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Line Detection
R w1 z1 w2 z2 ... w9 z9 wi zi
i 1 9
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Line Detection
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Line Detection (cont…)
Binary image of a wire bond mask
Environment controllable: such as the industrial inspection applications
Sensor controllable: such as
autonomous target acquisition, or near infrared imaging Algorithm controllable
6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12
0 -0.5 -1 -1.5 1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 1 2 3 4 5 5 5 5
0 0 0 1 0 0 0 0 -1 0 0
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Edge Detection
Conclusion: The first derivative can be used to detect the presence of an edge at a point in an image. (i.e. to determine if a point is on a ramp) Similarly, the sign of the second derivative can be used to determine whether an edge pixel lies on the dark or light side of an edge.
0 0 0 0 1 2 3 4 5 5 5 5
0 0 0 1 1 1 1 1 0 0 0
1
2
3
4
5
678Fra bibliotek910 11 12
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2nd Derivative
2 f f ( x 1) f ( x 1) 2 f ( x) 2 x
1.5 1 0.5
The formula for the 2nd derivative of a function is as follows:
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Derivatives & Noise
Firstly, we discuss Gradient operators and Laplacian operators
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Gradient Operator
The gradient vector points in the direction of maximum rate of change of f at (x,y).
We can see how derivatives are used to find discontinuities 1st derivative tells us where an edge is 2nd derivative can be used to show edge direction
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Edge Detection
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Edge Detection
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Derivatives & Noise
Derivative based edge detectors are extremely sensitive to noise
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Derivatives & Noise
i 1
9
Note: the mask response will be zero in areas of constant gray level.
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Point Detection (cont…)
dotdetection.m
X-ray image of a turbine blade
– The segmentation problem – Points detection – Lines detection – Edges detection
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Segmentation
The purpose of image segmentation is to partition an image into meaningful regions with respect to a particular application Segmentation should stop when the objects of interest in an application have been isolated The segmentation is based on measurements taken from the image and might be grey level, colour, texture, depth or motion
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Segmentation
Segmentation algorithms generally are based on of 2 basis properties of intensity values:
– Discontinuity: to partition an image based on abrupt changes in intensity (such as edges) – Similarity: to partition an image into regions that are similar according to a set of predefined criteria. Today, we will look at segmentation based on Discontinuity.
The reasons for blur: Optics sampling illumination conditions
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Edge Detection (more than one pixel width)
(more than one pixel width)
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Edges & Derivatives
We typically find discontinuities using masks and correlation
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Point Detection
Isolated point: a point whose gray level is significantly different from its background and which is located in a homogeneous or nearly homogeneous area. An isolated point will be quite different from its surroundings and thus be easily detectable by using a specially mask
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Point Detection
Point detection can be achieved simply using the mask below:
R w1 z1 w2 z2 ... w9 z9 wi zi
i 1
9
Basically, this formulation measures the weighted differences between the center point and its neighbors.
Not one pixel thick
Linedetection.m
Can be deleted by point detection
After processing with -45° line detector
Result of thresholding filtering result
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Edge Detection
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Edge Detection
Edge and Region boundary:
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Edge Detection
An edge is a set of connected pixels that lie on the boundary between two regions
Digital Image Processing
Image Segmentation
Luguangm@
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Contents
So far we have been considering image processing techniques used to transform images for human interpretation Today we will begin looking at automated image analysis by image segmentation:
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Segmentation
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Segmentation
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Segmentation
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Segmentation
most difficult tasks in image processing.
Image segmentation is one of the
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Spatial Differentiation