Topologically Constrained Template Estimation via Morse--Smale Complexes Controls Its Statistical Consistency

DOI10.1137/17M1129222zbMath1393.53014MaRDI QIDQ3174774

Nina Miolane, Susan P. Holmes, Xavier Pennec

Publication date: 18 July 2018

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

zbMATH Keywords

medical imagingdifferential geometrybiasstatisticstemplate

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Non-Euclidean differential geometry (53A35) Abstract manifolds and fiber bundles (category-theoretic aspects) (18F15)

Uses Software

• msr

Cites Work

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• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• A deconvolution approach to estimation of a common shape in a shifted curves model
• Curvatures of left invariant metrics on Lie groups
• On the consistency of Fréchet means in deformable models for curve and image analysis
• Biased Estimators on Quotient Spaces
• Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion
• Template Estimation in Computational Anatomy: Fréchet Means Top and Quotient Spaces Are Not Consistent
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Template Shape Estimation: Correcting an Asymptotic Bias
• Towards a Coherent Statistical Framework for Dense Deformable Template Estimation
• Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation
• Shapes and diffeomorphisms

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