1. Outline For Image Processing A Digital Image Processing System Image Representation and Formats 1. Sensing, Sampling, Quantization 2. Gray level and Color Images 3. Raw, RGB, Tiff, BMP, JPG, GIF, (JP2) Image Transform and Filtering Histogram, Enhancement and Restoration Segmentation, Edge Detection, Thinning Image Data Compression Image Pattern Analysis (Recognition and Interpretation) [1] R.C. Gonzalez, R.E. Woods, S.L. Eddins, Digital Image Processing Using MATLAB, Pearson Prentice Hall, 2004 [2] R.C. Gonzalez and R.E. Woods, Digital Image Processing, Prentice-Hall, 2002+

2. Examples of Digital Images

3. Image Processing System

4. Digital Image Analysis System A 2D image is nothing but a mapping from a region to a matrix A Digital Image Processing System consists of 1. Acquisition – scanners, digital camera, ultrasound, X-ray, MRI, PMT 2. Storage – HD (120GB), CD (700MB), DVD (4.7GB), Flash memory (512MB~4GB), 3.5” floppy diskettes, i-pod, … 3. Processing Unit – PC, Workstation, PC-cluster 4. Communication – telephone lines, cable, wireless, … 5. Display – LCD monitor, laser printer, laser-jet printer

5. Gray Level and Color Images

6. Pixels in a Gray Level Image

7. A Gray Level Image is a Matrix f(0,0) f(0,1) f(0,2) …. …. f(0,n-1) f(1,0) f(1,1) f(1,2) …. …. f(1,n-1)... f(m-1,0) f(m-1,1) f(m-1,2) … …. f(m-1,n-1) An image of m rows, n columns, f(i,j) is in [0,255]

8. Gray and Color Image Data 0, 64, 144, 196, 225, 169, 100, 36 (R, G, B) for a color pixel Red – (255, 0, 0) Green – ( 0, 255, 0) Blue – ( 0, 0, 255) Cyan – ( 0,255, 255) Magenta – (255, 0, 255) Yellow – (255, 255, 0) Gray – (128, 128, 128)

9. Image Representation (Gray/Color) A gray level image is usually represented by an M by N matrix whose elements are all integers in {0,1, …, 255} corresponding to brightness scales A color image is usually represented by 3 M x N matrices whose elements are all integers in {0,1, …, 255} corresponding to 3 primary primitives of colors such as Red, Green, Blue

10. Red, Green, Blue, Color Images

11. Sensing, Sampling, Quantization A 2D digital image is formed by a sensor which maps a region to a matrix Digitization of the spatial coordinates (x,y) in an image function f(x,y) is called Sampling Digitization of the amplitude of an image function f(x,y) is called Quantization

12. Gray Level and Color Images

13. Image File Formats (1/2) The American National Standards Institute (ANSI) sets standards for voluntary use in US. One of the most popular computer standards set by ANSI is the American Standard Code for Information Interchange (ASCII) which guarantees all computers can exchange text in ASCII format BMP – Bitmap format from Microsoft uses Raster-based 1~24-bit colors (RGB) without compression or allows a run-length compression for 1~8-bit color depths GIF – Graphics Interchange Format from CompuServe Inc. is Raster-based which uses 1~8-bit colors with resolutions up to 64,000*64,000 LZW (Lempel-Ziv-Welch, 1984) lossless compression with the compression ratio up to 2:1

14. Some Image File Formats (2/2) Raw – Raw image format uses a 8-bit unsigned character to store a pixel value of 0~255 for a Raster-scanned gray image without compression. An R by C raw image occupies R*C bytes or 8RC bits of storage space TIFF – Tagged Image File Format from Aldus and Microsoft was designed for importing image into desktop publishing programs and quickly became accepted by a variety of software developers as a standard. Its built-in flexibility is both a blessing and a curse, because it can be customized in a variety of ways to fit a programmer’s needs. However, the flexibility of the format resulted in many versions of TIFF, some of which are so different that they are incompatible with each other JPEG – Joint Photographic Experts Group format is the most popular lossy method of compression, and the current standard whose file name ends with “.jpg” which allows Raster-based 8-bit grayscale or 24-bit color images with the compression ratio more than 16:1 and preserves the fidelity of the reconstructed image EPS – Encapsulated PostScript language format from Adulus Systems uses Metafile of 1~24-bit colors with compression JPEG 2000

15. Image Transforms and Filtering Feature Extraction – find all ellipses in an image Bandwidth Reduction – eliminate the low contrast “coefficients” Data Reduction – eliminate insignificant coefficients of Discrete Cosine Transform (DCT), Wavelet Transform (WT) Smooth filtering can get rid of noisy signals

16. Discrete Cosine Transform Partition an image into nonoverlapping 8 by 8 blocks, and apply a 2d DCT on each block to get DC and AC coefficients. Most of the high frequency coefficients become insignificant, only the DC term and some low frequency AC coefficients are significant. Fundamental for JPEG Image Compression

17. Discrete Cosine Transform (DCT) X: a block of 8x8 pixels A=Q 8 : 8x8 DCT matrix as shown above Y=AXA t

18. DCT on a 8x8 Block

19. Quantized DCT Coefficients

20. Wavelet Transform Haar, Daubechie’s Four, 9/7, 5/3 transforms 9/7, 5/3 transforms was selected as the lossy and lossless coding standards for JPEG2000 A Comparison of JPEG and JPEG2000 shows that the latter is slightly better than the former, however, to replace the current image.jpg by image.jp2 needs time

21. Daubechies’ 4 Wavelet Transform X: an image W: Haar transform shown above with c i = 1/√2 Y=P*W*(X*W t *Q), where P and Q are permutation matrices

22. A Block and Its Daub4 Transform

23. Mean and Median Filtering X1 X2 X3 X4 X0 X5 X6 X7 X8 Replace the X0 by the mean of X0~X8 is called “mean filtering” X1 X2 X3 X4 X0 X5 X6 X7 X8 Replace the X0 by the median of X0~X8 is called “median filtering”

24. Example of Median Filtering

25. Image and Its Histogram

26. Enhancement and Restoration The goal of enhancement is to accentuate certain features for subsequent analysis or image display. The enhancement process is usually done interactively The restoration is a process that attempts to reconstruct or recover an image that has been degraded by using some unknown phenomenon

27. Segmentation and Edge Detection Segmentation is basically a process of pixel classification: the picture is segmented into subsets by assigning the individual pixels into classes Edge Detection is to find the pixels whose gray values or colors being abruptly changed

28. Image, Histogram, Thresholding

30. Binarization by Thresholding

31. Edge Detection -1 -2 -1 0 0 0  X 1 2 1 -1 0 1 -2 0 2  Y -1 0 1 Large (|X|+|Y|)  Edge

32. Thinning and Contour Tracing Thinning is to find the skeleton of an image which is commonly used for Optical Character Recognition (OCR) and Fingerprint matching Contour tracing is usually used to locate the boundaries of an image which can be used in feature extraction for shape discrimination

33. Image  Edge, Skeleton, Contour

34. Image Data Compression The purpose is to save storage space and to reduce the transmission time of information. Note that it requires 6 mega bits to store a 24-bit color image of size 512 by 512. It takes 6 seconds to download such an image via an ADSL (Asymmetric Digital Subscriber Line) with the rate 1 mega bits per second and more than 12 seconds to upload the same image Note that 1 byte = 8 bits, 3 bytes = 24 bits

35. Lenna Image vs. Compressed Lenna