Segmentation-Based Image Compression

以影像切割為基礎的影像壓縮技術

Speaker: Jiun-De HuangAdvisor: Jian-Jiun Ding

Graduate Institute of Communication EngineeringNational Taiwan University, Taipei, Taiwan, ROC

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Outline

• Introduction to Image Compression• Segmentation-Based Image Compression• Edge Detection• Image Segmentation• Boundary Description and Compression• Proposed Methods for Boundary Description• Internal Texture Compression• Comclution• Future Work

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Introduction to Image Compression

• Why we need to compress the image?– Save disk space– Save transformation bandwidth

• The common type of image compression– DCT-based method: JPEG– Wavelet-based method: JPEG2000

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Introduction to Image Compression

Color Component

of an Image

Transform Coding( DCT or Wavelet )

Quantization EntropyCoding

Bit-stream

• Image compression model

Bit-stream Transform DecodingEntropy

Decoding

Color Componentof an image

Encoder

Decoder

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Segmentation-Based Image Compression

Image segments of DCT:

Object-oriented segments:

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Segmentation-Based Image Compression

• Segmentation-based image compression model

Arbitrary-ShapedTransform Coding

Quantization &Entropy Coding

Bit-streamImage

Segmentation

Boundary Transform Coding

Quantization &Entropy Coding

Internal texure

Boundary

Coefficients oftransform bases

Boundarydescriptor

An image

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Segmentation-Based Image Compression

• Advantage– Pixels in the same segment have extremly high correlation, the c

ompression ratio can be higher.– The boundary of a segment is recorded separately, it may make

the image clear in high compression ratio.– Application in image recognize

• Disadvantage– Large time to encode and decode– Hard to find a common way to segment various images.

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Edge Detection

• First-order derivatives

• Second-order derivatives

• Hilbert transform

• Short time Hilbert transform

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Edge Detection

0 50 100

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(a) (b)

(c) (d)

(e) (f)

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(a) (b)

(c) (d)

(e) (f)

Using differentiation Using HLT

Sharp edge

Step edgeWith noise

Ramp edge

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Edge Detection

• Short Time Hilbert Transform– Impulse responses and their FTs of the SRHLT for different b. W

e can compare them with the impulse response of the differential operation and the original HLT.

-2 -1 0 1 2-1

0

1

-2 -1 0 1 2

-1

0

1(a) (b)

Time domain Frequency domain

Hilbert transformFT

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0

1

-2 -1 0 1 2-10

0

10(i) (j)differentiation

FT

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1

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(c) (d)

(e) (f)

(g) (h)

Time domain Frequency domain

SRHLT, b=0.25

SRHLT, b=1

SRHLT, b=4

FT

FT

FT

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Edge Detection

• Short Time Hilbert Transform– Using SRHLTs to detect the sharp edges, the step edges with n

oise, and the ramp edges. Here we choose b = 1, 4, 12, and 30.

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(i)

(k)

(h)

(j)

(l)

b = 12 b = 30

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(e)

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(f)

b = 1 b = 4

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Edge Detection

(a) Original image (b) Results of differentiation

(c) Results of the HLT (d) Results of the SRHLT, b=8 (c) Results of the HLT (d) Results of the SRHLT, b=8

(a) image+noise, SNR=32 (b) Results of differentiation

• Short Time Hilbert Transform

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Image Segmentation

• Thresholding

Gray-level histograms that can be partitioned by (a) Single threshold, and (b) multiple thresholds

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Image Segmentation

• Edge Linking– Hough transform

Two point in the coordinate The coefficient space

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Image Segmentation

• Edge Linking– Hough transform

Two points in thePolar coordinate

Coefficient space

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Image Segmentation

• Region Growing

• Region Splitting and Merging

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Image Segmentation

• Watershed

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Boundary Description and Compression

• Polygonal approximations– Merging techniques

– Splitting techniques

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Boundary Description and Compression

• Fourier descriptor– Set the coordinate of the K-point boundary as a series of comple

x number s(k), k=0,1,…,K-1.– The Fourier descriptor is define as the DFT of s(k).

( ) ( ) ( ), 0,1,...,s k x k jy k k K

12 /

0

1( ) ( ) , 0,1,..., 1

Kj uk K

k

a u s k e u KK

The DFT of s(k)

The inverse DFT of a(u)1

2 /

0

( ) ( ) , 0,1,..., 1K

j uk K

u

s k a u e k K

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Boundary Description and Compression

• Fourier descriptor– If we only use the first P coefficients, the detail of the recover

boundary will be lost. Smaller P becomes, more detail lost.

Original image R=30% R=20% R=10%

12 /

0

( ) ( )ˆP

j uk K

u

s k a u e

Compression rate: R = P/K

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Proposed Methods for Boundary Description

• Improvement of Fourier descriptor– We segment the boundary with the corner point and only comput

e the Fourier desriptor of the boundary segment– However, if we do not use the whole coefficients, the recovery b

oundary segment will be closed due to the discontinuous of the two end point

u

a(u)

0 P K

Boundarysegment

Fourierdescriptor

Recoverboundary

truncate

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Proposed Methods for Boundary Description

• Improvement of Fourier descriptor– To solve the non-closed problem, we adapt the following steps:

1. Record the coordinate of the two end of the boundary segment and shift them to the original of coordinate

2. Shift the other boundary points linearly according to its distance with the end point

3. Add a new boundary which is odd symmetry to the original one

Boundarysegment

Shift linearly

Add a new boundary

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Proposed Methods for Boundary Description

• Improvement of Fourier descriptor4. Compute the Fourier descriptor to the new boundary which is cl

osed and is continuous in the two end points

5. Because the new boundary is odd symmetry, the Fourier descriptor is odd symmetry, too. There is, we only need to record the first K points of the Fourier descriptor.

( ) ( )DFTx n X k

u

a(u)

0 K 2K-2

Fourierdescriptor

useless

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Proposed Methods for Boundary Description

• Improvement of Fourier descriptor– Simulation

R=20% R=10% R= 7%Originalimage

generalFourier

descriptor

modifiedFourier

descriptor

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Internal Texture Compression0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

v

uThe 8x8 DCT basis

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Internal Texture Compression0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

v

uThe Arbitraryly-shapedDCT basis

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Internal Texture Compression0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

v

uThe Arbitraryly-shapedDCT basis

Use zig-zag order to do Gram-Schmidt orthonormalize

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Internal Texture Compression

The Arbitraryly-shaped DCT orthnormal basis

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Internal Texture Compression

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An arbitraryly-shaped image

The 37 AS-DCT coefficients

AS-DCT

Example:

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Conclusion

• The compression rate depend on the complex of the image content.

• This compression method is better when the image content is simple.

• There are various method in each step, they suit different image respectly.

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Future Work

• Find a better method of segmentation which is suit to this compression method.

• Automatic analysis the property of the image and choose the fittest method in each step.

• How to apply this compression method to the image recognize technique.