형상 라이브러리를 이용한 응력발광 복합재료의 형태학적 특징 기반 미세구조 특성화 및 재구성

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2019. 2. 윤군진.이 논문에서는 응력 발광 세라믹 입자강화 복합재료에 대한 새로운 형상 특성에 의한 미세구조 특성화와 재구성이 진행되었다. 응력발광 세라믹 소재(Mechanoluminescent, ML)은 응력세기에 비례해서 빛을 방출한다. 이에 따라 응력발광 소재는 응력 센서로 활용하기 위한 연구가 진행되고 있다. 응력발광 소재가 빛 강도는 편향응력(deviatoric stress)에 비례한다는 점은 이미 알려져 있다. 응력발광 소재를 설계하는데 있어서, 입자가 받는 응력을 높일 수 있는 형상 특성을 찾는 것이 중요하다. 이런 선상에서 이 연구의 목적은 응력에 가장 민감하게 반응하는 형상 변수를 부피 평균한 폰 미제스 응력(volume averaged von Mises stress)과 형상 변수 사이의 통계적 상관관계 분석을 통해서 찾는 것이다. 응력발광 소재의 실제 형상을 확인하기 위해서 X선 마이크로컴퓨터 단층촬영으로 응력 발광 세라믹 복합재료의 단층 촬영해서 이미지를 확보하였다. 단층촬영 이미지 품질을 개선하고, 입자를 분리하기 위해서 가우시안 필터, 중앙값 필터, 워터셰드 알고리즘과 같은 이미지 처리 알고리즘을 사용하였다. 입자에 대한 13가지 형상 변수를 통해서 미세구조를 특성화했으며, 3차원 유한요소 해석을 통해서 각 입자에서 발생하는 부피 평균 폰 미제스 응력을 계산했다. 유한요소 해석 결과와 입자 형상 해석 결과를 연결해서 데이터베이스를 구축하고, 형상과 응력에 대한 상관관계를 조사했다. 이를 위해서 주성분 분석으로 형상변수와 부피평균응력의 상관행렬에서 독립된 성분을 찾았다. 통계적 해석을 통해서 입자 겉넓이와 shape index가 가장 부피평균응력에 민감하다는 것을 확인하였고, 이를 재구성 변수로 결정했다. 입자 분포는 최인접거리(nearest neighbor distance) 분포를 이용하였다. 이 연구에 도입된 아이디어로 실제 구성을 반영하기 위해서 복셀화된 9,687개 입자 단위 셀로 구성한 입자 형상 라이브러리를 사용했다. 목표 모델 변수와 재구성 모델 변수의 확률 분포를 일치하게 만드는 방법으로 성공적으로 재구성을 수행했다. 분포를 같게 만들기 위해서 최적화 기법인 담금질 기법(simulated annealing)을 사용했다. 재구성한 미세구조를 two point correlation function을 통해서 검증하였다. 그리고 재구성 모델의 데이터세트를 이용하여 형상 변수의 함수로 이루어진 새로운 TPCF 해석식을 도출하였다. 논문에서 제시한 알고리즘은 빠른 계산 속도에 장점이 있었으며, 입자 형상 라이브러리를 사용하여 실제 형상과 유사한 재구성 모델을 구성할 수 있다는 장점이 있다. 이 알고리즘을 통해서 생성한 수많은 미세구조 자료와 데이터 과학을 결합하여 응력발광 소재의 미세구조 설계에 활용을 기대할 수 있다.In this thesis, a new morphological feature-based microstructure characterization and reconstruction is developed for mechanoluminescent (ML) particulate composites. ML materials emit visible light proportional to the applied stresses. Therefore, ML materials have been studied for applications to stress sensor. It has also been known that the ML light intensity is proportional to the applied deviatoric stress in the particles. For the design of ML materials, it is critical to find out morphological features that can enhance the stress level within the particles. In the line of the research goal, morphological parameters that are most sensitive to stress enhancement were determined through statistical correlation analyses between a set of morphological parameters and volume-averaged von Mises stress (VAS) of ML particles. To use actual morphological shapes of ML particles, an X-ray micro-computed tomography (CT) is used. To improve the image quality and segment each particle, a series of image processing algorithms such as Gaussian filter, median filter, and watershed algorithm are applied. Microstructure characterization was conducted based on thirteen morphological variables. Three-dimensional finite element analyses were conducted to obtain the VAS for each particle. The database that consisted of particles morphological parameters and VAS was generated and used to find the correlation between morphology and VAS. To perform this, the principal component analysis (PCA) is adopted to find out spectral components of the correlation matrix between morphological parameters and VAS. As a result of statistical analysis, the surface area and the shape index were found to be the most sensitive morphological parameters to the VAS and used for reconstruction of microstructures. A local dispersion of ML particles was reconstructed by the nearest neighbor distance (NND). One of the novel approaches adopted in this thesis was using a particle shape library that consists of voxelized 9,687 particle unit cells. The reconstruction was successfully accomplished by matching their probabilistic distributions with those of target parameters. An optimization algorithm, simulated annealing (SA) was adopted for matching distributions. A two-point correlation function (TPCF) was used to verify the reconstructed microstructure. Also, the new analytical TPCF equation based on the morphological variables is generated with the reconstruction dataset. The algorithm proposed in this thesis has a salient advantage of computational efficiency and realistic microstructure reconstructed through the particle shape library. The combination of a dataset of reconstructed microstructure and novel data science is expected to be applied to the microstructure design of ML materials.Abstract I Table of Contents IV Table of Figures VI Chapter 1. Introduction 1 Chapter 2. Microstructure Characterization 5 2.1 Image Processing for Micro-Computed Tomography 5 2.2 Quantitative Morphological Variables of ML Particles 8 Chapter 3. Microstructure Sensitivity Analysis 11 3.1 Creation of Image-based FE Model 11 3.2 FE Mesh Sensitivity and Element Size Determination 13 3.3 3D Finite Element Analysis for VAS of Particles 15 3.4 Correlation between VAS and morphological variables 17 3.5. Design Parameters for Synthetic ML Particulate Composites 31 3.6 Principal Component Analysis 36 Chapter 4. Microstructure Reconstruction 43 4.1 Particle Sampling from Particle Shape Library 46 4.2 Particle Dispersion Matched Map 56 4.3 Particle Packing through Unit Cell Model 61 4.4 Verification with Two-Point Correlation Function 68 4.5 New Analytical Two-Points Correlation Function 73 Chapter 5. Conclusion 77 Bibliography 79 국문초록 82Maste

Learning Transferable Push Manipulation Skills in Novel Contexts

This paper is concerned with learning transferable forward models for push manipulation that can be applying to novel contexts and how to improve the quality of prediction when critical information is available. We propose to learn a parametric internal model for push interactions that, similar for humans, enables a robot to predict the outcome of a physical interaction even in novel contexts. Given a desired push action, humans are capable to identify where to place their finger on a new object so to produce a predictable motion of the object. We achieve the same behaviour by factorising the learning into two parts. First, we learn a set of local contact models to represent the geometrical relations between the robot pusher, the object, and the environment. Then we learn a set of parametric local motion models to predict how these contacts change throughout a push. The set of contact and motion models represent our internal model. By adjusting the shapes of the distributions over the physical parameters, we modify the internal model's response. Uniform distributions yield to coarse estimates when no information is available about the novel context (i.e. unbiased predictor). A more accurate predictor can be learned for a specific environment/object pair (e.g. low friction/high mass), i.e. biased predictor. The effectiveness of our approach is shown in a simulated environment in which a Pioneer 3-DX robot needs to predict a push outcome for a novel object, and we provide a proof of concept on a real robot. We train on 2 objects (a cube and a cylinder) for a total of 24,000 pushes in various conditions, and test on 6 objects encompassing a variety of shapes, sizes, and physical parameters for a total of 14,400 predicted push outcomes. Our results show that both biased and unbiased predictors can reliably produce predictions in line with the outcomes of a carefully tuned physics simulator.Comment: This work has been submitted to IEEE Transactions on Robotics journal in July 202

Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects with multiple (sometimes infinite) correct poses. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability given the input image and a candidate pose. Grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the probability at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to showcase the rich expressive power, we introduce a dataset of challenging symmetric and nearly-symmetric objects. We require no supervision on pose uncertainty -- the model trains only with a single pose per example. Nonetheless, our implicit model is highly expressive to handle complex distributions over 3D poses, while still obtaining accurate pose estimation on standard non-ambiguous environments, achieving state-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks

KOLMOGOROV-SMIRNOV TYPE TESTS UNDER SPATIAL CORRELATIONS

Kolmogorov-Smirnov test is a non-parametric hypothesis test that measures the probability of deviations, that the interested univariate random variable is drawn from a pre-specified distribution (one-sample KS) or has the same distribution as a second random variable (twosample KS). The test is based on the measure of the supremum (greatest) distance between an empirical distribution function (EDF) and a pre-specified cumulative distribution function (CDF) or the largest distance between two EDFs. KS test has been widely adopted in statistical analysis due to its virtue of more general assumptions compared to parametric test like t-test. In addition, the p-value derived from the KS test is more robust and distribution-free for a large class of random variables. However, the fundamental assumption of independence is usually overlooked and may potentially cause inaccurate inferences. The KS test in its original form assumes the interested random variable to be independently distributed while it’s not true in a lot of nature datasets, especially when we are dealing with more complicated situations like imgage analysis, geostatistical which may involve spatial dependence. I proposed a modified KS test with adjustment via spatial correlation. The dissertation concerns the following three aims. First, I conducted a systematical review on the KS test, the Cramer von Mise test, the Anderson-Darling test and the Chi-square test and evaluate their performance under normal distributions, Weibull distributions and multinomial distributions. In the review, I also studied how these tests perform when random variables are correlated. Second, I proposed a modified KS test that corrects the bias in estimating CDF/EDF when spatial dependence exists and calculate the informative sample size. Finally, I conducted a revisit analysis of coronary flow reserve and pixel distribution of coronary flow capacity by Kolmogorov-Smirnov with spatial correction to evaluate the efficiency of dipyridamole and regadenoson

The Bayesian sampler : generic Bayesian inference causes incoherence in human probability

Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017; Costello & Watts, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities and distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample

Structure-from-motion in Spherical Video using the von Mises-Fisher Distribution

In this paper, we present a complete pipeline for computing structure-from-motion from the sequences of spherical images. We revisit problems from multiview geometry in the context of spherical images. In particular, we propose methods suited to spherical camera geometry for the spherical-n-point problem (estimating camera pose for a spherical image) and calibrated spherical reconstruction (estimating the position of a 3-D point from multiple spherical images). We introduce a new probabilistic interpretation of spherical structure-from-motion which uses the von Mises-Fisher distribution to model noise in spherical feature point positions. This model provides an alternate objective function that we use in bundle adjustment. We evaluate our methods quantitatively and qualitatively on both synthetic and real world data and show that our methods developed for spherical images outperform straightforward adaptations of methods developed for perspective images. As an application of our method, we use the structure-from-motion output to stabilise the viewing direction in fully spherical video

Joint Rigid Registration of Multiple Generalized Point Sets With Anisotropic Positional Uncertainties in Image-Guided Surgery

In medical image analysis (MIA) and computer-assisted surgery (CAS), aligning two multiple point sets (PSs) together is an essential but also a challenging problem. For example, rigidly aligning multiple point sets into one common coordinate frame is a prerequisite for statistical shape modelling (SSM). Accurately aligning the pre-operative space with the intra-operative space in CAS is very crucial to successful interventions. In this article, we formally formulate the multiple generalized point set registration problem (MGPSR) in a probabilistic manner, where both the positional and the normal vectors are used. The six-dimensional vectors consisting of both positional and normal vectors are called as generalized points. In the formulated model, all the generalized PSs to be registered are considered to be the realizations of underlying unknown hybrid mixture models (HMMs). By assuming the independence of the positional and orientational vectors (i.e., the normal vectors), the probability density function (PDF) of an observed generalized point is computed as the product of Gaussian and Fisher distributions. Furthermore, to consider the anisotropic noise in surgical navigation, the positional error is assumed to obey a multi-variate Gaussian distribution. Finally, registering PSs is formulated as a maximum likelihood (ML) problem, and solved under the expectation maximization (EM) technique. By using more enriched information (i.e., the normal vectors), our algorithm is more robust to outliers. By treating all PSs equally, our algorithm does not bias towards any PS. To validate the proposed approach, extensive experiments have been conducted on surface points extracted from CT images of (i) a human femur bone model; (ii) a human pelvis bone model. Results demonstrate our algorithm's high accuracy, robustness to noise and outliers

Local Features, Structure-from-motion and View Synthesis in Spherical Video

This thesis addresses the problem of synthesising new views from spherical video or image sequences. We propose an interest point detector and feature descriptor that allows us to robustly match local features between pairs of spherical images and use this as part of a structure-from-motion pipeline that allows us to estimate camera pose from a spherical video sequence. With pose estimates to hand, we propose methods for view stabilisation and novel viewpoint synthesis. In Chapter 3 we describe our contribution in the area of feature detection and description in spherical images. First, we present a novel representation for spherical images which uses a discrete geodesic grid composed of hexagonal pixels. Second, we extend the BRISK binary descriptor to the sphere, proposing methods for multiscale corner detection, sub-pixel position and sub-octave scale refinement and descriptor construction in the tangent space to the sphere. In Chapter 4 we describe our contributions in the area of spherical structure-from-motion. We revisit problems from multiview geometry in the context of spherical images. We propose methods suited to spherical camera geometry for the spherical-n-point problem and calibrated spherical reconstruction. We introduce a new probabilistic interpretation of spherical structure-from-motion which uses the von Mises-Fisher distribution in spherical feature point positions. This model provides an alternate objective function that we use in bundle adjustment. In Chapter 5 we describe our contributions in the area of view synthesis from spherical images. We exploit the camera pose estimates made by our pipeline and use these in two view synthesis applications. The first is view stabilisation where we remove the effect of viewing direction changes, often present in first person video. Second, we propose a method for synthesising novel viewpoints