IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v22y2022i2d10.1007_s11067-019-09459-4.html
   My bibliography  Save this article

Properties of a Variational Model for Video Inpainting

Author

Listed:
  • Riccardo March

    (Consiglio Nazionale delle Ricerche)

  • Giuseppe Riey

    (Università della Calabria)

Abstract

We consider a variational model analyzed in March and Riey (Inverse Probl Imag 11(6): 997–1025, 2017) for simultaneous video inpainting and motion estimation. The model has applications in the field of recovery of missing data in archive film materials. A gray-value video content is reconstructed in a spatiotemporal region where the video data is lost. A variational method for motion compensated video inpainting is used, which is based on the simultaneous estimation of apparent motion in the video data. Apparent motion is mathematically described by a vector field of velocity, denoted optical flow, which is estimated through gray-value variations of the video data. The functional to be minimized is defined on a space of vector valued functions of bounded variation and the relaxation method of the Calculus of Variations is used. We introduce in the functional analyzed in March and Riey(Inverse Probl Imag 11(6): 997–1025, 2017) a suitable positive weight, and we show that diagonal minimizing sequences of the functional converge, up to subsequences as the weight tends to infinity, to minimizers of an appropriate limit functional. Such a limit functional is the relaxed version of a functional, modified with suitable improvements, proposed by Lauze and Nielsen (2004) and which permits an accurate joint reconstruction both of the optical flow and of the video content.

Suggested Citation

  • Riccardo March & Giuseppe Riey, 2022. "Properties of a Variational Model for Video Inpainting," Networks and Spatial Economics, Springer, vol. 22(2), pages 315-326, June.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:2:d:10.1007_s11067-019-09459-4
    DOI: 10.1007/s11067-019-09459-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-019-09459-4
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-019-09459-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:22:y:2022:i:2:d:10.1007_s11067-019-09459-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.