1. Medical Image Analysis Image Enhancement Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

2. Spatial Domain Methods Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Spatial domain methods ◦ Pixel-by-pixel transformation ◦ Histogram statistics ◦ Neighborhood operations ◦ Faster than frequency filtering Frequency filtering ◦ Better when the characteristic frequency components of the noise and features of interest are available

3. Histogram Transformation Histogram Histogram equalization

4. Figure 6.1. An X-ray CT image (top left) and T-2 weighted proton density image (top right) of human brain cross-sections with their respective histograms at the bottom. The MR image shows a brain lesion.

5. Figure 6.2. Histogram equalized images of the brain MR images shown in Figure 6.1 (top) and their histograms (bottom).

6. Histogram Modification Scaling Histogram modification

7. Histogram Modification Histogram modification ◦ Target histogram:

8. Image Averaging Averaging ◦ Enhancing signal-to-noise ratio

9. Image Subtraction Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Subtraction ◦ Enhance the information about the changes in imaging conditions ◦ Angiography: The anatomy with vascular structure is obtained first. An appropriate dye or tracer drug is then administered in the body, where it flows through the vascular structure. A second image of the same anatomy is acquired at the peak of the tracer flow.

10. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.3. An MR angiography image obtained through image subtraction method.

11. Neighborhood Operations Use a weight mask

12. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. f (-1,0) f (0,-1) f (0,0) f (0,1) f (1,0) f (-1,-1) f (-1,0) f (0,-1) f (0,0) f (0,1) f (0,-1) f (1,0) f (1,1) Figure 6.4: A 4-connected (left) and 8-connected neighborhood of a pixel f(0,0).

13. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. 121 242 121 Figure 6.5. A weighted averaging mask for image smoothing. The mask is used with a scaling factor of 1/16 that is multiplied to the values obtained by convolution of the mask with the image [Equation 6.11].

14. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.6. Smoothed image of the MR brain image shown in Figure 6.1 as a result of the spatial filtering using the weighted averaging mask shown in Figure 6.5.

15. Median Filter Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Median filter ◦ Order-statistics filter

16. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.7. The smoothed MR brain image obtained by spatial filtering using the median filter method over a fixed neighborhood of 3x3 pixels.

17. Adaptive Arithmetic Mean Filter Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Adaptive ◦ If the noise variance of the image is similar to the variance of gray values in the specified neighborhood of pixels,, the filter provides an arithmetic mean value of the neighborhood

18. Image Sharpening and Edge Enhancement Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Sobel ◦ The first-order gradient in and directions defined by and

19. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. -2 000 121 01 -202 01 Figure 6.8. Weight masks for first derivative operator known as Sobel. The mask at the left is for computing gradient in the x-direction while the mask at the right computes the gradient in the y direction.

20. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. 000 111 01 01 01 0 01 -011 011 01 0 Figure 6.9. Weight masks for computing first-order gradient in (clockwise from top left) in horizontal, 45 deg, vertical and 135 deg directions.

21. Image Sharpening and Edge Enhancement Laplacian ◦ The second-order dirivative operator ◦ Edge-based image enhancement

22. 00 8 0 0 8 (a) (b) Figure 6.10. (a) A Laplacian weight mask using 4-connected neighborrhod pixels only; (b) A laplacian weight mask with all neighbors in a window of 3x3 pixels; and (c) the resultant second- order gradient image obtained using the mask in (a).

23. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. 9 Figure 6.11. Laplacian based image enhancement weight mask with diagonal neighbors and the resultant enhanced image with emphasis on second-order gradient information.

24. Feature Enhancement Using Adaptive Neighborhood Processing Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Three types of adaptive neighborhoods ◦ Constant ratio: an inner neighborhood of size and an outer neighborhood of size ◦ Constant difference: the outer neighborhood of size ◦ Feature adaptive

25. Feature Enhancement Using Adaptive Neighborhood Processing Feature adaptive ◦ Center region: consisting of pixels forming the feature ◦ Surround region: consisting of pixels forming the background ◦ 1. The local contrast. : the average of the Center region. : the average of the Surround region

26. Feature Enhancement Using Adaptive Neighborhood Processing Feature adaptive ◦ 2. The Contrast Enhancement Function (CEF) : modify the contrast distribution by the contrast histogram ◦ 3. The enhanced image

27. Feature Enhancement Using Adaptive Neighborhood Processing Feature adaptive ◦ 3. The enhanced image

28. Figure 6.12. Region growing for a feature adaptive neighborhood: image pixel values in a 7x7 neighborhood (left) and Central and Surround regions for the feature adaptive neighborhood. XcXc XcXc Center Region Surround Region

29. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.13. (a) A part of a digitized breast film-mammogram with microcalcification areas. (b): Enhanced image through feature adaptive contrast enhancement algorithm. (c): Enhanced image through histogram equalization method. (a) (b)

30. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. (c) Figure 6.13. (a) A part of a digitized breast film-mammogram with microcalcification areas. (b): Enhanced image through feature adaptive contrast enhancement algorithm. (c): Enhanced image through histogram equalization method.

31. Frequency Domain Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. : an acquired image : the object : a Point Spread Function (PSF) : additive noise

32. Frequency Domain Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. The Fourier transform Inverse filtering

33. Wiener Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. : the power spectrum of the signal : the power spectrum of the noise

34. Wiener Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. : if it is white noise

35. Constrained Least Square Filtering Acquired image Optimization Subject to the smoothness constraint

36. Constrained Least Square Filtering The estimated image

37. Low-Pass Filtering Ideal ◦ : the frequency cut-off value ◦ : the distance of a point in the Fourier domain from the origin representing the dc value

38. Low-Pass Filtering Reduce ringing artifacts ◦ Butterworth or Gaussian Butterworth Gaussian

39. Figure 6.14: From top left clockwise: A low-pass filter function H(u,v) in the Fourier domain, the low-pass filtered MR brain image, the Fourier transform of the original MR brain image shown in Figure 6.1, and the Fourier transform of the low-pass filtered MR brain image

40. High-Pass Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. High-pass filtering ◦ Image sharpening and extraction of high- frequency information ◦ Edges Ideal

41. High-Pass Filtering Reduce ringing artifacts ◦ Butterworth or Gaussian Butterworth Gaussian

42. Figure 6.15: From top left clockwise: A high-pass filter function H(u,v) in the Fourier domain, the high-pass filtered MR brain image, and the Fourier transform of the high-pass filtered MR brain image.

43. Homomorphic Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. : illumination : reflectance In general

44. Homomorphic Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Frequency filtering in the logarithmic transform domain

45. Homomorphic Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

46. ln FT H(u,v ) IFTexp Figure 6.16. A schematic block diagram of homomorphic filtering.

47. Homomorphic Filtering Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. An example ◦ and components can represent, respectively, low- and high- frequency components ◦ A circularly symmetric homomorphic filter function

48. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. HH LL H(u,v) D(u,v) Figure 6.17: A circularly symmetric filter function for Homomorphic filtering.

49. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.18 The enhanced MR image obtained by Homomorphic filtering using the circularly symmetric function in Equation 3.43.

50. Wavelet Transform for Image Processing Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

51. Figure 6.19. (a) A multi-resolution signal decomposition using Wavelet transform and (b) the reconstruction of the signal from Wavelet transform coefficients. x[n]x[n]X (1) [2k+1] (a) (b) X (1) [2k] X (2) [2k+1] X (2) [2k] X (3) [2k+1] X (3) [2k] X (3) [2k+1] X (3) [2k] X (2) [2k+1] X (1) [2k+1]

52. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.20. Multiresolution decomposition of an image using the Wavelet transform.

53. Figure 6.21. The least asymmetric wavelet with eight coefficients.

54. Figure 6.22. Three-level wavelet decomposition of the MR brain image shown in Figure 6.1.

55. Figure 6.23. The MR brain image of Figure 6.1 reconstructed from the low-low frequency band using the wavelet decomposition shown in Figure 6.21.

56. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. Figure 6.24. The MR brain image of Figure 6.1 reconstructed from the low-high, high-low and high-high frequency bands using the wavelet decomposition shown in Figure 6.21.