On Complete Integrals and Uniqueness in Shape from Shading

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    In this paper, we analyze the problem of representing solutions of a first-order partial differential equation in terms of complete integrals. We show that some of the existing results referring to the representability problem are incomplete. Additionally, we analyze, in the context of complete integrals, the uniqueness problem for the shape recovery of a smooth Lambertian surface from an image obtained by illuminating this surface by an overhead, distant point light-source. Specifically, we revisit the uniqueness results already existing in the shape-from-shading literature that concern eikonal equations corresponding to the images of a Lambertian hemisphere and a Lambertian plane. We show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs.
    Original languageEnglish
    Pages (from-to)1-39
    JournalApplied Mathematics and Computation
    Volume73/1
    DOIs
    Publication statusPublished - 1995

    Fingerprint

    Shape from Shading
    Uniqueness
    Partial differential equations
    Light sources
    Eikonal Equation
    Representability
    Hemisphere
    Smooth surface
    First order differential equation
    Recovery
    Partial differential equation

    Cite this

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    title = "On Complete Integrals and Uniqueness in Shape from Shading",
    abstract = "In this paper, we analyze the problem of representing solutions of a first-order partial differential equation in terms of complete integrals. We show that some of the existing results referring to the representability problem are incomplete. Additionally, we analyze, in the context of complete integrals, the uniqueness problem for the shape recovery of a smooth Lambertian surface from an image obtained by illuminating this surface by an overhead, distant point light-source. Specifically, we revisit the uniqueness results already existing in the shape-from-shading literature that concern eikonal equations corresponding to the images of a Lambertian hemisphere and a Lambertian plane. We show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs.",
    author = "Ryszard Kozera",
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    language = "English",
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    On Complete Integrals and Uniqueness in Shape from Shading. / Kozera, Ryszard.

    In: Applied Mathematics and Computation, Vol. 73/1, 1995, p. 1-39.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - On Complete Integrals and Uniqueness in Shape from Shading

    AU - Kozera, Ryszard

    PY - 1995

    Y1 - 1995

    N2 - In this paper, we analyze the problem of representing solutions of a first-order partial differential equation in terms of complete integrals. We show that some of the existing results referring to the representability problem are incomplete. Additionally, we analyze, in the context of complete integrals, the uniqueness problem for the shape recovery of a smooth Lambertian surface from an image obtained by illuminating this surface by an overhead, distant point light-source. Specifically, we revisit the uniqueness results already existing in the shape-from-shading literature that concern eikonal equations corresponding to the images of a Lambertian hemisphere and a Lambertian plane. We show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs.

    AB - In this paper, we analyze the problem of representing solutions of a first-order partial differential equation in terms of complete integrals. We show that some of the existing results referring to the representability problem are incomplete. Additionally, we analyze, in the context of complete integrals, the uniqueness problem for the shape recovery of a smooth Lambertian surface from an image obtained by illuminating this surface by an overhead, distant point light-source. Specifically, we revisit the uniqueness results already existing in the shape-from-shading literature that concern eikonal equations corresponding to the images of a Lambertian hemisphere and a Lambertian plane. We show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs.

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    DO - 10.1016/0096-3003(94)00127-P

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