2.3.2 Contrast Stretching

1. 2.3.2 Contrast Stretching • Contrast • The contrast of an image is its distribution of light and dark pixels Fig. 2.12 Low and high contrast histogram.

2. Contrast Stretching • Contrast stretching • Clipping • thresholding

3. Contrast Stretching Contrast Stretching, a = 80, b= 160

4. Original Image Basic Contrast Stretching Original Image End-in Search Contrast Stretching

5. Contrast Stretching Original Image Convert Image

6. Red Green Blue

7. /******************************************** • * Func: auto_contrast_stretch • * Desc: performs basic contrast stretching on an image • * Params: source - pointer to source image • * cols - number of columns in the image * rows - height of image * • ********************************************* • void auto_contrast_stretch(image_ptr source, int cols, int rows) • { • long i; /* loop variable */ • long number_of_pixels; /* total number of pixels in image */

8. long histogram[256]; /* image histogram */ • unsigned char LUT[256]; /* Look-up table for point process */ • int lowthresh, highthresh; /* lower and upper thresholds */ • float scale_factor; /* scaling factor for contrast stretch */ • /* compute histogram */ • number_of_pixels = (long)cols * rows; • for(i=0; i<256; i++) • histogram[i]=0; • for(i=0; i<number_of_pixels; i++) • histogram[source[i]]++;

9. /* compute low and high thresholds */ • for(i=0; i<256; i++) • if(histogram[i]) { • lowthresh = i; • break; • } • for(i=255; i>0; i--) • if(histogram[i]) { • highthresh = i; • break; • }

10. printf("Low threshold is %d High threshold is %d\n", • lowthresh,highthresh); • /* compute new LUT */ • for(i=0; i<lowthresh; i++) • LUT[i]=0; • for(i=255; i>highthresh; i--) • LUT[i]=255;

11. scale_factor = 255.0 / (highthresh-lowthresh); • for(i=lowthresh; i<=highthresh; i++) • LUT[i]=(unsigned char)((i - lowthresh) * scale_factor); • /* transfer new image */ • for(i=0; i<number_of_pixels; i++) • source[i] = LUT[source[i]]; • }

12. 2.3.3 Intensity transformations • Digital negative • Applications • Display of medical images • Produce negative prints of images • Intensity level slicing • Applications : • Segmentation of certain gray level regions

13. Intensity transformations • Intensity transformation • Convert an old pixel into a new pixel based on some predefined function • Implemented with simple look-up tables • Simple transformation • Null transform • new pixel = old pixel • Image negative • y = -x+255 • Gamma correction function • Brightness of an image can be adjusted with a gamma correction transformation

14. Intensity transformations • Posterizing • reduces the number of gray levels in an images • Thresholding results when number of gray levels is reduced to 2. • A bounced threshold reduces the thresholding to a limited range and treats the other input pixels as null transformation • Figure 2.18(pp.63) Fig. 2.18 (a) 8-Level posterize transformation; (b) posterized image; (c) threshold transformation; (d) threshold image; (e) bounded threshold; (f) bounded threshold image.

15. Original gamma=0.45 gamma=2.20 Intensity transformations • Gamma correction

16. Intensity Transformation • Intensity Transformation • Intensity transformation is a point process that converts an old pixel into a new pixel base on some predefined function. This transformation is implemented with the LUT with ease. • Gamma Correction

17. Intensity Transformation

18. Intensity Transformation

19. Intensity Transformation

20. Intensity transformations Fig. 2.16 (a) Gamma collection transformation with gamma=0.45; (b) gamma collected image; (c) gamma collection transformation with gamma=2.2; (d) gamma collected image. Fig. 2.15 (a) Null transformation; (b) image; (c) negative transformation; (d) negative image. Page 60. 참조

21. Intensity transformations Fig. 2.17 (a) Contrast stretch transformation; (b) contrast stretched image; (c) Contrast compression transformation; (d) contrast compressed image. Fig. 2.18 (a) 8-Level posterize transformation; (b) posterized image; (c) threshold transformation; (d) threshold image; (e) bounded threshold; (f) bounded threshold image. Page 62. 참조

22. Intensity transformations Fig. 2.19 (a) 2-bit bit-clipping transformation; (b) resulting image. Fig. 2.21 (a) Iso-intensity contouring transformation; (b) contoured image. Fig. 2.20 Bit clipped image contrast stretched. Page 64. 참조

23. Intensity tranformations Fig. 2.22 (a) Range-highlighting transformation; (b) resulting image. Fig. 2.23 (a) Solarize transformation using a threshold of 150; (b) solarize image. Page 65. 참조

24. Fig. 2.24 (a) First parabola transformation; (b) transformed image; (c) second parabola transformation; (d) second transformed image.

25. HW – 03 a) Plot กราฟ histogram

26. HW – 03 b)

27. สจพ 2.4 Frequency-based Operations Fourier Transform DI&SP MTCT

28. Spatial Frequency • Efficient data representation • Provides a means for modeling and removing noise • Physical processes are often best described in “frequency domain” • Provides a powerful means of image analysis

29. What is spatial frequency? • Instead of describing a function (i.e., a shape) by a series of positions • It is described by a series of cosines • Fourier series • Fourier Transform

30. สจพ 1-D Fourier Transform DI&SP MTCT

31. Our starting place is the observation that a periodic function may be written as the sum of sines and cosines of varying amplitudes and frequencies.

32. it is possible to form any function as a summation of a series of sine and cosine terms of increasing frequency • For example, in figure we plot a function, and its decomposition into sine functions.

33. f(t)

34. We take the first three terms only (blue, green, red) to provide the approximation of the original function (purple). • The more terms of the series we take, the closer the sum will approach the original function.

35. Original function (purple) sines and cosines (1) where (2) Fourier coefficient Equations 1 and 2 are called Fourier transform pairs, and they exist if f(t) is continuous and integrable, and F(k) is integrable. These conditions are usually satisfied in practice.

36. f(t) => time-domain I 1 2 3 4 1 F(u) => frequency-domain 3 II 4 2

37. Any function can be represented in 2formats: • 1) time-domain representation, f(t), or spatial domain, f(x), and • 2) frequency-domain representationor Fourier domain, F(u) • In other words, any space ortime varying data can be transformed into a different domain called the frequencyspace.

38. Time-domain Frequency-domain

39. FT properties: If F(u) and G(u)are FT of function f(t) and g(t), respectively, • Time scaling • Frequency scaling

40. Time shifting • Frequency shifting

41. Convolution theorem • Correlation theorem

42. สจพ 2-D Fourier Transform DI&SP MTCT

43. แนวความคิดของการแปลงฟูเรียร์สามารถนำมาใช้กับฟังก์ชั่นหรือสัญญาณ 2 มิติ เช่น ภาพ ซึ่งจะเป็นการแปลงฟังก์ชั่นบน spatial domain (รูปภาพ) ไปเป็น frequency domain สมการคณิตศาสตร์แสดงความสัมพันธ์นี้เป็นดังนี้ IFT FT

44. ภาพแสดงความสัมพันธ์ระหว่างภาพใน spatial domain และความถี่ใน frequency (or Fourier) domain

45. พบว่าระยะถี่-ห่างทางตำแหน่งในภาพ (x-y ใน spatial domain) จะแปลงไปเป็นจุดใน frequency domain(u-v) • โดยบริเวณที่มีระยะห่าง (ซึ่งมีความถี่ทางตำแหน่งต่ำ) เช่น บริเวณตัวบ้านรวมทั้งหน้าต่าง-ประตู จะไปอยู่ในตำแหน่งที่ใกล้จุดกำเนิด • และในทางกลับกันบริเวณที่มีระยะถี่ (ซึ่งมีความถี่ทางตำแหน่งสูง) เช่น บริเวณที่มีลวดลายบนหลังคาบ้าน จะไปอยู่ในตำแหน่งที่ไกลจุดกำเนิดออกไป