We address the problem of restoring, while presenting possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicity into account. We develop a variational solution for the general case where each image feature may correspond to multiple n-D orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where discontinuities and orthonormal constraints are preserved by means of constrained minimization and /spl Phi/-function regularization, leading to a set of coupled anisotropic diffusion PDE. A geometric interpretation of the resulting equations, coming from the field of solid mechanics, is proposed for the 3D case. Two interesting restrictions of our framework are also tackled: the regularization of 30 rotation matrices and the direction diffusion (the parallel with previous works is made). Finally, we present a number of denoising results and applications.


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    Titel :

    Regularization of orthonormal vector sets using coupled PDE's


    Beteiligte:
    Tschumperle, D. (Autor:in) / Deriche, R. (Autor:in)


    Erscheinungsdatum :

    2001-01-01


    Format / Umfang :

    773259 byte




    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Regularization of Orthonormal Vector Sets Using Coupled PDE's

    Tschumperle, D. / Deriche, R. / Institute of Electrical and Electronics Engineers | British Library Conference Proceedings | 2001


    Orthonormal Vector Sets Regularization with PDEs and Applications

    Tschumperle, D. / Deriche, R. | British Library Online Contents | 2002


    Vector-Valued Image Regularization with PDE's: A Common Framework for Different Applications

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    Curvature-Preserving Regularization of Multi-valued Images Using PDE’s

    Tschumperlé, David | Springer Verlag | 2006

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