A Generic S hape D escriptor using B ezier C urves

1. A Generic Shape Descriptor using Bezier Curves Authors – Ferdous Ahmed Sohel Dr. Gour C. Karmakar Prof. Laurence S. Dooley Presenting by – Dr. Manzur Murshed Gippsland School of Computing and Information Technology Monash University, AUSTRALIA

2. Presentation Outline • Introduction • Existing Bezier curve (BC) based shape descriptors • Proposed shape descriptor (SDBC) • Control point determination • Control point coding • Results & Analysis • Conclusion and Future works Gippsland School of Computing and IT, Australia

3. Descriptor 0101010…….000110 Introduction • Applications of shape description: • Communication: Mobile multimedia communication, low bit rate coding. • Storage and retrieval: Digital library, indexing, digital archiving. • Interactive editing: Cartoons, digital films. Gippsland School of Computing and IT, Australia

4. Existing shape descriptor using BC • Arabic character descriptor proposed by Sarfraz and Khan. • Chinese calligraphic character descriptor using BC proposed by Yang et al. • Object shape description using cubic BC by Cinque et al. Gippsland School of Computing and IT, Australia

5. Shape description using cubic BC • Control point selection: • The shape is divided into a number of equi-length segments in terms of number of shape points. • For each segment – control points are selected at some specific distances. • Control point coding: • Control points are encoded parametrically. Gippsland School of Computing and IT, Australia

6. Shape description using cubic BC (Cont.) • The descriptor for each segment consists of: • The coordinate values of the 1st and 4th control point, • For the 2nd control point, the magnitude and the gradient of the tangent vector from the 1st control point and • For the 3rd control point, the magnitude and the gradient of the tangent vector from the 4th control point. Gippsland School of Computing and IT, Australia

7. R1 R2 Shape description using cubic BC (Cont.) Limitation 1:Due to the even spacing of the segments and control points – • Flat regions (e.g., R1) and sharp changing regions (R2) are both getting equal emphasis in control point selection – thus can lead to large distortion even with large number of segments. Gippsland School of Computing and IT, Australia

8. Shape description using cubic BC (Cont.) Limitation 2:According to the definition the magnitude and the gradient are all floating point numbers, hence will require larger size of descriptor. To overcome these limitations SDBC has been proposed Gippsland School of Computing and IT, Australia

9. Proposed SDBC • Control Point Calculation • Calculation of the set of significant points: • The set of the least number of shape points that can produce the shape with ZERO distortion. • Addition of the significant points: • Reduces the likelihood of losing potential significant points as a control point by considering curvature domain specific information. • Inserts supplementary at average distance of the significant points. Gippsland School of Computing and IT, Australia

10. Like Cinque et al.’s method, the control points for a segment starting from ith ABP is defined as Where z is the number of ABP in a segment and b the ABP set. Proposed SDBC(cont.) • Union of significant and supplementary points are referred to as approximated boundary points(ABP). • ABP are used in control point calculation. Gippsland School of Computing and IT, Australia

11. Proposed SDBC(cont.) • Control point coding • There is a periodic nature in the distance between the control points shown in following figure. • If the distance between the first and second control point is l number of ABP. • The distance between the 2nd and 3rd is 2*l ABP. • The distance between the 3rd and 4th is l ABP. • l, 2*l, l series for each additional segments. Gippsland School of Computing and IT, Australia

12. Proposed SDBC(cont.) • Dynamic fixed length coding (DFLCC) • A combination of run-length code and chain code. • Encodes the control points differentially. • Direction of the current control point from the previous is encoded by 6-bits. • The distance is the length of the run (for covering l ABP it is L1bits and for 2*l it is L2 bits, clearly L2=L1+1). Gippsland School of Computing and IT, Australia

13. Proposed SDBC(cont.) The complete descriptor looks like The starting 4- bits are reserved for the length of L1, which could be maximum 16-bit number and thus SDBC can encode a segment consisting of up to 4*216 shape points. Gippsland School of Computing and IT, Australia

14. Results and Analysis Class one – peak distortion in pel Class two – mean squared distortion in pel2 Fish 2 Fish 1 Results for Fish object shapes with 5 segments Gippsland School of Computing and IT, Australia

15. Results and Analysis Distortion measures for different number of segments (units: Max – pel and MS – pel2), SR= Number of segments. Gippsland School of Computing and IT, Australia

16. Results and Analysis Descriptor length in bits • Over 35% descriptor size reduction for each additional segments. • Around 30% overall descriptor size reduction. Gippsland School of Computing and IT, Australia

17. Conclusions and Future Works • SDBC addresses domain specific shape information. • Keeps the distortion lower. • The descriptor length is lower. • Consider the loops in shapes and cornerity of the shape at the shape points and divide the shape into segments. • For each segment apply the SDBC algorithm with a modification in the DFLC. Gippsland School of Computing and IT, Australia

18. Thank You Gippsland School of Computing and IT, Australia