Quasi-Bezier curves integrating localised information

Ferdous Sohel, G.C. Karmakar, L.S. Dooley, J.R. Arkinstall

    Research output: Contribution to journalArticle

    6 Citations (Scopus)
    169 Downloads (Pure)

    Abstract

    Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.
    Original languageEnglish
    Pages (from-to)531-542
    JournalPattern Recognition
    Volume41
    Issue number2
    DOIs
    Publication statusPublished - 2008

    Fingerprint

    Computational complexity
    Invariance
    Computer aided design
    Composite materials

    Cite this

    Sohel, Ferdous ; Karmakar, G.C. ; Dooley, L.S. ; Arkinstall, J.R. / Quasi-Bezier curves integrating localised information. In: Pattern Recognition. 2008 ; Vol. 41, No. 2. pp. 531-542.
    @article{5ac1bceffb214360ab970fe7e1050786,
    title = "Quasi-Bezier curves integrating localised information",
    abstract = "Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.",
    author = "Ferdous Sohel and G.C. Karmakar and L.S. Dooley and J.R. Arkinstall",
    year = "2008",
    doi = "10.1016/j.patcog.2007.07.002",
    language = "English",
    volume = "41",
    pages = "531--542",
    journal = "Pattern Recognition",
    issn = "0031-3203",
    publisher = "Elsevier",
    number = "2",

    }

    Sohel, F, Karmakar, GC, Dooley, LS & Arkinstall, JR 2008, 'Quasi-Bezier curves integrating localised information' Pattern Recognition, vol. 41, no. 2, pp. 531-542. https://doi.org/10.1016/j.patcog.2007.07.002

    Quasi-Bezier curves integrating localised information. / Sohel, Ferdous; Karmakar, G.C.; Dooley, L.S.; Arkinstall, J.R.

    In: Pattern Recognition, Vol. 41, No. 2, 2008, p. 531-542.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Quasi-Bezier curves integrating localised information

    AU - Sohel, Ferdous

    AU - Karmakar, G.C.

    AU - Dooley, L.S.

    AU - Arkinstall, J.R.

    PY - 2008

    Y1 - 2008

    N2 - Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.

    AB - Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.

    U2 - 10.1016/j.patcog.2007.07.002

    DO - 10.1016/j.patcog.2007.07.002

    M3 - Article

    VL - 41

    SP - 531

    EP - 542

    JO - Pattern Recognition

    JF - Pattern Recognition

    SN - 0031-3203

    IS - 2

    ER -