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

Outline Introduction Overview Method

- Thresholding

- Boolean Functions

- False Edge Rremoval Experimental Results Conclusion Q & A

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.

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

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)

Overview(2/2)

Local Global

MethodLocal

Global

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.

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.

Method(Thresholding)

Common types- TL = Mean- TL = Median- TL = (Max+Min) / 2- TL = (Max-Min) / 2

Use the mean value approach.

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

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.

Method(Boolean Functions 1/2)

[2] M A. Sid-Ahmed, “Image Processing”, McGraw-Hill, Inc.

Sixteen patterns

Prewitt compass masks

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)

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

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

Method The two resulting images are logically ANDed

to get the final edge map.

Experimental Results

Experimental Results

Experimental Results

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.

Q & A