Dynamic Bezier curves for variable rate-distortion

Ferdous Sohel, G.C. Karmakr, L.S. Dooley

    Research output: Contribution to journalArticle

    2 Citations (Scopus)
    131 Downloads (Pure)

    Abstract

    Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques.
    Original languageEnglish
    Pages (from-to)3153-3165
    JournalPattern Recognition
    Volume41
    Issue number10
    DOIs
    Publication statusPublished - 2008

    Fingerprint

    Invariance
    Computational complexity
    Computer aided design
    Composite materials

    Cite this

    Sohel, Ferdous ; Karmakr, G.C. ; Dooley, L.S. / Dynamic Bezier curves for variable rate-distortion. In: Pattern Recognition. 2008 ; Vol. 41, No. 10. pp. 3153-3165.
    @article{18f9b10b30e24861a44f12189875d471,
    title = "Dynamic Bezier curves for variable rate-distortion",
    abstract = "Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques.",
    author = "Ferdous Sohel and G.C. Karmakr and L.S. Dooley",
    year = "2008",
    doi = "10.1016/j.patcog.2008.03.006",
    language = "English",
    volume = "41",
    pages = "3153--3165",
    journal = "Pattern Recognition",
    issn = "0031-3203",
    publisher = "Elsevier",
    number = "10",

    }

    Dynamic Bezier curves for variable rate-distortion. / Sohel, Ferdous; Karmakr, G.C.; Dooley, L.S.

    In: Pattern Recognition, Vol. 41, No. 10, 2008, p. 3153-3165.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Dynamic Bezier curves for variable rate-distortion

    AU - Sohel, Ferdous

    AU - Karmakr, G.C.

    AU - Dooley, L.S.

    PY - 2008

    Y1 - 2008

    N2 - Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques.

    AB - Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques.

    U2 - 10.1016/j.patcog.2008.03.006

    DO - 10.1016/j.patcog.2008.03.006

    M3 - Article

    VL - 41

    SP - 3153

    EP - 3165

    JO - Pattern Recognition

    JF - Pattern Recognition

    SN - 0031-3203

    IS - 10

    ER -