276 research outputs found

    Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

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    Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

    Characterising Shape Variation in the Human Right Ventricle Using Statistical Shape Analysis: Preliminary Outcomes and Potential for Predicting Hypertension in a Clinical Setting

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    Variations in the shape of the human right ventricle (RV) have previously been shown to be predictive of heart function and long term prognosis in Pulmonary Hypertension (PH), a deadly disease characterised by high blood pressure in the pulmonary arteries. The extent to which ventricular shape is also affected by non-pathological features such as sex, body mass index (BMI) and age is explored in this thesis. If fundamental differences in the shape of a structurally normal RV exist, these might also impact the success of a predictive model. This thesis evaluates the extent to which non-pathological features affect the shape of the RV and determines the best ways, in terms of procedure and analysis, to adapt the model to consistently predict PH. It also identifies areas where the statistical shape analysis procedure is robust, and considers the extent to which specific, non-pathological, characteristics impact the diagnostic potential of the statistical shape model. Finally, recommendations are made on next steps in the development of a classification procedure for PH. The dataset was composed of clinically-obtained, cardiovascular magnetic resonance images (CMR) from two independent sources; The University of Pittsburgh Medical Center and Newcastle University. Shape change is assessed using a 3D statistical shape analysis technique, which topologically maps heart meshes through an harmonic mapping approach to create a unique shape function for each shape. Proper Orthogonal Decomposition (POD) was applied to the complete set of shape functions in order to determine and rank a set of shape features (i.e. modes and corresponding coefficients from the decomposition). MRI scanning protocol produced the most significant difference in shape; a shape mode associated with detail at the RV apex and ventricular length from apex to base strongly correlated with the MRI sequence used to record each subject. Qualitatively, a protocol which skipped slices produced a shorter RV with less detail at the apex. Decomposition of sex, age and BMI also derives unique RV shape descriptors which correspond to anatomically meaningful features. The shape features are shown to be able to predict presence of PH. The predictive model can be improved by including BMI as a factor, but these improvements are mainly concentrated in identification of healthy subjects

    Differential operators on sketches via alpha contours

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    A vector sketch is a popular and natural geometry representation depicting a 2D shape. When viewed from afar, the disconnected vector strokes of a sketch and the empty space around them visually merge into positive space and negative space, respectively. Positive and negative spaces are the key elements in the composition of a sketch and define what we perceive as the shape. Nevertheless, the notion of positive or negative space is mathematically ambiguous: While the strokes unambiguously indicate the interior or boundary of a 2D shape, the empty space may or may not belong to the shape’s exterior. For standard discrete geometry representations, such as meshes or point clouds, some of the most robust pipelines rely on discretizations of differential operators, such as Laplace-Beltrami. Such discretizations are not available for vector sketches; defining them may enable numerous applications of classical methods on vector sketches. However, to do so, one needs to define the positive space of a vector sketch, or the sketch shape. Even though extracting this 2D sketch shape is mathematically ambiguous, we propose a robust algorithm, Alpha Contours, constructing its conservative estimate: a 2D shape containing all the input strokes, which lie in its interior or on its boundary, and aligning tightly to a sketch. This allows us to define popular differential operators on vector sketches, such as Laplacian and Steklov operators. We demonstrate that our construction enables robust tools for vector sketches, such as As-Rigid-As-Possible sketch deformation and functional maps between sketches, as well as solving partial differential equations on a vector sketch

    Multi-site, Multi-domain Airway Tree Modeling (ATM'22): A Public Benchmark for Pulmonary Airway Segmentation

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    Open international challenges are becoming the de facto standard for assessing computer vision and image analysis algorithms. In recent years, new methods have extended the reach of pulmonary airway segmentation that is closer to the limit of image resolution. Since EXACT'09 pulmonary airway segmentation, limited effort has been directed to quantitative comparison of newly emerged algorithms driven by the maturity of deep learning based approaches and clinical drive for resolving finer details of distal airways for early intervention of pulmonary diseases. Thus far, public annotated datasets are extremely limited, hindering the development of data-driven methods and detailed performance evaluation of new algorithms. To provide a benchmark for the medical imaging community, we organized the Multi-site, Multi-domain Airway Tree Modeling (ATM'22), which was held as an official challenge event during the MICCAI 2022 conference. ATM'22 provides large-scale CT scans with detailed pulmonary airway annotation, including 500 CT scans (300 for training, 50 for validation, and 150 for testing). The dataset was collected from different sites and it further included a portion of noisy COVID-19 CTs with ground-glass opacity and consolidation. Twenty-three teams participated in the entire phase of the challenge and the algorithms for the top ten teams are reviewed in this paper. Quantitative and qualitative results revealed that deep learning models embedded with the topological continuity enhancement achieved superior performance in general. ATM'22 challenge holds as an open-call design, the training data and the gold standard evaluation are available upon successful registration via its homepage.Comment: 32 pages, 16 figures. Homepage: https://atm22.grand-challenge.org/. Submitte

    Exercise and Proximal Femur Bone Strength to Reduce Fall-Induced Hip Fracture

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    Bone mass and structure, constituting its strength, adapt to prevalent mechanical environment. Physical activity and exercise provide natural ways to apply the mechanical loading to bone. Finding effective osteogenic exercise types to improve proximal femur bone strength is of great importance to reduce hip fracture incidence and consequent substantial socioeconomic burden. Importantly, almost all hip fractures are caused by falls. Therefore, the primary objective of the present doctoral research was to find such effective exercise types by exploring the effect of long-term specific exercise loading on proximal femur bone strength in the fall situation using a finite element (FE) method. The secondary objective was to analyze 3D morphological adaptation of proximal femur cortical bone to the specific exercise loading. The results from this secondary objective were anticipated to help understanding the findings pertinent to the primary objective. To achieve these objectives, proximal femur MRI data were obtained from 91 young adult female athletes (aged 24.7 ± 6.1 years, > 8 years competing career) and 20 nonathletic but physically active controls (aged 23.7 ± 3.8 years). The athletes were classified into five distinct exercise loading groups based on the typical loading patterns of their sports: high-impact (H-I: triple- and high-jumpers), odd-impact (O-I: soccer/football and squash players), high-magnitude (H-M: powerlifters), repetitive-impact (R-I: endurance runners), and repetitive non-impact (R-NI: swimmers). Based on their MRI data, proximal femur FE models were first created in a single fall configuration (direction) to compare 1) cortical stresses in eight anatomical octants of femoral neck cross-sections in the proximal, middle, and distal femoral neck regions and 2) fracture behavior (load, location, and mode) between each exercise loading and control groups. The athletic bones are adapted to the long- term specific exercise loading characterized by not only the loading magnitude, rate, and frequency but also direction. Given this, the study was extended to simulate the FE models in multiple fall directions to examine whether potentially identified higher proximal femur bone strength to reduce fall-induced hip fracture risk, attributed to the long-term specific exercise loading, depends on the direction of the fall onto the greater trochanter or hip. For the secondary objective, a new computational anatomy method called Ricci-flow conformal mapping (RCM) was implemented to obtain 3D distribution of the cortical thickness within the proximal femur and to perform its spatial between-group statistical comparisons. Key results from the present research demonstrated that young adult females with the exercise loading history of high ground impacts (H-I), ground impacts from unusual/odd directions (O-I), or a great number of repetitive ground impacts (R-I) had 10-22%, 12-16%, and 14-23% lower fall-induced cortical stress at the fracture-prone superolateral femoral neck and 11-17%, 10-11%, and 22-28% higher fracture loads (higher proximal femur bone strength) in the fall situations compared to the controls, respectively. These results indicate that the long-term H-I, O-I, and R-I exercise loadings may reduce the fall-induced hip fracture risk. Furthermore, the present results showed that the higher proximal femur bone strength to reduce hip fracture risk in athletes engaged in the high-impact or repetitive-impact sports are robust and independent of the direction of fall. In contrast, the higher strength attributed to the odd-impact exercise loading appears more modest and specific to the fall direction. The analysis of the minimum fall strength spanning the multiple fall directions also supported the higher proximal femur bone strength in the athletes engaged in these impact exercises. In concordance with the literature, the present results also confirmed in these young adult females that 1) the fall-induced hip fracture most likely initiates from the superolateral femoral neck’s cortical bone, particularly at its posterior aspect (superoposterior cortex) in the distal femoral neck region, and 2) the most dangerous fracture-causing fall direction is the one where the impact is imposed to the posterolateral aspect of the greater trochanter. It would be ideal if impact exercise loading could induce beneficial cortical bone adaptation in the fracture-prone posterior aspect of superolateral femoral neck cortex. However, such apparently beneficial cortical adaptation was not observed in any of the impact or nonimpact exercise loading types examined in the present research based on the supplementary RCM-based 3D morphological analyses of proximal femur cortical bone. This analysis importantly showed that the higher proximal femur bone strengths to reduce fall-induced hip fracture risk in athletes engaged in the high- or odd-impact exercise types are likely due to thicker cortical layers in other femoral neck regions including the inferior, posterior, and/or superior-to-superoanterior regions. Interestingly, the higher proximal femur strength in the athletes with the repetitive-impact exercise loading was not supported by such cortical adaptation. This suggests that other structural/geometrical adaptation contributes to their higher strength. This calls for further studies to elucidate the source of the higher proximal femur bone strength in this type of athletes. In contrast to the impact exercise loading histories, the exercise loading history of the high-magnitude (e.g., powerlifting) or repetitive, non-impact (e.g., swimming) was not associated with higher proximal femur bone strength to reduce fall-induced hip fracture risk. This most likely reflects the lack of any beneficial structural adaptations of cortical bone around the femoral neck in the athletes with these exercise loading histories. Considering the loading characteristics of the exercise types examined in the present doctoral research, the moderate-to-high loading magnitude alone appears insufficient but needs to be generated at the high loading rate and/or frequency to induce the beneficial adaptation in the proximal femur cortical bone. Therefore, in addition to aforementioned three impact exercise loading types, other exercise or sport types satisfying this condition may also be effective to increase or maintain the proximal femur bone strength to reduce fall- induced hip fracture risk. As a clinical prospect, the present findings highlight the importance of impact exercise in combating fall-induced hip fracture. Compared to the high-impact loading exercises (e.g., triple/long and high jumping exercise), the odd-impact [ball or invasion games (e.g., football/soccer, tennis)] and/or repetitive-impact loading exercises (e.g., endurance running, jogging, and perhaps vigorous walking) likely provide a safer and more feasible choice for the populations covering the sedentary adults to old people. This is due to the relatively more moderate ground impact involved in the odd- and repetitive-impact loading exercises than in the high-impact exercises. For young, physically active, and/or fit people, the above-mentioned or similar jumping exercises and any other exercise types consisting of the high ground impact (e.g., volleyball, basketball, gymnastics) can also be incorporated into their habitual exercise routines. Lastly, the present results were observed in the young adult females who had engaged in sport-specific training from their childhood/adolescence to early adulthood. Therefore, this calls for the prospective and/or retrospective observational studies to investigate whether the higher proximal femur bone strength to reduce fall-induced hip fracture risk obtained from the long-term specific impact exercise loading during these early phases of life can sustain into the later stages, especially after age of 65 years when the hip fracture is generally more common

    Computational Geometry Contributions Applied to Additive Manufacturing

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    This Doctoral Thesis develops novel articulations of Computation Geometry for applications on Additive Manufacturing, as follows: (1) Shape Optimization in Lattice Structures. Implementation and sensitivity analysis of the SIMP (Solid Isotropic Material with Penalization) topology optimization strategy. Implementation of a method to transform density maps, resulting from topology optimization, into surface lattice structures. Procedure to integrate material homogenization and Design of Experiments (DOE) to estimate the stress/strain response of large surface lattice domains. (2) Simulation of Laser Metal Deposition. Finite Element Method implementation of a 2D nonlinear thermal model of the Laser Metal Deposition (LMD) process considering temperaturedependent material properties, phase change and radiation. Finite Element Method implementation of a 2D linear transient thermal model for a metal substrate that is heated by the action of a laser. (3) Process Planning for Laser Metal Deposition. Implementation of a 2.5D path planning method for Laser Metal Deposition. Conceptualization of a workflow for the synthesis of the Reeb Graph for a solid region in â„ť" denoted by its Boundary Representation (B-Rep). Implementation of a voxel-based geometric simulator for LMD process. Conceptualization, implementation, and validation of a tool for the minimization of the material over-deposition at corners in LMD. Implementation of a 3D (non-planar) slicing and path planning method for the LMD-manufacturing of overhanging features in revolute workpieces. The aforementioned contributions have been screened by the international scientific community via Journal and Conference submissions and publications

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Segmentation of 3D pore space from CT images using curvilinear skeleton: application to numerical simulation of microbial decomposition

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    Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).Comment: preprint, submitted to Computers & Geosciences 202
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