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Elastic Methods for Functions and Shapes with Applications to MRI-Derived Tumors and Health Assessment ICU Trajectories
Elastic Methods for Functions and Shapes with Applications to MRI-Derived Tumors and Health Assessment ICU Trajectories
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105828
- ISBN
- 9798297962439
- DDC
- 574
- 저자명
- Chen, Yi Tang.
- 서명/저자
- Elastic Methods for Functions and Shapes with Applications to MRI-Derived Tumors and Health Assessment ICU Trajectories
- 발행사항
- [Sl] : The Ohio State University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 159 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-05, Section: A.
- 주기사항
- Advisor: Kurtek, Sebastian.
- 학위논문주기
- Thesis (Ph.D.)--The Ohio State University, 2025.
- 초록/해제
- 요약The increasing availability of shape data across various disciplines, e.g., biology, medical imaging and computer vision, advances the study of shape data. Shape is considered a geometric property that remains unchanged regardless of changes in its location, size and orientation. Thus, representing the shapes of objects while respecting such invariance properties is the first major challenge in shape analysis prior to the comparison and statistical modeling of shapes. Function-based shape representation uses a continuous function to characterize the outline of an object, which introduces an additional source of nuisance variability that does not change the shape of an object, namely parameterization. The parameterization of curves can be leveraged to match similar geometric features across shapes, which can in turn improve shape comparisons. Srivastava et al. (2011a); Srivastava and Klassen (2016) propose the elastic shape analysis framework that uses a function-based shape representation, namely the square-root velocity function (SRVF), coupled with an elastic Riemannian metric. The resulting shape representation and distance are invariant to all shape-preserving transformations. Importantly, the associated distance incorporates registration with respect to rotation and reparameterization, which improves shape comparisons.Building on the elastic framework, we develop an integrated statistical framework to jointly analyze the shape and intensity information of brain tumor contours derived from magnetic resonance images (MRIs). We first use a 3D parameterized closed curve to jointly represent the shape and color intensity along the tumor outline, and transform it into the SRVF. We then define a distance that accounts for, or is invariant to, all sources of nuisance variability. The proposed shape+intensity representation and distance are invariant to shape and intensity preserving transformation and further enable joint statistical analysis of shape and intensity features. The statistical tools include statistical summarization like estimation of the average tumor shape and intensity in a sample, calculation of the overall sample variance, and exploration of variability via principal component analysis. The proposed framework can also be integrated with distance-based clustering for the purpose of identifying groups with distinct survival profiles.The elastic framework can also be applied to the problem of registration of real-valued functions, which aligns prominent function features, e.g., local extrema, to better summarize the common patterns for a sample of functions. Extending the elastic framework, we develop an elastic functional Cox regression model (EFCRM) that uses real-valued functions as functional predictors to predict a survival outcome. The model removes nuisance phase variation in the functional predictor by incorporating registration in the modeling framework. The estimation procedure involves an iterative algorithm that alternates between estimation of the regression coefficient function and removal of the nuisance phase variation. The removal of phase variation is supervised by the survival outcome, and can be viewed as a form of regularization. We apply the EFCRM to intensive care unit (ICU) data, where we use health assessment trajectories to predict the hazard of death.
- 일반주제명
- Biostatistics
- 일반주제명
- Medical imaging
- 일반주제명
- Medical personnel
- 키워드
- Elastic distance
- 키워드
- Clustering
- 기타저자
- The Ohio State University Biostatistics
- 기본자료저록
- Dissertations Abstracts International. 87-05A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798297962439
■035 ▼a(MiAaPQ)AAI32384285
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a574
■1001 ▼aChen, Yi Tang.
■24510▼aElastic Methods for Functions and Shapes with Applications to MRI-Derived Tumors and Health Assessment ICU Trajectories
■260 ▼a[Sl]▼bThe Ohio State University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a159 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-05, Section: A.
■500 ▼aAdvisor: Kurtek, Sebastian.
■5021 ▼aThesis (Ph.D.)--The Ohio State University, 2025.
■520 ▼aThe increasing availability of shape data across various disciplines, e.g., biology, medical imaging and computer vision, advances the study of shape data. Shape is considered a geometric property that remains unchanged regardless of changes in its location, size and orientation. Thus, representing the shapes of objects while respecting such invariance properties is the first major challenge in shape analysis prior to the comparison and statistical modeling of shapes. Function-based shape representation uses a continuous function to characterize the outline of an object, which introduces an additional source of nuisance variability that does not change the shape of an object, namely parameterization. The parameterization of curves can be leveraged to match similar geometric features across shapes, which can in turn improve shape comparisons. Srivastava et al. (2011a); Srivastava and Klassen (2016) propose the elastic shape analysis framework that uses a function-based shape representation, namely the square-root velocity function (SRVF), coupled with an elastic Riemannian metric. The resulting shape representation and distance are invariant to all shape-preserving transformations. Importantly, the associated distance incorporates registration with respect to rotation and reparameterization, which improves shape comparisons.Building on the elastic framework, we develop an integrated statistical framework to jointly analyze the shape and intensity information of brain tumor contours derived from magnetic resonance images (MRIs). We first use a 3D parameterized closed curve to jointly represent the shape and color intensity along the tumor outline, and transform it into the SRVF. We then define a distance that accounts for, or is invariant to, all sources of nuisance variability. The proposed shape+intensity representation and distance are invariant to shape and intensity preserving transformation and further enable joint statistical analysis of shape and intensity features. The statistical tools include statistical summarization like estimation of the average tumor shape and intensity in a sample, calculation of the overall sample variance, and exploration of variability via principal component analysis. The proposed framework can also be integrated with distance-based clustering for the purpose of identifying groups with distinct survival profiles.The elastic framework can also be applied to the problem of registration of real-valued functions, which aligns prominent function features, e.g., local extrema, to better summarize the common patterns for a sample of functions. Extending the elastic framework, we develop an elastic functional Cox regression model (EFCRM) that uses real-valued functions as functional predictors to predict a survival outcome. The model removes nuisance phase variation in the functional predictor by incorporating registration in the modeling framework. The estimation procedure involves an iterative algorithm that alternates between estimation of the regression coefficient function and removal of the nuisance phase variation. The removal of phase variation is supervised by the survival outcome, and can be viewed as a form of regularization. We apply the EFCRM to intensive care unit (ICU) data, where we use health assessment trajectories to predict the hazard of death.
■590 ▼aSchool code: 0168.
■650 4▼aBiostatistics
■650 4▼aMedical imaging
■650 4▼aMedical personnel
■653 ▼aMagnetic resonance images
■653 ▼aGlioblastoma multiforme
■653 ▼aElastic distance
■653 ▼aTumor heterogeneity
■653 ▼aClustering
■653 ▼aSurvival analysis
■690 ▼a0308
■690 ▼a0574
■690 ▼a0207
■71020▼aThe Ohio State University▼bBiostatistics.
■7730 ▼tDissertations Abstracts International▼g87-05A.
■790 ▼a0168
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17361293▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
