A phase field method for joint denoising, edge detection and motion estimation in image sequence processing

T. Preusser, M. Droske, C.S. Garbe, A.C. Telea, M. Rumpf

    Research output: Contribution to journalArticleAcademicpeer-review

    15 Citations (Scopus)
    73 Downloads (Pure)

    Abstract

    The estimation of optical flow fields from image sequences is incorporated in a Mumford–Shah approach for image denoising and edge detection. Possibly noisy image sequences are considered as input and a piecewise smooth image intensity, a piecewise smooth motion field, and a joint discontinuity set are obtained as minimizers of the functional. The method simultaneously detects image edges and motion field discontinuities in a rigorous and robust way. It is able to handle information on motion that is concentrated on edges. Inherent to it is a natural multiscale approximation that is closely related to the phase field approximation for edge detection by Ambrosio and Tortorelli. We present an implementation for two-dimensional image sequences with finite elements in space and time. This leads to three linear systems of equations, which have to be solved in a suitable iterative minimization procedure. Numerical results and different applications underline the robustness of the approach presented.
    Original languageEnglish
    Pages (from-to)599-618
    JournalSIAM Journal on Applied Mathematics
    Volume68
    Issue number3
    DOIs
    Publication statusPublished - 2007

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