Segmentation-Based Image Compression 以影像切割為基礎的影像壓縮技術

1. Segmentation-Based Image Compression以影像切割為基礎的影像壓縮技術 Speaker: Jiun-De Huang Advisor: Jian-Jiun Ding Graduate Institute of Communication Engineering National Taiwan University, Taipei, Taiwan, ROC

2. 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

3. 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

4. Introduction to Image Compression • Image compression model Encoder Transform Coding ( DCT or Wavelet ) EntropyCoding Quantization Bit-stream Color Component of an Image Decoder EntropyDecoding Transform Decoding Color Component of an image Bit-stream

5. Segmentation-Based Image Compression Image segments of DCT: Object-oriented segments:

6. Segmentation-Based Image Compression • Segmentation-based image compression model Boundary Boundary descriptor Boundary Transform Coding Quantization & Entropy Coding An image Image Segmentation Bit-stream Arbitrary-Shaped Transform Coding Quantization & Entropy Coding Internal texure Coefficients of transform bases

7. Segmentation-Based Image Compression • Advantage • Pixels in the same segment have extremly high correlation, the compression 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.

8. Edge Detection • First-order derivatives • Second-order derivatives • Hilbert transform • Short time Hilbert transform

9. Edge Detection Using differentiation Using HLT Sharp edge Step edge With noise Ramp edge

10. Frequency domain Time domain Frequency domain Time domain (c) (a) (d) (b) 1 1 1 1 SRHLT, b=0.25 Hilbert transform FT 0 FT 0 0 0 -1 -1 -1 -1 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 (e) (f) 1 1 SRHLT, b=1 (j) (i) 0 FT 0 1 10 differentiation -1 -1 FT 0 0 -2 -1 0 1 2 -2 -1 0 1 2 (g) (h) 1 -1 -10 1 SRHLT, b=4 -2 -1 0 1 2 -2 -1 0 1 2 FT 0 0 -1 -1 -2 -1 0 1 2 -2 -1 0 1 2 Edge Detection • Short Time Hilbert Transform • Impulse responses and their FTs of the SRHLT for different b. We can compare them with the impulse response of the differential operation and the original HLT.

11. b = 4 b = 12 b = 1 b = 30 (a) (h) (g) (b) 1 1 0.5 1 0 0 0 0 -1 -1 -0.5 -1 (c) (d) 0 50 100 0 50 100 100 0 50 100 (i) (j) 1 1 1 0.5 0 0 0 0 -1 -1 -0.5 -1 0 50 100 (e) 0 50 100 (k) 0 50 100 (f) (l) 0 50 100 1 1 1 0.5 0 0 0 0 -1 -1 -0.5 -1 0 50 100 0 50 100 0 50 100 0 50 100 Edge Detection • Short Time Hilbert Transform • Using SRHLTs to detect the sharp edges, the step edges with noise, and the ramp edges. Here we choose b = 1, 4, 12, and 30.

12. Edge Detection • Short Time Hilbert Transform (a) Original image (b) Results of differentiation (a) image+noise, SNR=32 (b) Results of differentiation

13. Image Segmentation • Thresholding Gray-level histograms that can be partitioned by (a) Single threshold, and (b) multiple thresholds

14. Image Segmentation • Edge Linking • Hough transform The coefficient space Two point in the coordinate

15. Image Segmentation • Edge Linking • Hough transform Two points in the Polar coordinate Coefficient space

16. Image Segmentation • Region Growing • Region Splitting and Merging

17. Image Segmentation • Watershed

18. Boundary Description and Compression • Polygonal approximations • Merging techniques • Splitting techniques

19. Boundary Description and Compression • Fourier descriptor • Set the coordinate of the K-point boundary as a series of complex number s(k), k=0,1,…,K-1. • The Fourier descriptor is define as the DFT of s(k). The DFT of s(k) The inverse DFT of a(u)

20. 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. Compression rate: R = P/K R=30% R=20% R=10% Original image

21. Proposed Methods for Boundary Description • Improvement of Fourier descriptor • We segment the boundary with the corner point and only compute the Fourier desriptor of the boundary segment • However, if we do not use the whole coefficients, the recovery boundary segment will be closed due to the discontinuous of the two end point a(u) truncate u 0 PK Recover boundary Boundary segment Fourier descriptor

22. Proposed Methods for Boundary Description • Improvement of Fourier descriptor • To solve the non-closed problem, we adapt the following steps: • Record the coordinate of the two end of the boundary segment and shift them to the original of coordinate • Shift the other boundary points linearly according to its distance with the end point • Add a new boundary which is odd symmetry to the original one Boundary segment Shift linearly Add a new boundary

23. Proposed Methods for Boundary Description • Improvement of Fourier descriptor • Compute the Fourier descriptor to the new boundary which is closed and is continuous in the two end points • 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. a(u) useless u 0 K 2K-2 Fourier descriptor

24. Proposed Methods for Boundary Description • Improvement of Fourier descriptor • Simulation Original image R= 7% R=20% R=10% general Fourier descriptor modified Fourier descriptor

25. Internal Texture Compression u The 8x8 DCT basis 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 v

26. Internal Texture Compression u The Arbitraryly-shaped DCT basis 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 v

27. Internal Texture Compression u The Arbitraryly-shaped DCT basis 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Use zig-zag order to do Gram-Schmidt orthonormalize v

28. Internal Texture Compression The Arbitraryly-shaped DCT orthnormal basis 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

29. Internal Texture Compression Example: An arbitraryly-shaped image The 37 AS-DCT coefficients AS-DCT

30. 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.

31. 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.