A DYNAMIC BEZIER CURVE MODEL Ferdous A' Sohel, Laurence S' Dooley, and Gour C' Karmakar Gippsland Sc

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A DYNAMIC BEZIER CURVE MODELFerdous A. Sohel,
Laurence S. Dooley, and Gour C. Karmakar
Gippsland School of Information
TechnologyMonash University, Victoria 3842,
AUSTRALIA.Ferdous.Sohel, Laurence.Dooley,
Gour.Karmakar_at_infotech.monash.edu.au
ABSTRACT Bezier curves (BC) are fundamental to a
wide range of applications from computer-aided
design through to object shape descriptions and
surface mapping. Since BC only consider global
information with respect to their control points,
this can lead to erroneous shape representations,
though integrating local control point
information minimises this error. This paper
presents a new Dynamic Bezier Curve (DBC) model
which combines both localised and global shape
information by making a parametric shift of the
BC points in the gap between the curve and its
control polygon. The value of the shifting
parameter is dynamically determined for a
prescribed maximum distortion. DBC retains the
kernel properties of the BC without increasing
computational complexity order. The models
performance has been empirically evaluated on a
number of arbitrary-shaped objects from geometric
modelling to shape coding. Both qualitative and
quantitative results confirm the improvement
achieved compared with the classical BC
representation.

• MOTIVATION
• Classical Bezier only considers global control
  point information which can lead to large gaps.
• Bezier variants degree elevation, composite and
  subdivision and refinements reduce this gap, BUT
  also increase the number of control points.

RESEARCH CHALLENGE Reduce the gap without
increasing the number of control points.
CONTRIBUTION Incorporate local information into
the global Bezier framework by shifting the
Bezier point towards the control polygon with the
Dynamic Bezier Curve (DBC) model.

• CONCLUSION
• New Bezier framework incorporating local
  geometric information for superior shape
  approximations.
• Admissible shape distortion can be maintained.
• Lower distortion than Bezier as well as smaller
  descriptor length.
• DBC retains the core properties of Bezier.
• Same computational complexity as Bezier.

Where P(x1,y1)Q(x2,y2) is the closest control
polygon edge from BC point for a particular t and
(J,K) is the closest point on PQ, Ex1-x2,
Fy1-y2, X and Y refer either (x1,y1) or (x2,y2)
pair. m is the shifting parameter and deduced by
Lagrangian multiplier method for a prescribed
distortion.
REFERENCE 1 F.A. Sohel, L.S. Dooley, G.C.
Karmakar, Accurate distortion measurement for
generic shape coding, Pattern Recognition
Letters, 27(2), pp.133-142, 2006.