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Chapter 6. Image Segmentation 1. Fundamentals 2. Point, Line, and Edge Detection 3. Thresholding 4. Image Segmentation Using Deep Learning Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 2
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1. Fundamentals ➢ Let R represent the entire spatial region occupied by an image. We may view image segmentation as a process that partitions R into n subregions, R1, R2, …, Rn, such that: where Q(Rk) is a logical predicate defined over the points in set Rk and is the null set. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 3
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1. Fundamentals ➢ Two regions Ri and Rj are said to be adjacent if their union forms a connected set. ➢ The regions are said to disjoint If the set formed by the union of two regions is not connected. ➢ The fundamental problem in segmentation is to partition an image into regions that satisfy the preceding conditions. ➢ Segmentation algorithms for monochrome images generally are based on one of two basic categories dealing with properties of intensity values: discontinuity and similarity. ▪ Edge-based segmentation ▪ Region-base segmentation Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 4
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1. Fundamentals (a) Image of a constant intensity region. (b) Boundary based on intensity discontinuities. (c) Result of segmentation. (d) Image of a texture region. (e) Result of intensity discontinuity computations (note the large number of small edges). (f) Result of segmentation based on region properties. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 5
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Chapter 6. Image Segmentation 1. Fundamentals 2. Point, Line, and Edge Detection 3. Thresholding 4. Image Segmentation Using Deep Learning Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 7
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2. Point, Line, and Edge Detection ➢ Detecting sharp, local changes in intensity ➢ The three types of image characteristics: isolated points, lines, and edges ➢ Edge pixels: the intensity of an image changes abruptly ➢ Edges (or edge segments): sets of connected edge pixels ➢ Edge detectors: local image processing tools designed to detect edge pixels Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 8
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2. Point, Line, and Edge Detection ➢ A line: ▪ a (typically) thin edge segment ▪ the intensity of the background on either side of the line is either much higher or much lower than the intensity of the line pixels. ▪ “roof edges” ➢ Isolated point: a foreground (background) pixel surrounded by background (foreground) pixels. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 9
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2. Point, Line, and Edge Detection ❖ Background ➢ an approximation to the first-order derivative at an arbitrary point x of a one- dimensional function f(x) x = 1 for the sample preceding x and x = -1 for the sample following x. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 10
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2. Point, Line, and Edge Detection ❖ Background ➢ an approximation to the first-order derivative at an arbitrary point x of a one- dimensional function f(x) Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 11
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2. Point, Line, and Edge Detection ❖ Background ➢ The forward difference ➢ The backward difference Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 12
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2. Point, Line, and Edge Detection ❖ Background ➢ The central difference ➢ The second order derivative based on a central difference Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 13
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2. Point, Line, and Edge Detection ❖ Background Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 14
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2. Point, Line, and Edge Detection ❖ Background ➢ For two variables Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 15
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2. Point, Line, and Edge Detection ❖ Background Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 16
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2. Point, Line, and Edge Detection ❖ Background ➢ Spatial filter kernel Where zk is the intensity of the pixel whose spatial location corresponds to the location of the kth kernel coefficient. A general 3x3 spatial filter kernel. The w’s are the kernel coefficients (weights). Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 17
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2. Point, Line, and Edge Detection ❖ Detection of Isolated Points ➢ Laplacian ➢ Detected points Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 18
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2. Point, Line, and Edge Detection ❖ Detection of Isolated Points ➢ Example (a) Laplacian kernel used for point detection. (b) X-ray image of a turbine blade with a porosity manifested by a single black pixel. (c) Result of convolving the kernel with the image. (d) Result of using Eq. (10-15) was a single point (shown enlarged at the tip of the arrow). Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 19
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2. Point, Line, and Edge Detection ❖ Line Detection ➢ EXAMPLE: Using the Laplacian for line detection. (a) Original image. (b) Laplacian image; the magnified section shows the positive/negative double-line effect characteristic of the Laplacian. (c) Absolute value of the Laplacian. (d) Positive values of the Laplacian. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 20
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2. Point, Line, and Edge Detection ❖ Line Detection ➢ EXAMPLE: Detecting lines in specified directions. Line detection kernels. Detection angles are with respect to the axis system in above figure, with positive angles measured counterclockwise with respect to the (vertical) x-axis. Rafael C. Gonzalez, Richard E. Woods, “Digital image processing,” Pearson (2018). 21
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