserves the signs of curvatures along the surface boundaries. Surface shapes are classified into eight types using the combinations of the signs of the Gaussian curvature K and mean curvature H, both of which change at different scale levels. Behaviour of surface shape features over multiple scale levels is discussed in terms of the stability of large shape features, the creation, remaining and fading of small shape features, the interaction between large and small features and the structure of behaviour of the nested shape features in the KH sign image. It provides a guidance for tracking the movement of shape features from fine to large scales and for setting up a surface shape description accordingly. A smoothed surface is partitioned into a set of regions based on curvature sign homogeneity. Surface segmentation is posed as a problem of approximating a surface up to the degree of Gaussian and mean curvature signs using the depth data alone How to obtain feasible solutions of this under-determined problem is discussed, which includes the surface curvature sign preservation, the reason that a sculptured surface can be segmented with the KH sign image alone and the selection of basis functions of surface fitting for obtaining the KH sign image or for region growing. A symbolic description of the segmented surface is set up at each scale level. It is composed of a dual graph and a geometrical property list for the segmented surface. The graph describes the adjacency and connectivity among different patches as the topological-invariant properties that allow some object's flexibility, whilst the geometrical property list is added to the graph as constraints that reduce uncertainty. With this organisation, a tower-like surface representation is obtained by tracking the movement of significant features of the segmented surface through different scale levels, from which a stable description can be extracted for inexact matching during object recognition

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Automatic detection of drusen associated with age-related macular degeneration in optical coherence tomography: a graph-based approach

Tese de Doutoramento em Líderes para Indústrias TecnológicasThe age-related macular degeneration (AMD) starts to manifest itself with the appearance of drusen. Progressively, the drusen increase in size and in number without causing alterations to vision. Nonetheless, their quantification is important because it correlates with the evolution of the disease to an advanced stage, which could lead to the loss of central vision. Manual quantification of drusen is impractical, since it is time-consuming and it requires specialized knowledge. Therefore, this work proposes a method for quantifying drusen automatically In this work, it is proposed a method for segmenting boundaries limiting drusen and another method for locating them through classification. The segmentation method is based on a multiple surface framework that is adapted for segmenting the limiting boundaries of drusen: the inner boundary of the retinal pigment epithelium + drusen complex (IRPEDC) and the Bruch’s membrane (BM). Several segmentation methods have been considerably successful in segmenting layers of healthy retinas in optical coherence tomography (OCT) images. These methods were successful because they incorporate prior information and regularization. However, these factors have the side-effect of hindering the segmentation in regions of altered morphology that often occur in diseased retinas. The proposed segmentation method takes into account the presence of lesion related with AMD, i.e., drusen and geographic atrophies (GAs). For that, it is proposed a segmentation scheme that excludes prior information and regularization that is only valid for healthy regions. Even with this segmentation scheme, the prior information and regularization can still cause the oversmoothing of some drusen. To address this problem, it is also proposed the integration of local shape priors in the form of a sparse high order potentials (SHOPs) into the multiple surface framework. Drusen are commonly detected by thresholding the distance among the boundaries that limit drusen. This approach misses drusen or portions of drusen with a height below the threshold. To improve the detection of drusen, Dufour et al. [1] proposed a classification method that detects drusen using textural information. In this work, the method of Dufour et al. [1] is extended by adding new features and performing multi-label classification, which allow the individual detection of drusen when these occur in clusters. Furthermore, local information is incorporated into the classification by combining the classifier with a hidden Markov model (HMM). Both the segmentation and detections methods were evaluated in a database of patients with intermediate AMD. The results suggest that both methods frequently perform better than some methods present in the literature. Furthermore, the results of these two methods form drusen delimitations that are closer to expert delimitations than two methods of the literature.A degenerescência macular relacionada com a idade (DMRI) começa a manifestar-se com o aparecimento de drusas. Progressivamente, as drusas aumentam em tamanho e em número sem causar alterações à visão. Porém, a sua quantificação é importante porque está correlacionada com a evolução da doença para um estado avançado, levar à perda de visão central. A quantificação manual de drusas é impraticável, já que é demorada e requer conhecimento especializado. Por isso, neste trabalho é proposto um método para segmentar drusas automaticamente. Neste trabalho, é proposto um método para segmentar as fronteiras que limitam as drusas e outro método para as localizar através de classificação. O método de segmentação é baseado numa ”framework” de múltiplas superfícies que é adaptada para segmentar as fronteiras que limitam as drusas: a fronteira interior do epitélio pigmentar + complexo de drusas e a membrana de Bruch. Vários métodos de segmentação foram consideravelmente bem-sucedidos a segmentar camadas de retinas saudáveis em imagens de tomografia de coerência ótica. Estes métodos foram bem-sucedidos porque incorporaram informação prévia e regularização. Contudo, estes fatores têm como efeito secundário dificultar a segmentação em regiões onde a morfologia da retina está alterada devido a doenças. O método de segmentação proposto toma em consideração a presença de lesões relacionadas com DMRI, .i.e., drusas e atrofia geográficas. Para isso, é proposto um esquema de segmentação que exclui informação prévia e regularização que são válidas apenas em regiões saudáveis da retina. Mesmo com este esquema de segmentação, a informação prévia e a regularização podem causar a suavização excessiva de algumas drusas. Para tentar resolver este problema, também é proposta a integração de informação prévia local sob a forma de potenciais esparsos de ordem elevada na ”framework” multi-superfície. As drusas são usalmente detetadas por ”thresholding” da distância entre as fronteiras que limitam as drusas. Esta abordagem falha drusas ou porções de drusas abaixo do ”threshold”. Para melhorar a deteção de drusas, Dufour et al. [1] propuseram um método de classificação que deteta drusas usando informação de texturas. Neste trabalho, o método de Dufour et al. [1] é estendido, adicionando novas características e realizando uma classificação com múltiplas classes, o que permite a deteção individual de drusas em aglomerados. Além disso, é incorporada informação local na classificação, combinando o classificador com um modelo oculto de Markov. Ambos os métodos de segmentação e deteção foram avaliados numa base de dados de pacientes com DMRI intermédia. Os resultados sugerem que ambos os métodos obtêm frequentemente melhores resultados que alguns métodos descritos na literatura. Para além disso, os resultados destes dois métodos formam delimitações de drusas que estão mais próximas das delimitações dos especialistas que dois métodos da literatura.This work was supported by FCT with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941. Furthermore, the Portuguese funding institution Fundação Calouste Gulbenkian has conceded me a Ph.D. grant for this work. For that, I wish to acknowledge this institution. Additionally, I want to thank one of its members, Teresa Burnay, for all her assistance with issues related with the grant, for believing that my work was worth supporting and for encouraging me to apply for the grant

Scale-Space Splatting: Reforming Spacetime for the Cross-Scale Exploration of Integral Measures in Molecular Dynamics

Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural information about the space/time localization of the studied phenomena. This leads to degenerate cases where the measures fail to capture distinct behaviour. In order to drill into these aggregate values, we propose a multi-scale visual exploration technique. Our novel representation, based on partial domain aggregation, enables the construction of a continuous scale-space for discrete datasets and the simultaneous exploration of scales in both space and time. We link these two scale-spaces in a scale-space space-time cube and model linked views as orthogonal slices through this cube, thus enabling the rapid identification of spatio-temporal patterns at multiple scales. To demonstrate the effectiveness of our approach, we showcase an advanced exploration of a protein-ligand simulation.Comment: 11 pages, 9 figures, IEEE SciVis 201

Image computing tools for the investigation of the neurological effects of preterm birth and corticosteroid administration

In this thesis we present a range of computational tools for medical imaging purposes within two main research projects. The first one is a methodological project oriented towards the improvement of the performance of a numerical computation utilised in diffeomorphic image registration. The second research project is a pre-clinical study aimed at the investigation of the effects of antenatal corticosteroids in a preterm rabbit animal model. In the first part we addressed the problem of integrating stationary velocity fields. This mathematical challenge had originated with early studies in fluid dynamics and had been subsequently mathematically formalised in the Lie group theory. Given a tangent velocity field defined in the tridimensional space as in input, the goal is to compute the position of the particles to which the velocity field is applied. This computation, also called numerical Lie exponential, is a fundamental component of several medical image registration algorithm based on diffeomorphisms, i.e. bijective differentiable maps with differentiable inverse. It is as well a widely utilised tool in computational anatomy to quantify the differences between two anatomical shapes measuring the parameters of the transformation that belongs to a metric vector space. The resulting new class of algorithms introduced in this thesis was created combining the known scaling and squaring algorithm with a class of numerical integrators aimed to solve systems of ordinary differential equations called exponential integrators. The introduced scaling and squaring based approximated exponential integrator algorithm have improved the computational time and accuracy respect to the state- of-the-art methods. The second part of the research is a pre-clinical trial carried forward in collab- oration with the Department of Development and Regeneration, Woman and Child Cluster at the KU Leuven University. The clinical research question is related to the understanding of the possible negative effects of administering antenatal cor- ticosteroids for preterm birth. To tackle this problem we designed and started a pre-clinical study using a New Zealand perinatal rabbit model. In this part of the research I was involved in the research team to provide the tools to automatise the data analysis and to eliminate the time consuming and non reproducible manual segmentation step. The main result of this collaboration is the creation of the first multi-modal multi-atlas for the newborn rabbit brain. This is embedded in a segmentation propagation and label fusion algorithm at the core of the proposed open-sourced automatic pipeline, having as input the native scanner format and as output the main MRI readouts, such as volume, fractional anisotropy and mean diffusivity

Surface fluid registration of conformal representation: Application to detect disease burden and genetic influence on hippocampus

abstract: In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistent surface fluid registration, and multivariate tensor-based morphometty (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometry difference between diagnostic groups. Experimental results show that the new system has better performance than two publicly available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E(is an element of)4 allele (ApoE4), which is considered as the most prevalent risk factor for AD. Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our work provides a new MRI analysis tool that may help presymptomatic AD research.NOTICE: this is the author’s version of a work that was accepted for publication in NEUROIMAGE. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neuroimage, 78, 111-134 [2013] http://dx.doi.org/10.1016/j.neuroimage.2013.04.01

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)