Recovering the control points of Bézier curves for line image indexing

This paper presents a fast and robust algorithm for recovering the control points of Be´ zier curves. The method is based on slope following and learning algorithm that provides an efficient way of finding the control points of any type of cubic Be´ zier curves. Experimental results demonstrate that our method is fast and efficient for recovering the control points accurately. The control points are applied to line image indexing and employed for the implementation of the identification of actors drawn in Japanese traditional painting pictures, known as Ukiyoe pictures.

[1]  Jens Gravesen,et al.  Adaptive Subdivision and the Length and Energy of Bézier Curves , 1997, Comput. Geom..

[2]  Jiwen Zheng C-Bézier curves and surfaces , 1999 .

[3]  Joe D. Warren,et al.  Degree reduction of Bézier simplexes , 1994, Comput. Aided Des..

[4]  Thomas W. Sederberg,et al.  Approximate Implicitization Using Monoid Curves and Surfaces , 1999, Graph. Model. Image Process..

[5]  Robert F. Sproull,et al.  Principles in interactive computer graphics , 1973 .

[6]  Richard R. Patterson,et al.  The uniqueness of Bézier control points , 1997, Comput. Aided Geom. Des..

[7]  Ron Goldman,et al.  Interpolation and approximation of curves and surfaces using Pólya polynomials , 1991, CVGIP Graph. Model. Image Process..

[8]  James D. Foley,et al.  Fundamentals of interactive computer graphics , 1982 .

[9]  Ron Goldman,et al.  Algebraic Geometry for Computer-Aided Geometric Design , 1986, IEEE Computer Graphics and Applications.

[10]  Les A. Piegl,et al.  On NURBS: A Survey , 2004 .

[11]  Desire L. Massart,et al.  Least median squares curve fitting using a genetic algorithm , 1995 .

[12]  Thomas Hermann On the derivatives of second and third degree rational Bézier curves , 1999, Comput. Aided Geom. Des..

[13]  Hao Zhou,et al.  Curve Fitting with Bézier Cubics , 1996, CVGIP Graph. Model. Image Process..

[14]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[15]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[16]  Christoph M. Hoffmann,et al.  Implicit curves and surfaces in CAGD , 1993, IEEE Computer Graphics and Applications.

[17]  J. J. Chou,et al.  Planar cubics through a point in a direction , 1993, Comput. Aided Des..

[18]  Shi-Min Hu,et al.  Generalized Subdivision of Bézier Surfaces , 1996, CVGIP Graph. Model. Image Process..

[19]  Les A. Piegl,et al.  Algorithm for degree reduction of B-spline curves , 1995, Comput. Aided Des..

[20]  Edwin Earl Catmull,et al.  A subdivision algorithm for computer display of curved surfaces. , 1974 .

[21]  Matthias Eck,et al.  Least squares degree reduction of Bézier curves , 1995, Comput. Aided Des..

[22]  Tony DeRose,et al.  The Beta2-spline: A Special Case of the Beta-spline Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[23]  Les A. Piegl,et al.  Data reduction using cubic rational B-splines , 1992, IEEE Computer Graphics and Applications.

[24]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[25]  Paul Sablonnière,et al.  Subharmonicity and convexity properties of Bernstein polynomials and Bézier nets on triangles , 1999, Comput. Aided Geom. Des..

[26]  Yuesheng Xu,et al.  Degree reduction of Bézier curves by uniform approximation with endpoint interpolation , 1995, Comput. Aided Des..

[27]  Alan Watt,et al.  Advanced animation and rendering techniques , 1992 .

[28]  Yves Mineur,et al.  A shape controled fitting method for Bézier curves , 1998, Comput. Aided Geom. Des..

[29]  Rida T. Farouki,et al.  Approximation by interval Bezier curves , 1992, IEEE Computer Graphics and Applications.

[30]  Xiuzi Ye,et al.  Generating Bézier points for curves and surfaces from boundary information , 1995, Comput. Aided Des..