Trajectories from Distribution-Valued Functional Curves: A Unified Wasserstein Framework

Anuja Sharma, Guido Gerig

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Temporal changes in medical images are often evaluated along a parametrized function that represents a structure of interest (e.g. white matter tracts). By attributing samples along these functions with distributions of image properties in the local neighborhood, we create distribution-valued signatures for these functions. We propose a novel, comprehensive framework which models their temporal evolution trajectories. This is achieved under the unifying scheme of Wasserstein distance metric. The regression problem is formulated as a constrained optimization problem and solved using an alternating projection algorithm. The solution simultaneously preserves the functional characteristics of the curve, models the temporal change in distribution profiles and forces the estimated distributions to be valid. Hypothesis testing is applied in two ways using Wasserstein based test statistics. Validation is presented on synthetic data. Estimation of a population trajectory is shown using diffusion properties along DTI tracts from a healthy population of infants. Detection of delayed growth is shown using a case study.

    Original languageEnglish (US)
    Title of host publicationMedical Image Computing and Computer Assisted Intervention – MICCAI 2020 - 23rd International Conference, Proceedings
    EditorsAnne L. Martel, Purang Abolmaesumi, Danail Stoyanov, Diana Mateus, Maria A. Zuluaga, S. Kevin Zhou, Daniel Racoceanu, Leo Joskowicz
    PublisherSpringer Science and Business Media Deutschland GmbH
    Pages343-353
    Number of pages11
    ISBN (Print)9783030597276
    DOIs
    StatePublished - 2020
    Event23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020 - Lima, Peru
    Duration: Oct 4 2020Oct 8 2020

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume12267 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020
    CountryPeru
    CityLima
    Period10/4/2010/8/20

    Keywords

    • Diffusion-MRI
    • Neurodevelopment
    • Spatiotemporal regression

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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