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

3. Histogram Transformation
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
Target histogram:

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

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

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

11. Neighborhood Operations
Use a weight mask

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

13. 1 2 4
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].
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

14. Figure 6. 6. Smoothed image of the MR brain image shown in Figure 6
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.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

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

17. Adaptive Arithmetic Mean Filter
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
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

19. -1 -2 1 2 -1 1 -2 2
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.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

20. -1 1 -1 1 -1 1 -0 1 -1
Figure 6.9. Weight masks for computing first-order gradient in (clockwise from top left) in horizontal, 45 deg, vertical and 135 deg directions.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

22. -1 8
(a) -1 8
(b)
Figure (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. -1 9
Figure Laplacian based image enhancement weight mask with diagonal neighbors and the resultant enhanced image with emphasis on second-order gradient information.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

24. Feature Enhancement Using Adaptive Neighborhood Processing
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
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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. Xc
Center Region
Surround Region
Figure 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.

29. (a)
(b)
Figure (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.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

30. (c)
Figure (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.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

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

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

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

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

41. High-Pass Filtering Reduce ringing artifacts Butterworth Gaussian
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
: illumination
: reflectance
In general
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

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

46. IFT
exp ln FT
H(u,v)
Figure A schematic block diagram of homomorphic filtering.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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

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

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

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

51. 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]
Figure (a) A multi-resolution signal decomposition using Wavelet transform and (b) the reconstruction of the signal from Wavelet transform coefficients.

52. 2 H 1
Horizontal
Subsampling
Vertical
Low-Low Aj
High-High Dj3
High-Low Dj2
Low-High Dj1
Figure Multiresolution decomposition of an image using the Wavelet transform.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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
Figure 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. Figure 6. 24. The MR brain image of Figure 6
Figure 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.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.