View in EDS HTML Full Text PDF Full Text

Estimation of 3D facial dynamics with nonlinear filters for position tracking*.

Saved in:
Bibliographic Details
Title: Estimation of 3D facial dynamics with nonlinear filters for position tracking*.
Authors: Thieu, Thoa1 (AUTHOR) thoa.thieu@utrgv.edu, Melnik, Roderick2 (AUTHOR)
Source: Applied Mathematics in Science & Engineering. Dec2025, Vol. 33 Issue 1, p1-26. 26p.
Subjects: Kalman filtering, Nonlinear estimation, Estimation theory, Mean square algorithms, Monte Carlo method, Position tracking (Virtual reality)
Abstract: This study presents a comparative evaluation of three nonlinear state estimation filters, the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF), for the task of 3D facial landmark tracking. Using a publicly available dataset, we assess each filter's performance under both deterministic (noise-free) and stochastic (noisy) conditions. Metrics such as mean squared error (MSE), convergence rates of state and covariance estimates, and consistency over time are used to quantify tracking performance. Results show that the EKF consistently outperforms the UKF and PF, achieving faster convergence and lower estimation error, particularly in scenarios characterized by mild nonlinearity. Heatmap analyses under varying noise conditions further highlight the EKF's robustness and accuracy, especially in low-noise regimes, while PF performance deteriorates with increased process noise. Our findings suggest that while UKF and PF offer advantages in highly nonlinear or non-Gaussian environments, the EKF provides the best trade-off between computational efficiency and estimation accuracy for the facial tracking task studied in mild nonlinearity. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 190352393
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Estimation of 3D facial dynamics with nonlinear filters for position tracking*.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Thieu%2C+Thoa%22">Thieu, Thoa</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> thoa.thieu@utrgv.edu</i><br /><searchLink fieldCode="AR" term="%22Melnik%2C+Roderick%22">Melnik, Roderick</searchLink><relatesTo>2</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+in+Science+%26+Engineering%22">Applied Mathematics in Science & Engineering</searchLink>. Dec2025, Vol. 33 Issue 1, p1-26. 26p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Kalman+filtering%22">Kalman filtering</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+estimation%22">Nonlinear estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+square+algorithms%22">Mean square algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Position+tracking+%28Virtual+reality%29%22">Position tracking (Virtual reality)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study presents a comparative evaluation of three nonlinear state estimation filters, the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF), for the task of 3D facial landmark tracking. Using a publicly available dataset, we assess each filter's performance under both deterministic (noise-free) and stochastic (noisy) conditions. Metrics such as mean squared error (MSE), convergence rates of state and covariance estimates, and consistency over time are used to quantify tracking performance. Results show that the EKF consistently outperforms the UKF and PF, achieving faster convergence and lower estimation error, particularly in scenarios characterized by mild nonlinearity. Heatmap analyses under varying noise conditions further highlight the EKF's robustness and accuracy, especially in low-noise regimes, while PF performance deteriorates with increased process noise. Our findings suggest that while UKF and PF offer advantages in highly nonlinear or non-Gaussian environments, the EKF provides the best trade-off between computational efficiency and estimation accuracy for the facial tracking task studied in mild nonlinearity. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190352393
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/27690911.2025.2546793
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 1
    Subjects:
      – SubjectFull: Kalman filtering
        Type: general
      – SubjectFull: Nonlinear estimation
        Type: general
      – SubjectFull: Estimation theory
        Type: general
      – SubjectFull: Mean square algorithms
        Type: general
      – SubjectFull: Monte Carlo method
        Type: general
      – SubjectFull: Position tracking (Virtual reality)
        Type: general
    Titles:
      – TitleFull: Estimation of 3D facial dynamics with nonlinear filters for position tracking*.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Thieu, Thoa
      – PersonEntity:
          Name:
            NameFull: Melnik, Roderick
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 27690911
          Numbering:
            – Type: volume
              Value: 33
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Applied Mathematics in Science & Engineering
              Type: main
ResultId 1