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Chapter 3. Intensity Transformations and Spatial Filtering ❖Two principal categories of spatial processing are intensity transformations and spatial filtering. ➢ Intensity transformations operate on single pixels of an image for tasks such as contrast manipulation and image thresholding. ➢ Spatial filtering performs operations on the neighborhood of every pixel in an image. ➢ Examples of spatial filtering include image smoothing and sharpening. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 2
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Chapter 3. Intensity Transformations and Spatial Filtering 1. Background 2. Some Basic Intensity Transformation Functions 3. Histogram Processing 4. Fundamentals of Spatial Filtering 5. Smoothing (Lowpass) Spatial Filters 6. Sharpening (Highpass) Spatial Filters 7. Highpass, Bandreject, and Bandpass Filters from Lowpass Filters 8. Combining Spatial Enhancement Methods Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 3
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1. Background ❖The Basics of Intensity Transformations and Spatial Filtering ➢The spatial domain processes are based on the expression where f(x, y) is an input image, g(x, y) is the output image, and T is an operator on f defined over a neighborhood of point (x, y). A 3x3 neighborhood about a point (x0, y0) in an image. The neighborhood is moved from pixel to pixel in the image to generate an output image. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 4
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1. Background ❖The Basics of Intensity Transformations and Spatial Filtering ➢intensity (also called a gray-level, or mapping) transformation function Intensity transformation functions. (a) Contrast stretching function. (b) Thresholding function. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 5
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Chapter 3. Intensity Transformations and Spatial Filtering 1. Background 2. Some Basic Intensity Transformation Functions 3. Histogram Processing 4. Fundamentals of Spatial Filtering 5. Smoothing (Lowpass) Spatial Filters 6. Sharpening (Highpass) Spatial Filters 7. Highpass, Bandreject, and Bandpass Filters from Lowpass Filters 8. Combining Spatial Enhancement Methods Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 6
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2. Some Basic Intensity Transformation Functions ❖Three basic types of functions ➢ linear (negative and identity transformations) ➢ logarithmic (log and inverse-log transformations) ➢ power-law (nth power and nth root transformations) Some basic intensity transformation functions. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 7
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2. Some Basic Intensity Transformation Functions ❖Image Negatives (a) A digital mammogram. (b) Negative image obtained using Eq. (3-3) . (Image (a) Courtesy of General Electric Medical Systems.) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 8
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2. Some Basic Intensity Transformation Functions ❖Log Transformations where c is a constant and it is assumed that r 0 (a) Fourier spectrum displayed as a grayscale image. (b) Result of applying the log transformation in Eq. (3-4) with c = 1. Both images are scaled to the range [0, 255]. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 9
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2. Some Basic Intensity Transformation Functions ❖Power-Law (Gamma) Transformations where c and are positive constants Plots of the gamma equation s = cr for various values of (c = 1 in all cases). Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 10
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2. Some Basic Intensity Transformation Functions ❖Power-Law (Gamma) Transformations (a) Image of a human retina. (b) Image as as it appears on a monitor with a gamma setting of 2.5 (note the darkness). (c) Gammacorrected image. (d) Corrected image, as it appears on the same monitor (compare with the original image). (Image (a) courtesy of the National Eye Institute, NIH) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 11
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2. Some Basic Intensity Transformation Functions ❖Power-Law (Gamma) Transformations ➢Contrast enhancement using power-law intensity transformations. a) Magnetic resonance image (MRI) of a fractured human spine (the region of the fracture is enclosed by the circle). (b)–(d) Results of applying the transformation in Eq. (3-5) with and and 0.3, respectively. (Original image courtesy of Dr. David R. Pickens, Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center.) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 12
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2. Some Basic Intensity Transformation Functions ❖Power-Law (Gamma) Transformations ➢Another illustration of power-law transformations. (a) Aerial image. (b)–(d) Results of applying the transformation in Eq. (3-5) with = 3.0, 4.0 and 5.0, respectively. (c = 1 in all cases.) (Original image courtesy of NASA.) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 13
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2. Some Basic Intensity Transformation Functions ❖Piecewise Linear Transformation Functions ➢Contrast Stretching where rmin and rmax denote the minimum and maximum where m is the mean intensity intensity levels in the input level in the image image, respectively Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 14
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2. Some Basic Intensity Transformation Functions ❖Piecewise Linear Transformation Functions ➢Intensity-Level Slicing Figure 2: (a) Aortic angiogram. (b) Result of using a slicing transformation of the type illustrated in Fig. 1(a) , with the range of intensities of interest Figure 1: (a) This transformation function highlights range [A, B] and selected in the upper end of the gray scale. (c) Result of using the reduces all other intensities to a lower level. (b) This function highlights transformation in Fig. 1(b) , with the selected range set near black, so that range [A, B] and leaves other intensities unchanged. the grays in the area of the blood vessels and kidneys were preserved. (Original image courtesy of Dr. Thomas R. Gest, University of Michigan Medical School.) 15 Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018).
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2. Some Basic Intensity Transformation Functions ❖Piecewise Linear Transformation Functions ➢Bit-Plane Slicing Bit-planes of an 8-bit image. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 16
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2. Some Basic Intensity Transformation Functions ❖Piecewise Linear Transformation Functions ➢Bit-Plane Slicing (a) An 8-bit gray-scale image of size pixels. (b) through (i) Bit planes 8 through 1, respectively, where plane 1 contains the least significant bit. Each bit plane is a binary image. Figure (a) is an SEM image of a trophozoite that causes a disease called giardiasis. (Courtesy of Dr. Stan Erlandsen, U.S. Center for Disease Control and Prevention.) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 17
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2. Some Basic Intensity Transformation Functions ❖Piecewise Linear Transformation Functions ➢Bit-Plane Slicing Image reconstructed from bit planes: (a) 8 and 7; (b) 8, 7, and 6; (c) 8, 7, 6, and 5. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 18
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Chapter 3. Intensity Transformations and Spatial Filtering 1. Background 2. Some Basic Intensity Transformation Functions 3. Histogram Processing 4. Fundamentals of Spatial Filtering 5. Smoothing (Lowpass) Spatial Filters 6. Sharpening (Highpass) Spatial Filters 7. Highpass, Bandreject, and Bandpass Filters from Lowpass Filters 8. Combining Spatial Enhancement Methods Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 19
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3. Histogram Processing ❖Histogram ➢The unnormalized histogram: where rk is the k-th intensity level of an L-level digital image f(x, y); nk is the number of pixels in f with intensity rk and the subdivisions of the intensity scale are called histogram bins. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 20
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3. Histogram Processing ❖Histogram ➢The normalized histogram: 𝐿−1 𝑝 𝑟𝑘 = 1 𝑘=1 where M and N are the number of image rows and columns, respectively. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 21
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