Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

RibSeg v2: A Large-scale Benchmark for Rib Labeling and Anatomical Centerline Extraction

Automatic rib labeling and anatomical centerline extraction are common prerequisites for various clinical applications. Prior studies either use in-house datasets that are inaccessible to communities, or focus on rib segmentation that neglects the clinical significance of rib labeling. To address these issues, we extend our prior dataset (RibSeg) on the binary rib segmentation task to a comprehensive benchmark, named RibSeg v2, with 660 CT scans (15,466 individual ribs in total) and annotations manually inspected by experts for rib labeling and anatomical centerline extraction. Based on the RibSeg v2, we develop a pipeline including deep learning-based methods for rib labeling, and a skeletonization-based method for centerline extraction. To improve computational efficiency, we propose a sparse point cloud representation of CT scans and compare it with standard dense voxel grids. Moreover, we design and analyze evaluation metrics to address the key challenges of each task. Our dataset, code, and model are available online to facilitate open research at https://github.com/M3DV/RibSegComment: 10 pages, 6 figures, journa

Customizable tubular model for n-furcating blood vessels and its application to 3D reconstruction of the cerebrovascular system

Understanding the 3D cerebral vascular network is one of the pressing issues impacting the diagnostics of various systemic disorders and is helpful in clinical therapeutic strategies. Unfortunately, the existing software in the radiological workstation does not meet the expectations of radiologists who require a computerized system for detailed, quantitative analysis of the human cerebrovascular system in 3D and a standardized geometric description of its components. In this study, we show a method that uses 3D image data from magnetic resonance imaging with contrast to create a geometrical reconstruction of the vessels and a parametric description of the reconstructed segments of the vessels. First, the method isolates the vascular system using controlled morphological growing and performs skeleton extraction and optimization. Then, around the optimized skeleton branches, it creates tubular objects optimized for quality and accuracy of matching with the originally isolated vascular data. Finally, it optimizes the joints on n-furcating vessel segments. As a result, the algorithm gives a complete description of shape, position in space, position relative to other segments, and other anatomical structures of each cerebrovascular system segment. Our method is highly customizable and in principle allows reconstructing vascular structures from any 2D or 3D data. The algorithm solves shortcomings of currently available methods including failures to reconstruct the vessel mesh in the proximity of junctions and is free of mesh collisions in high curvature vessels. It also introduces a number of optimizations in the vessel skeletonization leading to a more smooth and more accurate model of the vessel network. We have tested the method on 20 datasets from the public magnetic resonance angiography image database and show that the method allows for repeatable and robust segmentation of the vessel network and allows to compute vascular lateralization indices. Graphical abstract: [Figure not available: see fulltext.]</p

Shape analysis and description based on the isometric invariances of topological skeletonization

ilustracionesIn this dissertation, we explore the problem of how to describe the shape of an object in 2D and 3D with a set of features that are invariant to isometric transformations. We focus to based our approach on the well-known Medial Axis Transform and its topological properties. We aim to study two problems. The first is how to find a shape representation of a segmented object that exhibits rotation, translation, and reflection invariance. The second problem is how to build a machine learning pipeline that uses the isometric invariance of the shape representation to do both classification and retrieval. Our proposed solution demonstrates competitive results compared to state-of-the-art approaches. We based our shape representation on the medial axis transform (MAT), sometimes called the topological skeleton. Accepted and well-studied properties of the medial axis include: homotopy preservation, rotation invariance, mediality, one pixel thickness, and the ability to fully reconstruct the object. These properties make the MAT a suitable input to create shape features; however, several problems arise because not all skeletonization methods satisfy all the above-mentioned properties at the same time. In general, skeletons based on thinning approaches preserve topology but are noise sensitive and do not allow a proper reconstruction. They are also not invariant to rotations. Voronoi skeletons also preserve topology and are rotation invariant, but do not have information about the thickness of the object, making reconstruction impossible. The Voronoi skeleton is an approximation of the real skeleton. The denser the sampling of the boundary, the better the approximation; however, a denser sampling makes the Voronoi diagram more computationally expensive. In contrast, distance transform methods allow the reconstruction of the original object by providing the distance from every pixel in the skeleton to the boundary. Moreover, they exhibit an acceptable degree of the properties listed above, but noise sensitivity remains an issue. Therefore, we selected distance transform medial axis methods as our skeletonization strategy, and focused on creating a new noise-free approach to solve the contour noise problem. To effectively classify an object, or perform any other task with features based on its shape, the descriptor needs to be a normalized, compact form: $\Phi$ should map every shape $\Omega$ to the same vector space $\mathrm{R}^{n}$. This is not possible with skeletonization methods because the skeletons of different objects have different numbers of branches and different numbers of points, even when they belong to the same category. Consequently, we developed a strategy to extract features from the skeleton through the map $\Phi$, which we used as an input to a machine learning approach. After developing our method for robust skeletonization, the next step is to use such skeleton into the machine learning pipeline to classify object into previously defined categories. We developed a set of skeletal features that were used as input data to the machine learning architectures. We ran experiments on MPEG7 and ModelNet40 dataset to test our approach in both 2D and 3D. Our experiments show results comparable with the state-of-the-art in shape classification and retrieval. Our experiments also show that our pipeline and our skeletal features exhibit some degree of invariance to isometric transformations. In this study, we sought to design an isometric invariant shape descriptor through robust skeletonization enforced by a feature extraction pipeline that exploits such invariance through a machine learning methodology. We conducted a set of classification and retrieval experiments over well-known benchmarks to validate our proposed method. (Tomado de la fuente)En esta disertación se explora el problema de cómo describir la forma de un objeto en 2D y 3D con un conjunto de características que sean invariantes a transformaciones isométricas. La metodología propuesta en este documento se enfoca en la Transformada del Eje Medio (Medial Axis Transform) y sus propiedades topológicas. Nuestro objetivo es estudiar dos problemas. El primero es encontrar una representación matemática de la forma de un objeto que exhiba invarianza a las operaciones de rotación, translación y reflexión. El segundo problema es como construir un modelo de machine learning que use esas invarianzas para las tareas de clasificación y consulta de objetos a través de su forma. El método propuesto en esta tesis muestra resultados competitivos en comparación con otros métodos del estado del arte. En este trabajo basamos nuestra representación de forma en la transformada del eje medio, a veces llamada esqueleto topológico. Algunas propiedades conocidas y bien estudiadas de la transformada del eje medio son: conservación de la homotopía, invarianza a la rotación, su grosor consiste en un solo pixel (1D), y la habilidad para reconstruir el objeto original a través de ella. Estas propiedades hacen de la transformada del eje medio un punto de partida adecuado para crear características de forma. Sin embargo, en este punto surgen varios problemas dado que no todos los métodos de esqueletización satisfacen, al mismo tiempo, todas las propiedades mencionadas anteriormente. En general, los esqueletos basados en enfoques de erosión morfológica conservan la topología del objeto, pero son sensibles al ruido y no permiten una reconstrucción adecuada. Además, no son invariantes a las rotaciones. Otro método de esqueletización son los esqueletos de Voronoi. Los esqueletos de Voronoi también conservan la topología y son invariantes a la rotación, pero no tienen información sobre el grosor del objeto, lo que hace imposible su reconstrucción. Cuanto más denso sea el muestreo del contorno del objeto, mejor será la aproximación. Sin embargo, un muestreo más denso hace que el diagrama de Voronoi sea más costoso computacionalmente. Por el contrario, los métodos basados en la transformada de la distancia permiten la reconstrucción del objeto original, ya que proporcionan la distancia desde cada píxel del esqueleto hasta su punto más cercano en el contorno. Además, exhiben un grado aceptable de las propiedades enumeradas anteriormente, aunque la sensibilidad al ruido sigue siendo un problema. Por lo tanto, en este documento seleccionamos los métodos basados en la transformada de la distancia como nuestra estrategia de esqueletización, y nos enfocamos en crear un nuevo enfoque que resuelva el problema del ruido en el contorno. Para clasificar eficazmente un objeto o realizar cualquier otra tarea con características basadas en su forma, el descriptor debe ser compacto y estar normalizado: $\Phi$ debe relacionar cada forma $\Omega$ al mismo espacio vectorial $\mathrm{R}^{n}$. Esto no es posible con los métodos de esqueletización en el estado del arte, porque los esqueletos de diferentes objetos tienen diferentes números de ramas y diferentes números de puntos incluso cuando pertenecen a la misma categoría. Consecuentemente, en nuestra propuesta desarrollamos una estrategia para extraer características del esqueleto a través de la función $\Phi$, que usamos como entrada para un enfoque de aprendizaje automático. % TODO completar con resultados. Después de desarrollar nuestro método de esqueletización robusta, el siguiente paso es usar dicho esqueleto en un modelo de aprendizaje de máquina para clasificar el objeto en categorías previamente definidas. Para ello se desarrolló un conjunto de características basadas en el eje medio que se utilizaron como datos de entrada para la arquitectura de aprendizaje automático. Realizamos experimentos en los conjuntos de datos: MPEG7 y ModelNet40 para probar nuestro enfoque tanto en 2D como en 3D. Nuestros experimentos muestran resultados comparables con el estado del arte en clasificación y consulta de formas (retrieval). Nuestros experimentos también muestran que el modelo desarrollado junto con nuestras características basadas en el eje medio son invariantes a las transformaciones isométricas. (Tomado de la fuente)Beca para Doctorados Nacionales de Colciencias, convocatoria 725 de 2015DoctoradoDoctor en IngenieríaVisión por computadora y aprendizaje automátic

Statistical Medial Model dor Cardiac Segmentation and Morphometry

In biomedical image analysis, shape information can be utilized for many purposes. For example, irregular shape features can help identify diseases; shape features can help match different instances of anatomical structures for statistical comparison; and prior knowledge of the mean and possible variation of an anatomical structure\u27s shape can help segment a new example of this structure in noisy, low-contrast images. A good shape representation helps to improve the performance of the above techniques. The overall goal of the proposed research is to develop and evaluate methods for representing shapes of anatomical structures. The medial model is a shape representation method that models a 3D object by explicitly defining its skeleton (medial axis) and deriving the object\u27s boundary via inverse-skeletonization . This model represents shape compactly, and naturally expresses descriptive global shape features like thickening , bending , and elongation . However, its application in biomedical image analysis has been limited, and it has not yet been applied to the heart, which has a complex shape. In this thesis, I focus on developing efficient methods to construct the medial model, and apply it to solve biomedical image analysis problems. I propose a new 3D medial model which can be efficiently applied to complex shapes. The proposed medial model closely approximates the medial geometry along medial edge curves and medial branching curves by soft-penalty optimization and local correction. I further develop a scheme to perform model-based segmentation using a statistical medial model which incorporates prior shape and appearance information. The proposed medial models are applied to a series of image analysis tasks. The 2D medial model is applied to the corpus callosum which results in an improved alignment of the patterns of commissural connectivity compared to a volumetric registration method. The 3D medial model is used to describe the myocardium of the left and right ventricles, which provides detailed thickness maps characterizing different disease states. The model-based myocardium segmentation scheme is tested in a heterogeneous adult MRI dataset. Our segmentation experiments demonstrate that the statistical medial model can accurately segment the ventricular myocardium and provide useful parameters to characterize heart function

복부 CT에서 간과 혈관 분할 기법

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 신영길.복부 전산화 단층 촬영 (CT) 영상에서 정확한 간 및 혈관 분할은 체적 측정, 치료 계획 수립 및 추가적인 증강 현실 기반 수술 가이드와 같은 컴퓨터 진단 보조 시스템을 구축하는데 필수적인 요소이다. 최근 들어 컨볼루셔널 인공 신경망 (CNN) 형태의 딥 러닝이 많이 적용되면서 의료 영상 분할의 성능이 향상되고 있지만, 실제 임상에 적용할 수 있는 높은 일반화 성능을 제공하기는 여전히 어렵다. 또한 물체의 경계는 전통적으로 영상 분할에서 매우 중요한 요소로 이용되었지만, CT 영상에서 간의 불분명한 경계를 추출하기가 어렵기 때문에 현대 CNN에서는 이를 사용하지 않고 있다. 간 혈관 분할 작업의 경우, 복잡한 혈관 영상으로부터 학습 데이터를 만들기 어렵기 때문에 딥 러닝을 적용하기가 어렵다. 또한 얇은 혈관 부분의 영상 밝기 대비가 약하여 원본 영상에서 식별하기가 매우 어렵다. 본 논문에서는 위 언급한 문제들을 해결하기 위해 일반화 성능이 향상된 CNN과 얇은 혈관을 포함하는 복잡한 간 혈관을 정확하게 분할하는 알고리즘을 제안한다. 간 분할 작업에서 우수한 일반화 성능을 갖는 CNN을 구축하기 위해, 내부적으로 간 모양을 추정하는 부분이 포함된 자동 컨텍스트 알고리즘을 제안한다. 또한, CNN을 사용한 학습에 경계선의 개념이 새롭게 제안된다. 모호한 경계부가 포함되어 있어 전체 경계 영역을 CNN에 훈련하는 것은 매우 어렵기 때문에 반복되는 학습 과정에서 인공 신경망이 스스로 예측한 확률에서 부정확하게 추정된 부분적 경계만을 사용하여 인공 신경망을 학습한다. 실험적 결과를 통해 제안된 CNN이 다른 최신 기법들보다 정확도가 우수하다는 것을 보인다. 또한, 제안된 CNN의 일반화 성능을 검증하기 위해 다양한 실험을 수행한다. 간 혈관 분할에서는 간 내부의 관심 영역을 지정하기 위해 앞서 획득한 간 영역을 활용한다. 정확한 간 혈관 분할을 위해 혈관 후보 점들을 추출하여 사용하는 알고리즘을 제안한다. 확실한 후보 점들을 얻기 위해, 삼차원 영상의 차원을 먼저 최대 강도 투영 기법을 통해 이차원으로 낮춘다. 이차원 영상에서는 복잡한 혈관의 구조가 보다 단순화될 수 있다. 이어서, 이차원 영상에서 혈관 분할을 수행하고 혈관 픽셀들은 원래의 삼차원 공간상으로 역 투영된다. 마지막으로, 전체 혈관의 분할을 위해 원본 영상과 혈관 후보 점들을 모두 사용하는 새로운 레벨 셋 기반 알고리즘을 제안한다. 제안된 알고리즘은 복잡한 구조가 단순화되고 얇은 혈관이 더 잘 보이는 이차원 영상에서 얻은 후보 점들을 사용하기 때문에 얇은 혈관 분할에서 높은 정확도를 보인다. 실험적 결과에 의하면 제안된 알고리즘은 잘못된 영역의 추출 없이 다른 레벨 셋 기반 알고리즘들보다 우수한 성능을 보인다. 제안된 알고리즘은 간과 혈관을 분할하는 새로운 방법을 제시한다. 제안된 자동 컨텍스트 구조는 사람이 디자인한 학습 과정이 일반화 성능을 크게 향상할 수 있다는 것을 보인다. 그리고 제안된 경계선 학습 기법으로 CNN을 사용한 영상 분할의 성능을 향상할 수 있음을 내포한다. 간 혈관의 분할은 이차원 최대 강도 투영 기반 이미지로부터 획득된 혈관 후보 점들을 통해 얇은 혈관들이 성공적으로 분할될 수 있음을 보인다. 본 논문에서 제안된 알고리즘은 간의 해부학적 분석과 자동화된 컴퓨터 진단 보조 시스템을 구축하는 데 매우 중요한 기술이다.Accurate liver and its vessel segmentation on abdominal computed tomography (CT) images is one of the most important prerequisites for computer-aided diagnosis (CAD) systems such as volumetric measurement, treatment planning, and further augmented reality-based surgical guide. In recent years, the application of deep learning in the form of convolutional neural network (CNN) has improved the performance of medical image segmentation, but it is difficult to provide high generalization performance for the actual clinical practice. Furthermore, although the contour features are an important factor in the image segmentation problem, they are hard to be employed on CNN due to many unclear boundaries on the image. In case of a liver vessel segmentation, a deep learning approach is impractical because it is difficult to obtain training data from complex vessel images. Furthermore, thin vessels are hard to be identified in the original image due to weak intensity contrasts and noise. In this dissertation, a CNN with high generalization performance and a contour learning scheme is first proposed for liver segmentation. Secondly, a liver vessel segmentation algorithm is presented that accurately segments even thin vessels. To build a CNN with high generalization performance, the auto-context algorithm is employed. The auto-context algorithm goes through two pipelines: the first predicts the overall area of a liver and the second predicts the final liver using the first prediction as a prior. This process improves generalization performance because the network internally estimates shape-prior. In addition to the auto-context, a contour learning method is proposed that uses only sparse contours rather than the entire contour. Sparse contours are obtained and trained by using only the mispredicted part of the network's final prediction. Experimental studies show that the proposed network is superior in accuracy to other modern networks. Multiple N-fold tests are also performed to verify the generalization performance. An algorithm for accurate liver vessel segmentation is also proposed by introducing vessel candidate points. To obtain confident vessel candidates, the 3D image is first reduced to 2D through maximum intensity projection. Subsequently, vessel segmentation is performed from the 2D images and the segmented pixels are back-projected into the original 3D space. Finally, a new level set function is proposed that utilizes both the original image and vessel candidate points. The proposed algorithm can segment thin vessels with high accuracy by mainly using vessel candidate points. The reliability of the points can be higher through robust segmentation in the projected 2D images where complex structures are simplified and thin vessels are more visible. Experimental results show that the proposed algorithm is superior to other active contour models. The proposed algorithms present a new method of segmenting the liver and its vessels. The auto-context algorithm shows that a human-designed curriculum (i.e., shape-prior learning) can improve generalization performance. The proposed contour learning technique can increase the accuracy of a CNN for image segmentation by focusing on its failures, represented by sparse contours. The vessel segmentation shows that minor vessel branches can be successfully segmented through vessel candidate points obtained by reducing the image dimension. The algorithms presented in this dissertation can be employed for later analysis of liver anatomy that requires accurate segmentation techniques.Chapter 1 Introduction 1 1.1 Background and motivation 1 1.2 Problem statement 3 1.3 Main contributions 6 1.4 Contents and organization 9 Chapter 2 Related Works 10 2.1 Overview 10 2.2 Convolutional neural networks 11 2.2.1 Architectures of convolutional neural networks 11 2.2.2 Convolutional neural networks in medical image segmentation 21 2.3 Liver and vessel segmentation 37 2.3.1 Classical methods for liver segmentation 37 2.3.2 Vascular image segmentation 40 2.3.3 Active contour models 46 2.3.4 Vessel topology-based active contour model 54 2.4 Motivation 60 Chapter 3 Liver Segmentation via Auto-Context Neural Network with Self-Supervised Contour Attention 62 3.1 Overview 62 3.2 Single-pass auto-context neural network 65 3.2.1 Skip-attention module 66 3.2.2 V-transition module 69 3.2.3 Liver-prior inference and auto-context 70 3.2.4 Understanding the network 74 3.3 Self-supervising contour attention 75 3.4 Learning the network 81 3.4.1 Overall loss function 81 3.4.2 Data augmentation 81 3.5 Experimental Results 83 3.5.1 Overview 83 3.5.2 Data configurations and target of comparison 84 3.5.3 Evaluation metric 85 3.5.4 Accuracy evaluation 87 3.5.5 Ablation study 93 3.5.6 Performance of generalization 110 3.5.7 Results from ground-truth variations 114 3.6 Discussion 116 Chapter 4 Liver Vessel Segmentation via Active Contour Model with Dense Vessel Candidates 119 4.1 Overview 119 4.2 Dense vessel candidates 124 4.2.1 Maximum intensity slab images 125 4.2.2 Segmentation of 2D vessel candidates and back-projection 130 4.3 Clustering of dense vessel candidates 135 4.3.1 Virtual gradient-assisted regional ACM 136 4.3.2 Localized regional ACM 142 4.4 Experimental results 145 4.4.1 Overview 145 4.4.2 Data configurations and environment 146 4.4.3 2D segmentation 146 4.4.4 ACM comparisons 149 4.4.5 Evaluation of bifurcation points 154 4.4.6 Computational performance 159 4.4.7 Ablation study 160 4.4.8 Parameter study 162 4.5 Application to portal vein analysis 164 4.6 Discussion 168 Chapter 5 Conclusion and Future Works 170 Bibliography 172 초록 197Docto

Automatic correction of Ma and Sonka's thinning algorithm using P-simple points

International audienceMa and Sonka proposed a fully parallel 3D thinning algorithm which does not always preserve topology. We propose an algorithm based on P-simple points which automatically corrects Ma and Sonka's Algorithm. As far as we know, our algorithm is the only fully parallel curve thinning algorithm which preserves topology

Liver segmentation using 3D CT scans.

Master of Science in Computer Science. University of KwaZulu-Natal, Durban, 2018.Abstract available in PDF file

Sparse Volumetric Deformation

Volume rendering is becoming increasingly popular as applications require realistic solid shape representations with seamless texture mapping and accurate filtering. However rendering sparse volumetric data is difficult because of the limited memory and processing capabilities of current hardware. To address these limitations, the volumetric information can be stored at progressive resolutions in the hierarchical branches of a tree structure, and sampled according to the region of interest. This means that only a partial region of the full dataset is processed, and therefore massive volumetric scenes can be rendered efficiently. The problem with this approach is that it currently only supports static scenes. This is because it is difficult to accurately deform massive amounts of volume elements and reconstruct the scene hierarchy in real-time. Another problem is that deformation operations distort the shape where more than one volume element tries to occupy the same location, and similarly gaps occur where deformation stretches the elements further than one discrete location. It is also challenging to efficiently support sophisticated deformations at hierarchical resolutions, such as character skinning or physically based animation. These types of deformation are expensive and require a control structure (for example a cage or skeleton) that maps to a set of features to accelerate the deformation process. The problems with this technique are that the varying volume hierarchy reflects different feature sizes, and manipulating the features at the original resolution is too expensive; therefore the control structure must also hierarchically capture features according to the varying volumetric resolution. This thesis investigates the area of deforming and rendering massive amounts of dynamic volumetric content. The proposed approach efficiently deforms hierarchical volume elements without introducing artifacts and supports both ray casting and rasterization renderers. This enables light transport to be modeled both accurately and efficiently with applications in the fields of real-time rendering and computer animation. Sophisticated volumetric deformation, including character animation, is also supported in real-time. This is achieved by automatically generating a control skeleton which is mapped to the varying feature resolution of the volume hierarchy. The output deformations are demonstrated in massive dynamic volumetric scenes

Shape segmentation and retrieval based on the skeleton cut space

3D vormverzamelingen groeien snel in veel toepassingsgebieden. Om deze effectief te kunnen gebruiken bij modelleren, simuleren, of 3D contentontwikkeling moet men 3D vormen verwerken. Voorbeelden hiervan zijn het snijden van een vorm in zijn natuurlijke onderdelen (ook bekend als segmentatie), en het vinden van vormen die lijken op een gegeven model in een grote vormverzameling (ook bekend als opvraging). Dit proefschrift presenteert nieuwe methodes voor 3D vormsegmentatie en vormopvraging die gebaseerd zijn op het zogenaamde oppervlakskelet van een 3D vorm. Hoewel allang bekend, dergelijke skeletten kunnen alleen sinds kort snel, robuust, en bijna automatisch berekend worden. Deze ontwikkelingen stellen ons in staat om oppervlakskeletten te gebruiken om vormen te karakteriseren en analyseren zodat operaties zoals segmentatie en opvraging snel en automatisch gedaan kunnen worden. We vergelijken onze nieuwe methodes met moderne methodes voor dezelfde doeleinden en laten zien dat ons aanpak kwalitatief betere resultaten kan produceren. Ten slotte presenteren wij een nieuwe methode om oppervlakskeletten te extraheren die is veel simpeler dan, en heeft vergelijkbare snelheid met, de beste technieken in zijn klasse. Samenvattend, dit proefschrift laat zien hoe men een complete workflow kan implementeren voor het segmenteren en opvragen van 3D vormen gebruik makend van oppervlakskeletten alleen