Image Processing
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Transcript of Image Processing
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Image ProcessingImage Processing
SegmentationSegmentation
1.1. Process of partitioning a digital Process of partitioning a digital image into multiple segments (sets image into multiple segments (sets of pixels).of pixels).
2. Clustering pixels into salient image regions, i.e., regions corresponding to individual surfaces, objects, or natural parts of objects.
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Image ProcessingImage Processing
SegmentationSegmentation3.3. Used to locate objects and Used to locate objects and
boundaries (lines, curves, etc.) in boundaries (lines, curves, etc.) in images. images.
4.4. Process of assigning a label to every Process of assigning a label to every pixel in an image such that pixels pixel in an image such that pixels with the same label share certain with the same label share certain visual characteristics.visual characteristics.
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Image ProcessingImage Processing
SegmentationSegmentation
Two of the most common techniques: Two of the most common techniques:
thresholdingthresholding and and
edgeedge findingfinding
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Image ProcessingImage Processing
SegmentationSegmentationTwo of the most common techniques: Two of the most common techniques:
thresholdingthresholdingedgeedge findingfinding
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Image ProcessingImage Processing
B. Detection of discontinuities B. Detection of discontinuities
The objects in image:
Three basic types of gray-level discontinuities in a digital image:
points,lines.edges.
The original image:
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Image ProcessingImage Processing
The common way The common way run a mask through the image
R = f(x-1, y-1) * M1 + f(x, y-1) * M2 + f(x+1, y-1) * M3
+ f(x-1, y) * M4 + f(x, y) * M5 + f(x+1, y) * M6
+ f(x-1, y+1)* M7 + f(x, y+1)* M8 + f(x+1, y+1)* M9
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Image ProcessingImage Processing
The common way The common way
run a mask through the image
R = f(x-1, y-1) * M1 + f(x, y-1) * M2 + f(x+1, y-1) * M3
+ f(x-1, y) * M4 + f(x, y) * M5 + f(x+1, y) * M6
+ f(x-1, y+1)* M7 + f(x, y+1)* M8 + f(x+1, y+1)* M9
Select some threshold . If |R(x,y)| then (x,y) to belong to object (background).
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Image ProcessingImage Processing
ExampleExample
a) b)
Original and segmented images:
a) Mask H8
b) Threshold = 2
If R(x,y) 2 Then g(x,y) = 1
Else g(x,y) = 0
H8=
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Image ProcessingImage Processing
Line detectionLine detection
A masks are usualy used for detection of isolated points in an image are:
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Image ProcessingImage Processing
Example of line detectionExample of line detection
The original I image and segmented image Io with horizotal mask
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Image ProcessingImage Processing
Example of line detectionExample of line detection
The original I image and segmented image I45 with 45o mask
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Image ProcessingImage Processing
Example of line detectionExample of line detection
The original I image and segmented image Iv with vertical mask
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Image ProcessingImage Processing
Example of line detectionExample of line detection
The original I image and segmented image I135 with 135o mask
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Image ProcessingImage Processing
Example of line detectionExample of line detection
The original I image and segmented image I8 with H8 mask
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Image ProcessingImage Processing
Formula:Formula:
Set (x,y):
R=0for k=1 to 3for q=1 to 3
R = R + f(x+k-2,y+q-2)*M(k,q)If R Then g(x,y) = 255 (object)
Else g(x,y) = 0 (non-object)
1 x ImageWidth1 y ImageHeight
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Image ProcessingImage Processing
Egde detection:Egde detection:
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Image ProcessingImage Processing
Egde detection:Egde detection:
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
The function f(x) is defined as horizontal gray-level of the image.
The first derivative f’(x) is positive at the point of transition into and out of the ramp as moving from left to right along the profile.
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
A point M is being an edge point if its two-dimention first order derivative is greater than a specified threshold.
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
If using the second-derivative to define the edge points in an image as the zero crossing of its second derivative.
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
The signs of second derivative can be used to determine an edge pixel lies on the dark or light side of an edge
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
The zero crossing property of the second derivative is quite useful for locating the centers of thick edges.
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Image ProcessingImage Processing
Gradient-based procedure:Gradient-based procedure:
The first is gradient vector of an image f(x, y), and
The second is quantity (magnitude) of gradient vector
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Image ProcessingImage Processing
The Prewitt gradient vector for detecting x-direction (y-The Prewitt gradient vector for detecting x-direction (y-direction) and direction) and
the Prewitt gradient vectors for detecting diagonal the Prewitt gradient vectors for detecting diagonal edges:edges:
-1 -1 -1 -1 0 1
0 0 0 -1 0 1
1 1 1 -1 0 1
0 1 1 -1 -1 0
-1 0 1 -1 0 1
-1 -1 0 0 1 1
Gx = (W2 + W3 + W6) – (W4 + W7 + W8)
Gy = (W6 + W8 + W9) – (W1 + W2 + W4)
Gx = (W7 + W8 + W9) – (W1 + W2 + W3)
Gy = (W3 + W6 + W9) – (W1 + W4 + W7)
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Image ProcessingImage Processing
The general formulaThe general formulafor i = 2 to Height-1for i = 2 to Height-1
for j = 2 to Width-1for j = 2 to Width-1
{ {
t1 = 0t1 = 0
t2 = 0t2 = 0
for p = 1 to 3 for p = 1 to 3
for q = 1 to 3for q = 1 to 3
{ {
t1 = t1 + Gt1 = t1 + G11[p, q] * f[i+p-2, j+q-2][p, q] * f[i+p-2, j+q-2]
t2 = t2 + Gt2 = t2 + G22[p, q] * f[i+p-2, j+q-2]}[p, q] * f[i+p-2, j+q-2]}
ts = Abs(t1) + Abs(t2)ts = Abs(t1) + Abs(t2)
if ts > if ts > thenthen Q[i,j] = 1Q[i,j] = 1elseelse Q[i,j] = 0Q[i,j] = 0
}}
}}
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Image ProcessingImage Processing
ExampleExample
1 1 1 3 1 1
1 1 1 3 1 1
1 1 1 3 1 1
3 3 3 3 3 3
1 1 1 3 1 1
1 1 1 3 1 1W
For the window W from image I, caculating the valueR(3,3) = |Dx*W| + |Dy*W|
= |-6+12| + |-6+12| = 12For all pixels of I, except boundary of I, we have matrix R:
0 8 0 8
8 12 4 12
0 4 0 4
8 12 4 120 0 0 0
0 1 0 1
0 0 0 0
0 1 0 1
If using threshold at 10:
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Image ProcessingImage Processing
The Prewitt gradient vector for detecting x-direction (y-The Prewitt gradient vector for detecting x-direction (y-direction) and direction) and
the Prewitt gradient vectors for detecting diagonal the Prewitt gradient vectors for detecting diagonal edges:edges:
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Image ProcessingImage Processing
The Sobel gradient vector for detecting x-The Sobel gradient vector for detecting x-direction and y-direction edges: direction and y-direction edges:
G1= (W2 + 2W3 + W6 ) – (W4 + 2W7 + W8)G2= (W6 + 2W9 + W8 ) – (W2 + 2W1 + W4)
Gx = (W7 + 2W8 + W9) – (W1 + 2W2 + W3)Gy = (W3 + 2W6 + W9 )– (W1 + 2W4 + W7)
-1 -2 -1 -1 0 1
0 0 0 -2 0 2
1 2 1 -1 0 1
The Sobel gradient vector for detecting diagonal edges:
0 1 2 -2 -1 0
-1 0 1 -1 0 1
-2 -1 0 0 1 2
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Image ProcessingImage Processing
Examples Examples
ofof
Sobel Sobel
filter filter
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Image ProcessingImage Processing
Second-order derivative: The Second-order derivative: The LaplacianLaplacian
2
2
2
22
y
f
x
ff
0 -1 0 -1 -1 -1
-1 4 -1 -1 8 -1
0 -1 0 -1 -1 -1
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Image ProcessingImage Processing
Second-order derivative: The Second-order derivative: The LaplacianLaplacian 0 0 -1 0 0
0 -1 -2 -1 0
-1 -2 16 -2 -1
0 -1 -2 -1 0
0 0 -1 0 0
The Laplacian is not used in its original form for edge detection (because of sensitive to noise).The Laplacian is combined with smoothing as a precursor to finding
edges via zero-crossing.