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

Histogram Transformation Histogram equalization

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.

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

Histogram Modification Scaling Histogram modification

Histogram Modification Target histogram:

Image Averaging Averaging Enhancing signal-to-noise ratio

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.

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.

Neighborhood Operations Use a weight mask

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.

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.

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.

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

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.

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.

-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.

-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.

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

-1 8 (a) -1 8 (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).

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

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.

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

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

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

Xc Center Region Surround Region 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.

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

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.

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

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.

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

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

Constrained Least Square Filtering The estimated image

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

Low-Pass Filtering Reduce ringing artifacts Butterworth Gaussian Butterworth or Gaussian Butterworth Gaussian

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

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.

High-Pass Filtering Reduce ringing artifacts Butterworth Gaussian Butterworth or Gaussian Butterworth Gaussian

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.

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

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

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

IFT exp ln FT H(u,v) Figure 6.16. A schematic block diagram of homomorphic filtering. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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.

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.

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.

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

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

2 H 1 Horizontal Subsampling Vertical Low-Low Aj High-High Dj3 High-Low Dj2 Low-High Dj1 Figure 6.20. Multiresolution decomposition of an image using the Wavelet transform. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

Figure 6.21. The least asymmetric wavelet with eight coefficients.

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

Figure 6. 23. The MR brain image of Figure 6 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.

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