A Generic Shape Descriptor using Bezier Curves Presenting by – Dr. Manzur Murshed Authors –...

A Generic Shape Descriptor using Bezier Curves

A Generic Shape Descriptor using Bezier Curves

Presenting by –

Dr. Manzur Murshed

Authors –

Ferdous Ahmed Sohel

Dr. Gour C. Karmakar

Prof. Laurence S. Dooley

Gippsland School of Computing and Information Technology

Monash University, AUSTRALIA

Gippsland School of Computing aGippsland School of Computing and IT, Australiand IT, Australia

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Presentation Outline

1. Introduction

2.Existing Bezier curve (BC) based shape descriptors

3.Proposed shape descriptor (SDBC)

i. Control point determination

ii. Control point coding

4.Results & Analysis

5.Conclusion and Future works


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Introduction

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

0101010…….000110Descriptor

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.


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Existing shape descriptor using BC

1. Arabic character descriptor proposed by Sarfraz and Khan.

2. Chinese calligraphic character descriptor using BC proposed by Yang et al.

3. Object shape description using cubic BC by Cinque et al.


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Shape description using cubic BC

1. Control point selection:i. The shape is divided into a number

of equi-length segments in terms of number of shape points.

ii. For each segment – control points are selected at some specific distances.

2. Control point coding:

i. Control points are encoded parametrically.


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Shape description using cubic BC (Cont.)

1. The descriptor for each segment consists of:

i. The coordinate values of the 1st and 4th control point,

ii. For the 2nd control point, the magnitude and the gradient of the tangent vector from the 1st control point and

iii.For the 3rd control point, the magnitude and the gradient of the tangent vector from the 4th control point.


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Limitation 1: Due to the even spacing of the segments and control points –

R1

R2

i. 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.



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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


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• Control Point Calculation

1. Calculation of the set of significant points:

i. The set of the least number of shape points that can produce the shape with ZERO distortion.

Proposed SDBC

2. Addition of the significant points:i. Reduces the likelihood of losing

potential significant points as a control point by considering curvature domain specific information.

ii. Inserts supplementary at average distance of the significant points.


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3. Union of significant and supplementary points are referred to as approximated boundary points (ABP).

i. ABP are used in control point calculation.

Proposed SDBC (cont.)

13210 ;;;43

4 ziiii bvbvbvbv zz

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.


1111

There is a periodic nature in the distance between the control points shown in following figure.

1. If the distance between the first and second control point is l number of ABP.

2. The distance between the 2nd and 3rd is 2*l ABP.

3. The distance between the 3rd and 4th is l ABP.

4. l, 2*l, l series for each additional segments.

Start-ing

point

ll 2*l2*l ll ll 2*l2*l ll … ll 2*l2*l

First Segment Next segment … Last Segment

Proposed SDBC (cont.)•Control point coding


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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).


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Proposed SDBC (cont.)

4- bit for

length of L1

Start-ing

point

DirDir

++

LL11

DirDir

++

LL22

DirDir

++

LL11

DirDir

++

LL11

DirDir

++

LL22

DirDir

++

LL11

… DirDir

++

LL11

DirDir

++

LL22

First Segment Next segment … Last Segment

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.


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Results and Analysis

Class one – peak distortion in pel

Class two – mean squared distortion in pel2

0 20 40 60

0

20

40

60

BCSDBCshape

BCSDBCshape

0 20 40 60 80 100

0

20

40

60

BCSDBCshape

BCSDBCshape

Results for Fish object shapes with 5 segments

Fish 1 Fish 2


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Fish SR = 5 SR = 6 SR = 7 SR =8

Max MS Max MS Max MS Max MS

1 BC 9.5 14 7.0 6.7 6.4 4.1 5.1 2.9

SDBC 8.1 10.2 6.3 6 5.8 3.1 4.5 1.8

2 BC 7.6 9.1 7.0 5.8 6.0 4.3 5.2 2.8

SDBC 6 6.6 5.6 3.5 5.4 3.6 4.8 1.8

Results and Analysis

Distortion measures for different number of segments (units: Max – pel and MS – pel2), SR= Number of segments.


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Fish SR = 5 SR = 6 SR = 7 SR =8

1BC 240 288 336 384

SDBC 165 196 227 258

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BC 240 288 336 384

SDBC 165 196 227 258

Results and AnalysisDescriptor length in bits

Over 35% descriptor size reduction for each additional segments.

Around 30% overall descriptor size reduction.


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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.


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A Generic Shape Descriptor using Bezier Curves Presenting by – Dr. Manzur Murshed Authors –...

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