LOCAL THRESHOLD AND BOOLEAN FUNCTION BASED EDGE DETECTION
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LOCAL THRESHOLD AND BOOLEAN FUNCTION BASED EDGE DETECTION
IEEE Transactions on Consumer Electronics, Vol. 45, No. 1, AUGUST 1999
Muhammad Bilal Ahmad and Tae-Sun Choi, Senior Member,IEEE
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Outline Introduction Overview Method
- Thresholding
- Boolean Functions
- False Edge Rremoval Experimental Results Conclusion Q & A
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Introduction(1/2)
The edge detection methods can be classified into two types, namely, directional operators, and non-directional operators.- two masks, convolutions vs single masks, convolutions.
- zero-crossing vs gradient-based The popular gradient operators are that of
Sobel,Prewitt, Robert, Laplacian, etc.
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Introduction(2/2)
The operator based on derivatives of Gaussian is Laplacian of Gaussian. Gradient based operators use thresholding for edge detection. - less than the threshold set to black(0), otherwise set to white(1).
Threshold128
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Overview(1/2)
Two types thresholding- (a) local techniques
- (b) global techniques The algorithm is based on local operations, global
operations, and Boolean algebra.- Thresholding (Local operation)
- Boolean Functions (Local operation)
- False Edge Rremoval (Global Thresholding)
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Overview(2/2)
Local Global
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MethodLocal
Global
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Method Take window of size (3x3) of the original gray-
level image. Local threshold is found on the basis of local
mean value.- converts the gray-level image into binary image.
Use Boolean functions in the cross-correlation of the image window.- true edges as well as false edges.
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Method The global threshold is preselected,
considering the presence of noise in the image.- remove false edges
The resulting intermediate edge map is logically ANDed with the intermediate edge map from local threshold.
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Method(Thresholding)
Common types- TL = Mean- TL = Median- TL = (Max+Min) / 2- TL = (Max-Min) / 2
Use the mean value approach.
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Method(Thresholding 1/2)
Formula
Mean μ = where N=3,
Local threshold shown belowTL(X,Y) = (μ - C), where C is a constant(preselected).
NyN,x
0y0,x
y)W(x,1NN
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Method(Thresholding 2/2)
WL (X,Y) = 1 if W(X,Y) > TL(X,Y)WL (X,Y) = 0 otherwise
1 set to white, 0 set to black.- binary image
WL is the binary image(0,1) and then we can get the edge we find.- Boolean operation.
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Method(Boolean Functions 1/2)
[2] M A. Sid-Ahmed, “Image Processing”, McGraw-Hill, Inc.
Sixteen patterns
Prewitt compass masks
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Method(Boolean Functions 2/2)
For edge finding, the window WL(x,y) is cross-correlated with sixteen edge like patterns.
Any pattern which matches the window WL(x,y) is called an edge at the center of the window W(x,y).
B0 = !B(0,0) ×B(0,1) × B(0,2) ×!B(1,0) × B(1,1) × B(1,2) ×!B(2,0) × B(2,1) × B(2,2)
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Method(False Edge Rremoval 1/2)
False edges are detected due to the presence of noise.
We take a new threshold TN(preselected), whose value is related with the noise level in the image.
We calculate as variance value.xy2
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Method(False Edge Rremoval)
Formula
where g(x,y) is the intensity value of the window W(x,y), μ is the mean of the neighbors (3x3) at (x,y) position, and NxN is the window size.B (X,Y) = 1 if > TN(X,Y)B (X,Y) = 0 otherwise
1
0
1
0
2,
2 ]),([1 Nx
x
Ny
yyxxy yxg
NN
xy2
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Method The two resulting images are logically ANDed
to get the final edge map.
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Experimental Results
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Experimental Results
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Experimental Results
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Conclusions The global threshold(TN) and the constent C in
Mean value approach are preselected. The proposed method detects edges in two
processes.- (local)image is locally thresholded and using Boolean algebra(true and false edge)
- (global)detects the true edges only. Minimizes the noise, and also edge lines are
thinner.
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Q & A