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丁建均 (Jian-Jiun Ding) National Taiwan University 辦公室：明達館 723 室， 實驗室：明達館 531 室

丁建均 (Jian-Jiun Ding) National Taiwan University 辦公室：明達館 723 室， 實驗室：明達館 531 室. 聯絡電話： (02)33669652 Major ： Digital Signal Processing Digital Image Processing. Research Fields [A. Image Processing] (1) Image Compression (page 4)

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丁建均 (Jian-Jiun Ding) National Taiwan University 辦公室：明達館 723 室， 實驗室：明達館 531 室

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  1. 丁建均 (Jian-Jiun Ding) National Taiwan University 辦公室：明達館723室， 實驗室：明達館531室 聯絡電話： (02)33669652 Major：Digital Signal Processing Digital Image Processing

  2. Research Fields [A. Image Processing] (1)Image Compression (page 4) (2) Edge and Corner Detection (page 14) (3) Segmentation (page 17) (4) Pattern Recognition (Face, Character) (page 19) (5) Optical Image Processing (page 23) (6) Others: Biomedical Image Processing, Banknote Reconstruction, Dehaze, Scene Classification (page 31) [B. Time-Frequency Analysis] (7) Time-Frequency Analysis (page 38) (8) Music Signal Analysis (page 56) (9) Wavelet Transform (page 60)

  3. [C. Fast Algorithms] (10) Integer Transforms (including Walsh transforms, Number Theory)(page 64) [D. Applications of Signal Processing] (11)Bioinformatics (page 70) (12) 3-D Accelerometer (page 74) [E. Other Topics] (13) ECG Signal Analysis (page 77) (14) Structure Similarity (15) Others (Quaternion, Filter Design, …) 實驗室的規定 (page 81)

  4. 1. Image Compression Conventional JPEG method: Separate the original image into many 8*8 blocks, then using the DCT to code each blocks. DCT: discrete cosine transform PS: 感謝 2008年畢業的黃俊德同學

  5. 壓縮的基本原理： 影像在經過 discrete cosine transform (DCT) 之後，大部分的能量都集中在低頻 DCT

  6. JPEG是當前最普及的影像壓縮格式。 問題：壓縮率高的時候，會產生 blocking effect Compression ratio = 53.4333 RMSE = 10.9662

  7. New Method: Edge-Based Segmentation and Compression 和小時候畫圖的方法類似

  8. Segmentation-based image compression Boundary Boundary Compression Image Segmentation Bit stream An image Image Segment Compression Image Segment

  9. Original Image By JPEG By Proposed Method An 100x100 image Bytes: 1295, RMSE: 2.39 Bytes: 456, RMSE: 2.54

  10. 使用 JPEG (692 bytes) 原圖 (10000 bytes) 使用 JPEG (233 bytes) 使用新方法 (165 bytes)

  11. 折衷的方法： 既不按照 88 的方格來做切割，也不完全按照物體的形狀 Triangular and Trapezoid (梯形) Block Segmentation J. J. Ding, Y. W. Huang, P. Y. Lin, S. C. Pei, H. H. Chen, and Y. H. Wang, "Two-dimensional orthogonal DCT expansion in trapezoid and triangular blocks and modified JPEG image compression," IEEE Trans. Image Processing, vol. 22, issue 9, pp. 3664-3675, Sept. 2013

  12. 技術上的問題： (1) 如何找到物體的邊緣並切割？(努力中) (2) 如何針對不規則的區域，找到 orthogonal transform (已解決) (3) 如何避免讓邊緣區域的高頻成分影響到壓縮的結果 (已解決) (4) 如何用最小的資料量，對邊界的部分做紀錄 (已解決) (5) 如何用最小的資料量，對內部的部分做紀錄 (已解決) (6) 減少壓縮和解壓縮的運算時間 (努力中) (7) 減少 buffer size 的需求，讓演算法能在手機中執行 (努力中) (8) 如何在少影響人眼視覺的前提下，讓資料量減少至極限？ (努力中) J. J. Ding, P. Y. Lin, J. D. Huang, T. H. Lee, and H. H. Chen, “Morphology-based shape adaptive compression,” Lecture Notes in Computer Science, vol. 6524, pp. 168-176, Jan. 2011 J. J. Ding, H. H. Chen, and W. Y. Wei, “Adaptive Golomb code for joint geometrically distributed data and its application in image coding,” IEEE Trans. Circuits Syst. Video Technol., vol. 23, issue 4, pp. 661-670, Apr. 2013

  13. 什麼是影像壓縮技術的極限？

  14. 2. Edge and Corner Detection Why should we perform edge and corner detection? --Segmentation --Compression --Efficient for Processing

  15. The most efficient way to trace an object in video: (1) Edges (2) Corners (3) SIFT Points (4) SURF, FAST, BRISK, ORB, FREAK….. Other Feature Points 當前 edge detection 技術 已經有很好的效果 (Ex: Canny’s algorithm) 但 corner detection 的結果，仍常受到 noise 影響

  16.  Corner Detection by Harris’ algorithm by proposed algorithm

  17. 3. Segmentation Important for (i) compression (ii) biomedical engineering (iii) pattern recognition, object identification

  18. Conventional method: 97.87 sec New method: 1.02 sec

  19. 4. Pattern Recognition including face recognition character recognition 應用很廣： security, identification, computer vision …………

  20. 文字辨識： (1) 辨識所寫的文字 (2) 辨識筆跡 (辨識書寫者) 這部分的研究，和政府機關合作 文字辨識 A B 1

  21. 人臉辨識 Class 1 Class 2 Class 3

  22. 最簡單的方法： matched filter 但技術上的問題頗多………. scaling shadow rotation partially distortion 目前較常用的方法： Feature Extraction + Machine Learning 臉有哪些特徵？

  23. 5. Optical Image Processing 這部分的研究，目前正在和工研院以及 Qualcomm 合作 Depth recovery: 如何由照片由影像的模糊程度，來判斷物體的距離 並且進一步重建出清楚的影像

  24. Model for Blurred Images i[m, n]: the original image b[m, n]: blurred image k[m, n]: some point spread function *: convolution σ[m, n]: noise A blurred image may cause from (1) defocus (和工研院合作) (2) hand-shaking (和 Qualcomm 合作)

  25. Simplest way What is the problem? Alternative ways: (1) Wiener filter (2) Richardson-Lucy Methods (3) Fourier Optics (4) Norm-Prior Based Methods (Levin, Krishnan) (5) Others

  26. Reconstructed Image Blurred Image Blurred Image Reconstructed Image W. D. Chang, J. J. Ding, Y. Chen, C. W. Chang, and C. C. Chang, “Edge-membership based blurred image reconstruction algorithm,” APSIPA Annual Summit and Conference, Hollywood, USA, Dec. 2012

  27. Blurred Image

  28. Reconstructed Image Y. Chen, J. J. Ding, W. S. Lai, Y. J. Chen, C. W. Chang, and C. C. Chang, “High quality image deblurring scheme using the pyramid hyper-Laplacian L2 norm priors algorithm,” Advances in Multimedia Information Processing, Lecture Notes in Computer Science, vol. 8294, pp. 134-145, Dec. 2013

  29. 手晃動造成的手機模糊影像還原 • Blurred: • Deblurred:

  30. lens, (focal length = f) free space, (length = z1) free space, (length = z2) • f = z1 = z2Fourier Transform • fz1, z2 but z1 = z2 Fractional Fourier Transform • fz1z2 Fractional Fourier Transform multiplied by a chirp

  31. 6. Other Applications of Image Processing (1) Biomedical Image Processing (曾經和應力所、光電所合作) (2) Banknote Reconstruction (曾經和政府機關合作) (3) Image Dehaze (影像去霧去霾，目前和 Qualcomm 合作) (4) Scene Classification (將來將和 Qualcomm 合作)

  32. 未受過傷的老鼠肌肉纖維 受過傷的老鼠肌肉纖維

  33. 未受過傷的老鼠肌肉纖維「分區」的結果

  34. 受過傷的老鼠肌肉纖維「分區」的結果 J. J. Ding, Y. H. Wang, L. L. Hu, W. L. Chao, and Y. W. Shau, “Muscle injury determination by image segmentation,” VCIP, accepted, Tainan, Nov. 2011

  35. 大腦核磁共振影像 (Brain MRI Image) (a) Brain MRI Image (b) White Matter (白質) (c) Gray Matter (灰質) (d) 腦髓液蛋白，頭蓋骨 http://mouldy.bic.mni.mcgill.ca/brainweb/

  36. Banknote Reconstruction

  37. Dehaze 將受到霾害或是霧的影響所照出來的照片，還原成和沒有霧的情形一樣 Scene Classification Mountain River Outdoors Ocean Images Street Indoors

  38. 7. Time-Frequency Analysis http://djj.ee.ntu.edu.tw/TFW.htm Fourier transform (FT) Time-Domain  Frequency Domain Some things make the FT not practical: (1) Only the case where t0tt1 is interested. (2) Not all the signals are suitable for analyzing in the frequency domain. It is hard to analyze the signal whose instantaneous frequency varies with time.

  39. Example: x(t) = cos( t) when t < 10, x(t) = cos(3 t) when 10  t < 20, x(t) = cos(2 t) when t 20 (FM signal)

  40. Using Time-Frequency analysis • x(t) = cos( t) when t < 10,x(t) = cos(3 t) when 10  t < 20, • x(t) = cos(2 t) when t 20 (FM signal) • Left：using Gray level to represent the amplitude of X(t, f) • Right：slicing along t = 15 f -axis t -axis t -axis

  41. Several Time-Frequency Distribution Short-Time Fourier Transform (STFT) with Rectangular Mask Gabor Transform avoid cross-term less clarity Wigner Distribution Function with cross-term high clarity Gabor-Wigner Transform (Proposed) avoid cross-term high clarity

  42. Cohen’s Class Distribution where S Transform Hilbert-Huang Transform

  43. 自然界瞬時頻率會隨時間而改變的例子 音樂 語音信號 Doppler effect seismic waves Optics radar system, rectangular function, ……………………… In fact, in addition to sinusoid-like functions, the instantaneous frequencies of other functions will inevitably vary with time.

  44. Applications of Time-Frequency Analysis (1) Finding Instantaneous Frequency (2) Signal Decomposition (3) Filter Design (4) Sampling Theory (5) Modulation and Multiplexing (6) Electromagnetic Wave Propagation (7) Optics (8) Radar System Analysis (9) Random Process Analysis (10) Music Signal Analysis (11) Biomedical Engineering (12) Acoustics (13) Spread Spectrum Analysis (14) System Modeling (15) Image Processing (16) Economic Data Analysis (17) Signal Representation (18) Data Compression (19) Seismology (20) Geology (21) Astronomy, Space Technology (22) Oceanography

  45. Conventional Sampling Theory Nyquist Criterion New Sampling Theory (1) t can vary with time (2) Number of sampling points == Area of time frequency distribution

  46. Modulation and Multiplexing spectrum of signal 1 -B1 B1 spectrum of signal 2 not overlapped B2 -B2

  47. Filter Design (1) Adaptive cutoff criterion (2) With the fractional Fourier transform

  48. Fractional Fourier Transform • Performing the Fourier transform a times (a can be non-integer) •  Fourier Transform (FT) • generalization •  Fractional Fourier Transform (FRFT) • ,  = a/2 • When  = 0.5, the FRFT becomes the FT. When  = 0.1 performing the FT 0.2 times; When  = 0.25 performing the FT 0.5 times; When  = /6  performing the FT 1/3 times;

  49.  Physical Meaning:Transform a Signal into the Fractional domain, which is the intermediate of the time domain and the frequency domain.

  50. 以時頻分析的觀點，傳統濾波器是垂直於 f-axis做切割的 f-axis stop band f0 cutoff line pass band t-axis 而用 fractional Fourier transform 設計的濾波器是，是由斜的方向作切割 f-axis  stop band cutoff line 和 f-axis 在逆時針方向的夾角為  u0 pass band cutoff line

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